Discussion Meeting on Quantum Measurements Centre for Quantum Information and Quantum Computation Indian Institute of Science, Bangalore 22-24 October 2014

Organizing Committee

N.D. Hari Dass CMI, Chennai (Chairman) Dipankar Home Bose Institute, Kolkata Anil Kumar IISc, Bangalore (Convener) T.S. Mahesh IISER, Pune Archan S. Majumdar SNBNCBS, Kolkata Kota Murali IBM, Bangalore Apoorva Patel IISc, Bangalore Arun K. Pati HRI, Allahabad R. Simon IMSc, Chennai Urbasi Sinha RRI, Bangalore Rajamani Vijayaraghavan TIFR, Mumbai Talks

9:30-10:20 22 October 2014 Quantum measurement theory and the uncertainty principle Masanao Ozawa Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya, Japan

Heisenberg’s uncertainty principle was originally formulated in 1927 as a quantitative relation between the “mean error” of a measurement of one observable and the “discontinuous change” (or the disturbance) thereby caused on another observ- able, typically explained through the gamma ray microscope thought experiment. Heisenberg derived this relation under an additional assumption on quantum measurements that is consistent with the so-called repeatability hypothesis, which was pos- tulated in von Neumann’s measurement theory and supported by Schroedinger and contemporaries. However, the repeatability hypothesis has been abandoned in the modern quantum measurement theory, originated by Davies and Lewis in the 1970’s. Later, the universal validity of Heisenberg’s uncertainty principle was questioned typically in a debate on the sensitivity limit to gravitational wave detectors in the 1980’s. A universally valid form of the error-disturbance relation was derived in the modern framework for general quantum measurements by the present speaker in 2003. Since then we have experienced a considerable progress in theoretical and experimental studies of universally valid reformulation of Heisenberg’s uncertainty principle. This talk will give an up-to-date survey on the historical background and the recent progress and in particular discuss debates on the quantum mechanical generalizations of the notion of root-mean-square error and disturbance.

10:20-11:10 22 October 2014 Fundamental phenomena in quantum mechanics studied with neutrons: Error-disturbance uncertainty relation and quantum Cheshire-cat Yuji Hasegawa Atominstitut, TU-Wien, Vienna, Austria

Interferometer and polarimeter experiments with neutrons matter-wave serve as almost ideal tools to investigate foundation of quantum mechanics. The former device explicitly exhibits quantum interference between spatially separated beams and is used for studies, e.g., of intra-partite entanglement, i.e., entanglements between degrees of freedom. In contrast, interference effects between two spin eingenstates are exposed in the latter apparatus, where quantum manipulation with extremely high precision is accomplished. Exploiting both strategies, alternative theories of quantum mechanics, Kochen-Specker theorem and a crypto-contextual model suggested by Leggett are studied. Recently, an experimental test of the error-disturbance uncertainty relation by Heisenberg is carried out, which confirmed clearly the violation of the original relation and support a new relation proposed by Ozawa. In addition, new neutron optical experiments studying weak-values are developed: a new counter-intuitive phenomenon, called a quantum Cheshire-cat, is observed in a neutron interferometer experiment. In my talk, I am going to give an overview of neutron optical approach to investigations of fundamental aspect of quantum mechanics.

11:30-12:20 22 October 2014 A disturbance tradeoff principle for quantum measurements M.D. Srinivas Centre for Policy Studies, Chennai

We demonstrate a fundamental principle of disturbance trade-off for quantum measurements, along the lines of the celebrated uncertainty principle: The disturbances associated with measurements performed on distinct yet identically prepared ensem- bles of systems in a pure state cannot all be made arbitrarily small. Indeed, we show that the average of the disturbances associated with a set of projective measurements is strictly greater than zero whenever the associated observables do not have a common eigenvector. For such measurements, we have an equivalence between disturbance tradeoff measured in terms of fidelity and the entropic uncertainty principle formulated in terms of the Tsallis entropy (T2). We also consider the disturbance tradeoff for POV observables, where the disturbance tradeoff differs significantly from the uncertainty tradeoff. Specifically, for the class of Luders¨ instruments, we show that the disturbance tradeoff for POV observables can be zero even when the corresponding uncertainty tradeoff is strictly greater than zero. 12:20-13:10 22 October 2014 Experimental test of error-disturbance uncertainty relations by weak measurement Keiichi Edamatsu Research Institute of Electrical Communication, Tohoku University, Aoba-ku, Sendai, Japan In collaboration with: So-Young Baek, Fumihiro Kaneda, Masanao Ozawa

We experimentally test the error-disturbance uncertainty relation (EDR) exploiting a weak measurement for a single-photon polarization qubit. The test is carried out by linear optical devices that realize variable measurement strength from weak measurement to projection measurement. The results show that Heisenberg EDR is violated throughout the range of our measurement strength and yet validates Ozawa and Branciard EDRs. A correct understanding and experimental confirmation of the error-disturbance uncertainty relation will not only foster an insight into fundamental limitations of measurements but also advance the precision measurement technology in quantum information processing.

14:30-15:00 22 October 2014 Weak measurements: Typical weak and superweak values Pragya Shukla Department of Physics, Indian Institute of Technology, Kharagpur

Weak values, resulting from the action of an operator on a pre-selected state when measured after post-selection by a different state, can lie outside the spectrum of eigenvalues of the operator: they can be ‘super-weak’. This phenomenon can be quantified by averaging over an ensemble of the two states, and calculating the probability distribution of the weak values. Our main results indicate an unanticipated universality in the distribution of weak and super-weak values. If there are many eigenvalues, distributed within a finite range, this distribution takes a simple universal generalized Lorentzian form, and the ’super-weak probability’, of weak values outside the spectrum, can be as large as 0.293 (almost 30% chance of a weak value being super- weak). By contrast, the familiar expectation values always lie within the spectral range, and their distribution, although approximately Gaussian for many eigenvalues, is not universal. We also explore the connection between large shifts of a pointer in a weak measurement and fast oscillations in functions associated with pre- and post-selected states. Our results reveal how the supershifts emerge as the uncertainty in the initial pointer position increases. This happens if the initial pointer wavefunction is Gaussian or Lorentzian but not if it is an exponential. [1] M.V. Berry and P. Shukla, J. Phys. A: Math. & Theo. 43 (2010) 354024. [2] M.V. Berry and P. Shukla, J. Phys. A: Math. & Theo. 45 (2012) 015301. [3] M.V. Berry, M.R. Dennis, B. McRoberts and P. Shukla, J. Phys. A: Math. & Theo. 44 (2011) 20530. [4] M.V. Berry, N. Brunner, S. Popescu and P. Shukla, J. Phys. A: Math. & Theo. 44 (2011) 492001.

15:00-15:50 22 October 2014 Protective measurements: Probing single quantum systems Tabish Qureshi Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi

Protective measurements, introduced by Aharonov, Anandan and Vaidman, are described and critically analyzed. Several subtleties involved in the process are discussed. Implications for the reality of the quantum state is critically examined. Some proposals for experimental realization of protective measurements are discussed.

16:10-16:40 22 October 2014 Beating entropic uncertainty bound using unsharp measurements A.R. Usha Devi Department of Physics, Bangalore University, Bangalore

One of the peculiar aspect of quantum theory is that the outcomes of measurements of non-commuting observables cannot be predicted accurately. This feature is captured quantitatively in terms of uncertainty relations, which give upper bounds on the precision with which the measurement outcomes of incompatible observables can be predicted. Massen-Uffink entropic uncertainty relation [1] constrains the sum of entropies associated with the measurements of a pair of non-commuting ob- servables. An extended entropic uncertainty relation proposed by Berta et al. [2], brought out that it is possible to beat the entropic uncertainty bound when the state of the system is entangled with a quantum memory. In this talk, we discuss the entropic uncertainty bound in the presence of a quantum memory, when unsharp POVM measurements are employed. We show that when the POVMs are jointly measurable [3], beating the entropic uncertainty bound implies violation of an entropic steering inequality [4]. Very recently, it has been established that non-steerability and joint measurability of POVMs imply one another [5]. As a consequence, it is clearly seen that the reduction in the entropic uncertainty bound (which is in turn connected with steerability) is possible iff the POVMs are not jointly measurable. We also discuss an extended entropic un- certainty relation, wherein we have shown [6] that there is a reduction in the uncertainty bound, if the measurement outcomes of non-commuting observables are conditioned by sequential projective measurements of temporally separated observables on a single quantum system. We identify that it is not possible to beat the uncertainty bound if the sequential measurements are done using compatible (jointly measurable) POVMs. [1] H. Maassen and J.B.M. Uffink, Phys. Rev. Lett. 60 (1988) 1103. [2] M. Berta, M. Christandl, R. Colbeck, J.M. Renes and R. Renner, Nature Physics 6 (2010) 659. [3] P. Busch, Phys. Rev. D 33 (1986) 2253. [4] J. Schneeloch, C.J. Broadbent, S.P. Walborn, E.G. Cavalcanti and J.C. Howell, Phys. Rev. A 87 (2013) 062103. [5] M.T. Quintino, T. Vertesi, and N. Brunner, arXiv:1406.6976; R. Uola, T. Moroder, and O. Guhne, arXiv:1407.2224. [6] H.S. Karthik, A.R. Usha Devi, J. Prabhu Tej and A.K. Rajagopal, arXiv: 1310.5079.

16:40-17:10 22 October 2014 A class of distance-based incompatibility measures for quantum measurements Prabha Mandayam Department of Physics, Indian Institute of Technology Madras, Chennai

We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. For finite dimensional systems, we obtain a tight upper bound on the incompatibility of any set of observables and show that the bound is attained when the observables are totally non- degenerate and associated with mutually unbiased bases. In the process, we also establish an important connection between the incompatibility of a pair of observables and the maximal disturbances due to their measurements. Finally, we indicate how these measures of incompatibility and disturbance can be extended to the more general class of non-projective measurements. In particular, we obtain a non-trivial upper bound on the incompatibility of one Luders¨ instrument with another. Reference: P. Mandayam and M.D. Srinivas, Phys. Rev. A 89 (2014) 062112.

17:10-17:40 22 October 2014 Probing gravity in quantum systems with protective measurement Patrick Dasgupta Department of Physics and Astrophysics, University of Delhi, Delhi

Anandan in 1993 had presented an interesting quantum mechanical analysis of a test particle interacting gravitationally with a bound state formed by superposing two spatially separated energy eigenstates [1]. Mapping the problem mathematically to a Stern-Gerlach type system, he had argued that it is possible to protect the bound system from becoming entangled with the states of the test particle. I revisit the problem and critically assess the conditions required for such a protective measurement. It is seen that even a feeble interaction like gravitation leads to a phase difference between the spatially separated energy eigenstates. Then, I study the case of a superposed BoseEinstein condensate (BEC) of cold atoms interacting gravitationally with a test particle, and consider the possibility of measuring the phase difference induced by gravitation. BEC of bosonic atoms trapped in honeycomb optical lattice are described by a nonlinear Dirac equation in the long wavelength limit [2]. In this context, the effect of a test particles gravity on the wavefunction components associated with inequivalent sites A and B of the optical sublattice, making up the hexagonal structure, is investigated. [1] J. Anandan, Found. Phys. Lett. 6 (1993) 505532. [2] Patrick Das Gupta, Samiran Raj and Debapriya Chaudhuri, arXiv:1012.0976, and references therein. 9:30-10:20 23 October 2014 Three results on weak measurements N.D. Hari Dass Centre for Quantum Information and Quantum Computing, Indian Institute of Science, Bangalore Chennai Mathematical Institute, Chennai

In this talk I shall present three important results on weak measurements that I have obtained recently. They are: i) repeated mea surements on a single copy can not provide any information on it and further that in the limit of very large such measure- ments, weak measurements have exactly the same characterstics as strong measurements, ii) the apparent non-invasiveness of weak measurements is no more advantageous than strong measurements in the specific context of Leggett-Garg measure- ments when errors are properly taken into account and finally, iii) weak value measurements are optimal, in the precise sense of Wootters and Fields, when the post-selected states are mutually unbiased with respect to the eigenstates of the observable whose weak values are being measured.

10:20-11:10 23 October 2014 Quantum measurement with superconducting circuits Rajamani Vijayaraghavan Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai

The past three decades have seen a tremendous rise in experiments probing the quantum nature of various atomic, photonic and solid-state systems. Though primarily driven by the promise of powerful quantum computing machines, these developments are allowing us to revisit some of the very fundamental ideas in quantum mechanics by providing a near ideal experimental platform. One such architecture is based on constructing quantum two level systems or qubits with superconducting electrical circuits operating at a temperature of approximately 10 mK. A near ideal quantum measurement setup is then implemented by coupling these qubits to electromagnetic cavities and probing them with microwave signals. I will describe this so called circuit Quantum Electro Dynamics (cQED) architecture and how one can control the rate of quantum measurement by controlling the microwave power. In particular, I will focus on superconducting parametric amplifiers which allow us to monitor the measurement signals with high efficiency. I will discuss different quantum measurement regimes and how one can use such measurements to implement quantum feedback to stabilize various quantum states. Finally I will discuss their application to quantum error correction which is crucial for the development of practical quantum computing systems.

11:30-12:20 23 October 2014 Experimental tests of macrorealism: An assessment Anupam Garg Department of Physics and Astronomy, Northwestern University, Evanston, IL, USA

I will discuss the expeimental test of Leggett and Garg’s macrorealistic inequality by Palacios-Laloy et al. [Nature Physics 6 (2010) 442-447]. The key question, of course, is what new bearing this experiment has on the issue of macrorealism, but additional goals include understanding the purported macrovariable, the quantity being measured, the measurement method, and additional assumptions that might be needed in applying the inequality to this particular setup.

12:20-13:10 23 October 2014 Some recent studies related to the Leggett-Garg inequality Dipankar Home Department of Physics, Bose Institute, Kolkata

After an introduction to the basics of the Leggett-Garg inequality (LGI), its underlying motivation and its various forms, a brief indication will be given of the various directions of studies being pursued by our group concerning various aspects of LGI, including a few interesting features of LGI in the context of unsharp or imprecise measurements. The remainder of the talk will be mainly concentrated on discussing our recently studied application of LGI in revealing non-classicality of the harmonic oscillator coherent state and probing its macrolimit, along with results relevant to realizable experimental study. 14:30-15:00 23 October 2014 An evolutionary formalism for weak measurements Apoorva Patel Centre for High Energy Physics, Indian Institute of Science, Bangalore

Unitary evolution and projective measurement are the conventional axioms of quantum mechanics. Even though projective measurement yields one of the eigenstates of the measured operator as the outcome, there is no theory that predicts which eigenstate will be observed in which experimental run. There exists only an ensemble description, which predicts probabilities of various outcomes over many experimental runs. We propose a dynamical evolution equation for the projective collapse of the quantum state in individual experimental runs. In case of gradual weak measurements, its predictions for ensemble evolution are different from those of Born’s rule. It is an open question whether or not suitably designed experiments can observe this alternate evolution. 15:00-15:50 23 October 2014 Model study of coherence and decoherence Sushanta Dattagupta Visva-Bharati, Santiniketan, West Bengal

One of the critical issues of quantum information processing, in general and quantum computing, in particular, is the mainte- nance of Coherence. Unfortunately however, small systems (which are ideal for quantum applications) are invariably under the influence of the environment that leads to De-coherence, The environmental effects manifest as noise, dissipation, de- phasing etc. I will present a few examples in which these issues can be studied effectively. The examples are in the context of Tunneling Systems, Landau Diamagnetism, the Aharonov-Bohm effect and Telegraphic Noise in Qubits. The last case will be dealt with in some detail, wherein we will discuss how coherence can be partially salvaged even though the quantum device is strongly under the impact of a classical noise source.

16:10-17:00 23 October 2014 Quantum non-demolition experiments: Concepts, theory and practice C.S. Unnikrishnan Department of High Energy Physics, Tata Institute of Fundamental Research, Mumbai

The focus of this talk is quantum non-demolition (QND) experiments in the general sense of a measurement on a quantum system without uncontrolled change of the uncertainty dispersion associated with the state of the system, for the observable being measured. The fundamental ideas, relevant theory and the conditions and scope for applicability will be discussed. There are several types and flavors of such measurements, but the most common are the ones called the ’back-action’ evading measurements. Precision measurements have indeed gained from developing QND measurements and some examples from quantum optics, gravitational wave detectors and spin-magnetometry will be discussed. The distinction between QND measurements and some other types of commonly discussed quantum-specific measure- ments, like interaction-free measurements, Zeno-measurements, weak measurements etc. will be brought out, briefly.

17:00-17:30 23 October 2014 Can weak value amplification be singled out in atomic resonance fluorescence process by pre- and post-selection of system states? Andal Narayanan Light and Matter Physics, Raman Research Institute, Bangalore In collaboration with: U. Satya Sainadh, R. Vathsan, S.N. Sandhya

In Quantum Mechanics, a weak measurement refers to a measurement process wherein the system which is being measured is only slightly disturbed by the measuring apparatus (pointer). A pointer shift during weak measurement, after post-selection of the system in a chosen final state through a strong projective measurement, is called the weak value. For some pre- and post-selected states, the pointer shift may correspond to a measurement result which is well outside the eigenspectrum of the measured observable: a process known as weak value amplification. In a recent paper [I. Shomroni et al., Phys. Rev. Lett. 111 (2013) 023604] an experimental demonstration of weak value amplification was presented for an atomic V system in coherent interaction with electromagnetic fields. The weak value amplification was shown as an increase of spontaneous emission lifetime of the atom in the excited state, for particular pre- and post-selected system states. In this talk, we present the result of our density matrix calculations for this very system, which shows that, the increase in lifetime has more to do with the coherent nature of atom-photon interaction than the weak measurement process employed. As an important corollary to this study, we address the more fundamental question of whether decoherence processes induced by system-bath interaction can naturally lead to final states which can be interpreted as weak value amplified states.

17:30-18:00 23 October 2014 A controlled photon-router as a node of a quantum network Deepak Kumar School of Physical Sciences, Jawaharlal Nehru University, New Delhi In collaboration with: Santosh Kumar, Gaurav Gautam, Saikat Ghosh

Secure information transfer protocols and quantum simulators are envisioned on a quantum network of nodes consisting of material objects like single or ensemble of atoms, ions, solid-state qubits or opto-mechanical elements. The nodes in turn are usually interconnected by a network of photonic bus consisting of single photons. While the photons carry quantum information robustly, the nodes apply controlled unitary operators, either applying phase shifts or redirecting the photons toward specific directions. In particular, there has been recent interest to realize physical systems for controllable photon routers, that can route single photons and in general, form a beam-splitter with full control on the corresponding unitary. Here we propose a scheme to realize such a controlled unitary transformation. The scheme consists of a geometrical unit of two optical cavities with overlapping cavity waists along with a transiting atom. We show that this system can transfer coherently a single photon from one cavity mode to the other via an adiabatic rotation of a dark state, triggered by passage of a single atom through the cavity waist along with modulation of classical optical pulses. In particular, the scheme works for small values of g (the cavity coupling constant), compared to other couplings and accordingly, is effective in the bad cavity limit. A parameter regime is pointed out where the unit can operate in this router regime and redirect a photon with almost unit efficiency and minimal losses. Furthermore, by tuning the velocity of the atom, one can operate the system in a beamsplitter regime, controlling the transmission and reflection coefficients of the underlying unitary. We derive an effective Hamiltonian A B and the corresponding unitary matrix connecting the two the initial photonic (or cavity) modes to the transformed  C D  ones, by adiabatically eliminating the atom which is weakly coupled to the cavities. The resulting analytic expression for the unitary agrees well with an exact simulation of the full system. In particular, we find that by keeping the width and height of the classical pulses constant while uniformly changing the velocity of transit of the atom, one can continuously tune the elements of the unitary. This scheme therefore provides complete control over the two overlapping cavity modes with bad cavities. One can repeat this unit to construct a network or a lattice. An analysis of states corresponding to two such unit cells is presented. It is found that there is a global dark state through which a single photon can be transferred from one unit to the other. Such a network can be realized physically in systems including single atoms either free falling or on optical conveyor belts or tweezers, transiting the overlapping waist of two low-finesse optical cavities. Effects of losses and their scaling with increasing nodes is analysed and it is found that there is a suppression of loss due to the dark state involved in the unitary.

9:30-10:20 24 October 2014 Ancilla assisted quantum measurements T.S. Mahesh Department of Physics and NMR Research Centre, Indian Institute of Science Education and Research, Pune In collaboration with: Abhishek Shukla, Sharad Joshi, Hemant Katiyar, Koteswara Rao

The concept of ancillary space in quantum measurements is well known. In fact, a generalized quantum measurement (POVM) can be visualized as a projective measurement in the presence of an appropriate ancillary space. It has also been shown that ancilla qubits may assist in noninvasive quantum measurements. After pointing out such advantages of ancilla qubits in quan- tum measurements, we shall discuss some important applications of ancilla space in ensemble measurements. First we shall describe ‘Ancilla-Assisted Quantum State Tomography’, which greatly reduces the number of independent measurements. If the size of the ancilla space is sufficiently large, then a single ensemble measurement of a set of commuting observables suffices to reconstruct the entire density matrix of ‘system’ qubits. Ancillary qubits may also be exploited in quantum pro- cess tomography (QPT), which involves characterization of the χ-matrix describing a general quantum process. The standard method of QPT involves a series of independent experiments each of which requiring an initialization of the system qubitstoa particular element of a complete basis set, followed by the application of the process to be characterized, and finally a quantum state tomography of the corresponding output state. Again, ancilla qubits may help in greatly reducing the total number of initializations. For sufficiently large ancilla, it is even possible to realize entire QPT in a single ensemble measurement of a set of commuting observables. We also describe the experimental demonstrations of these concepts in two to five qubit systems using nuclear magnetic resonance techniques.

10:20:11:10 24 October 2014 Friction and measurements that preserve rather than destroy quantum entanglement Michel Devoret Applied Physics, Yale University, New Haven, CT, USA

Entangled states constitute a key resource in fundamental quantum physics, quantum cryptography and quantum computa- tion. It has generally been assumed that the creation of such states requires the system to avoid contact with a dissipative environment, and the suppression of all sources of dephasing. Some recent theoretical studies have shown, however, that dissipative interactions combined with an adequately chosen drive can be employed to preserve coherence. Following these ideas, we have built experimentally an autonomous feedback scheme that counteracts both dissipation and dephasing. This led to the demonstration of the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time [1]. Furthermore, fidelity of the Bell state can be increased by continuously monitoring one dissipative channel involved in the stabilization. The general approach we are following may be applied in the future to build a logical qubit holding quantum information in a fault-tolerant way and with minimal hardware [2]. [1] S. Shankar et al., Nature 504 (2013) 419. [2] M. Mirrahimi et al., New J. Phys. 16 (2014) 045014.

11:30-12:20 24 October 2014 Measuring a quantum system with a quantum probe Anil Shaji School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram

In conventional quantum limited metrology schemes, a quantum probe is used to estimate the value of a parameter that is associated with a classical system. The measured system is classical in the sense that the quantum probe does not disturb or change the value of the measured parameter. On the other hand if the measured parameter is associated with a quantum system, then the act of measuring it using a quantum probe will itself introduce an unavoidable disturbance on the parameter. We use a simple model to analyze this disturbance and quantify its effect on the quantum Cramer-Rao bound on the achievable minimum uncertainty in such a quantum limited measurement protocol.

12:20-13:10 24 October 2014 Limits on measurement: Decoherence and a universal bound on precision Saikat Ghosh Department of Physics, Indian Institute of Technology, Kanpur In collaboration with: H.M. Bharath

Here we will consider two aspects that limit measurements in general. The first of these is decoherence, a practical limitations for all quantum measurements. We will discuss experimental aspects of ects of decoherence in relation to preparing, storing and detecting single photons. In particular, experimental examples of preparing single photons from a cold atomic ensemble coupled to bad (low-finesse) optical cavity will be discussed along with examples of how one can use dark states that are decoupled from the environment to store a single photon polarization-state in atoms or use it to entangle two large atomic ensembles. The second half will focus on a proposal for a fundamental information theoretic bound on precision in estimation of a single parameter. For any general measurement of a single parameter with M distinct outcomes, it is observed that the precision is bounded below by 1/M and the mutual information between the parameter and the estimated value is bounded above by log(M). The number M, defined here as the precision capacity for the estimation, is independent of the dynamics of the model, setting an absolute and universal bound on the achievable precision. The corresponding probability distribution that saturates the bound is explicitly constructed. Analysing few standard Heisenberg-limited estimation strategies (Kitaev’s phase estimation strategy and quantum metrol- ogy with GHZ-like states), we demonstrate that saturating the Heisenberg limit is not a subjectivecient condition for exhausting the precision capacity or saturating the information-theoretic bound. In effect, this work demonstrates that exhausting the precision capacity and thereby attaining the absolute precision limit of 1/M is equivalent to optimizing the overall measurement scheme, including optimal probe states along with judiciously chosen operators to measure for an estimate of the parameter. Accordingly, a question of interest is what is the best one can do in terms of precision, using N probe particles and any amount of classical or quantum correlations? We nd that the answer depends on the choice of symmetry. For distinguishable particles, it is found that Kitaev’s phase esti- mation algorithm saturates the bound proposed here, without any quantum enhancement. With N indistinguishable particles, while the upper bound on precision capacity is N for a classical estimation, it scales as N 2 for an optimal quantum estimation strategy. Finally, the optimal set of operators that achieve this precision limit of 1/N 2 are constructed explicitly.

14:30-15:00 24 October 2014 Coherent states in magnetic resonance Navin Khaneja Electrical Engineering, Harvard University, Cambridge, MA, USA Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai

In NMR experiments, interaction of quantized radio-frequency field leads to entanglement of nuclear spin with the electromag- netic field. In an entangled state, the nuclear spins are depolarized with no net magnetization, which cannot give a detectable signal in inductive detection. We show that if the electromagnetic field is in coherent state, then inductive detection is possible. The talk develops the mathematics needed to describe this phenomenon.

15:00-15:50 24 October 2014 Arthurs-Kelly measurements and applications S.M. Roy Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai

Arthurs and Kelly generalized the von Neumann model of measurement of a single observable to joint measurement of non-commuting observables including conjugate observables like position and momentum. They obtained the result that the product of the measurement uncertainties, ∆p∆q, must be greater than or equal to h/(2π), which is twice the usual Heisenberg preparation uncertainty. We may not make both the uncertainties arbitrarily small in the same experiment. We discuss some applications. 1.The experimental joint probability distribution is just the Husimi distribution which has been used by Wehrl [1] to define a semi-classical entropy that is greater than or equal to von Neumann entropy. 2. Inspite of the impossibility of simultaneous accurate measurements of position and momentum, exact quantum correlations of conjugate variables may be determined from joint quadrature measurements using the Arthurs-Kelly interaction [2]. In this way semi-classical phase space densities may be experimentally tested. 3. We have developed an interaction based method for remote tomography and entanglement swapping utilising the Arthurs-Kelly interaction between a system photon and two apparatus photons [3]. [1] A. Wehrl, Rev. Mod. Phys. 50 (1978) 221. [2] S.M. Roy, Physics Letters A 377(34-36) (2013) 2011-2015. [3] S.M. Roy, Abhinav Deshpande and Nitica Sakharwade, Phys. Rev. A 89 (2014) 052107.

16:10-16:40 24 October 2014 Measurement in quantum and statistical mechanics Joseph Samuel Theoretical Physics, Raman Research Institute, Bangalore In collaboration with: Supurna Sinha, Anirudh Reddy, Kumar Shivam

We compare the role played by Measurement in Quantum Physics and in Statistical Physics. In both theories evolution is fun- damentally described by deterministic equations (given by Schrodinger or Newton), but measurements and their description drive us towards probabilistic methods. We use an operational approach to formulate and analyze simple thought experi- ments in which information is transferred between systems in statistical and quantum mechanics. We conclude that ideas of information, entropy and their transfer involve subjective elements consistent with the Bayesian view of Probability. Posters

18:00-19:30 22 and 23 October 2014 Quantum state estimation by weak measurements Debmalya Das Department of Physical Sciences, Indian Institute of Science Education and Research, Mohali

The possibility of using weak measurements to carry out quantum state tomography is explored via numerical simulations. With a fixed small number of copies of identically prepared states of a qubit, we perform state tomography using weak as well as projective measurements. After a projective measurement, the state cannot be re-used due to the collapse of the state after measurement. However, with a weaker coupling strength between the quantum system and the measurement device, we can significantly lower the disturbance caused to the state. This then allows us to re-use the same member of the ensemble for further measurements and thus extract more information from the system, though this happens at the cost of getting imprecise information from the first measurement. The scheme is implemented for a single qubit and it is shown that under certain circumstances, this prescription can outperform the projective measurement based tomography scheme. This opens up the possibility of new ways of extracting information from quantum ensembles. We study the efficacy of this scheme for different coupling strengths, and different ensemble sizes. References: [1] P. Busch and P. J. Lahti, Phys. Rev. D 29 (1984) 1634. [2] Y. Aharonov, D. Z. Albert and L. Vaidman, Phys. Rev. Lett. 60 (1988) 1351. [3] S. Marcovitch and B. Reznik, arXiv:1005.3236 (2010). [4] Debmalya Das and Arvind, arXiv:1402.0447 (2014).

Engineered decoherence: Characterization and suppression Swathi S. Hegde Department of Physics and NMR Research Centre, Indian Institute of Science Education and Research, Pune In collaboration with: T.S. Mahesh

Due to omnipresent environmental interferences, quantum coherences inevitably undergo irreversible transformations over certain time-scales, thus leading to the loss of encoded information. This process, known as decoherence, has been a major obstacle in realizing efficient quantum information processors. Understanding the mechanism of decoherence is crucial in developing tools to inhibit it. In this work, we utilize a method proposed by Teklemariam et al. [Phys. Rev. A 67, 062316 (2003)] to engineer artificial decoherence in the system qubits by randomly perturbing their surrounding ancilla qubits. Using a two qubit nuclear magnetic resonance quantum register, we characterize the artificial decoherence by noise spectroscopy and quantum process tomography. Further, we study the efficacy of dynamical decoupling sequences in suppressing the artificial decoherence. Here we describe the experimental results and their comparisons with theoretical simulations. Reference: S.S. Hegde and T.S. Mahesh, Physical Review A 89 (2014) 062317.

Entangled complex quantum trajectories Moncy V. John Department of Physics, St. Thomas College, Kozencherry, Kerala In collaboration with: Kiran Mathew

Entanglement in the context of modified de Broglie-Bohm(MdBB) representation of quantum mechanics is investigated. Complex quantum trajectories of some simple, bound entangled systems are drawn and analysed. Such trajectories, which are not obtainable in the conventional de Broglie-Bohm (dBB) scheme, shows how indistinguishability of fundamental particles can be viewed as arising out of of dynamical laws. The characteristics of boson and fermion trajectories are elaborated. Quantum enhanced measurements using Bose-Einstein condensates in a toroidal trap Salini Jose School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram

Aim of quantum metrology is to improve the precision of measurements using quantum resources such as squeezing and entanglement. With these resources, the 1/N scaling is the best possible scaling in any single parameter estimation scheme where N is the number of elementary units in the “quantum probe used to estimate the parameter. Here N is an effective placeholder for the relevant resources needed for the measurement. This 1/N scaling is known as Heisenberg limited scaling. Nonlinear interactions between the N elementary units can improve the scaling beyond this Heisenberg scaling. It is possible to get a scaling of 1/N k with k-body couplings and entanglement between the probe units while it is 1/N k1/2 without entanglement. Hence with 2-body couplings scaling will be 1/N 3/2. A Bose-Einstein condensate is a system in which 2-body couplings exist naturally. Hence using a BEC it should be possible to achieve a scaling of 1/N 3/2 for a measurement under ideal conditions. A number of theoretical assumptions were made in the theoretical analysis to get the 1/N 3/2 scaling using 3/2 a BEC. With all these simplifying assumptions and calculations the scaling we get is 1/N ηN where ηN is a measure of 3/2 the inverse volume occupied by the ground state wave function. So to get the 1/N scaling ηN should have no dependence on N. But as N increases BEC wave function expands. It affects ηN and scaling. Hence to avoid the expansion we use highly anisotropic traps. Hence expansion will be only along longitudinal dimension at least over a range of N. We can still reduce the uncertainty scaling by using a toroidal trap for the BEC. Here BEC will be toroidal in shape which will be held in a cylindrically symmetric trap. The first step is to find the ground state wave function. We have calculated the ground state wave function of a BEC held in a toroidal trap for different number of atoms and found the N dependence of η. We found that toroidal trap gives a better scaling.

Equivalence between joint unsharp measurements and positivity of moment matrix H.S. Karthik Light and Matter Physics, Raman Research Institute, Bangalore

Non-commutativity sets quantum mechanics apart from classical theory. In terms of measurements, which by itself is a confounding notion in quantum theory, commutativity of projective valued measurements (PVM), representing two or more Hermitian observables, imply that they are jointly measurable (i.e. (sharp) joint or simultaneous reality exists), and via this way the existence of a grand joint probability distribution (JPD) of measurement outcomes is ensured. However, in recent years generalized measurements in terms of Positive Operator Valued Measures (POVM) or effects have been extensively analyzed to gain deeper insights into the nature of unsharp joint realities in the quantum scenario [1,2,3]. One of the ways to generalize the compatibility of measurements is via the notion of joint measurability (JM). In our work, we investigate the notion of JM for the case of three unsharp measurements (di-chotomic POVMs) by constructing the moment matrix. The moment matrix being positive implies the existence of a grand joint probability distribution of measurement outcomes [4].We show that joint measurability of three POVMs (which sets a bound on the unsharpness parameter) coincides with the positivity of the moment matrix—in turn confirming the existence of a joint probability distribution for the unsharp measurement outcomes. [1] P. Busch, Phys. Rev. D 33 (1986) 2253. [2] T. Heinosaari, D. Reitzner and P. Stano, Found. Phys. 38 (2008) 1133. [3] M.T. Quintino, T. Vertesi and N. Brunner, arXiv:1406.6976 (2014); R. Uola, T. Moroder and O. Guehne, arXiv:1407.2224 (2014). [4] H.S. Karthik, A.R. Usha Devi, A.K. Rajagopal, Sudha, J. Prabhu Tej and A. Narayanan, Proceedings of 13th Asian Quantum Information Science Conference, 25-30 August 2013, pp.38-39.

Weak measurements and feedback Parveen Kumar Centre for High Energy Physics, Indian Institute of Science, Bangalore In collaboration with: Apoorva Patel

Strong measurement collapses a quantum system by projecting a superposition of possible states into a single probabilistic outcome. The time scale of this instantaneous projection can be stretched using weak measurement, by decreasing the rate at which the information is extracted from the system. Since system evolution can be monitored continuously during weak measurement, one can use feedback technique to protect the quantum state from unwanted decay. We present a formalism to describe how the system evolution changes due to weak measurement, and how that change can be compensated by feedback. Using this formalism, we study the evolution of a two qubit system, initially starting from the maximally entangled Bell state.

Experimental demonstration of quantum contextuality in 1-D quantum harmonic oscillator C.S. Sudheer Kumar Department of Physics and NMR Research Centre, Indian Institute of Science Education and Research, Pune In collaboration with: Hemant Katiyar, T.S. Mahesh

We routinely approximate many of the potentials we come across with that of 1-D Quantum Harmonic Oscillator (QHO). For example a cavity mode in cavity QED can be described via the Hamiltonian of QHO, which has important role in building a quantum computer. Hence it is important to know when a QHO behaves quantum mechanically and when classically. Here we experimentally demonstrate strong violation of a Noncontextual Hidden Variable (NCHV) inequality, under specific experi- mental arrangements, by the four eigenstates of 1-D QHO. We encoded the four eigenstates of 1-D QHO onto four Zeeman states of two spin-half nuclear spins precessing in an external magnetic field. We also demonstrate weak violation of NCHV inequality by maximally mixed states in nuclear spins, there by showing that states which behave classically (maximally mixed states, coherent states) do possess certain amount of quantumness, which manifests itself under certain special conditions.

A statistical approach to quantum tunnelling Kiran Mathew Department of Physics, St. Thomas College, Kozencherry, Kerala In collaboration with: Moncy V. John

We present a new statistical method to find the tunnelling probability using complex quantum trajectories. The trajectories we consider orginate from a modified de Broglie-Bohm approach. In this work we calculate the tunnelling probability for symmetric Eckart potential and soft potential step using the new method and find that they are comparable with those obtained in standard quantum mechanics. The analysis indicates the prospects of finding the density distribution of trajectories along the imaginary direction.

Joint weak value for all order coupling Alok Kumar Pan Department of Physics, National Institute of Technology, Patna In collaboration with: P. Panigrahi

Several theoretical and experimental works have recently been reported demonstrating the joint weak value of two observables by restricting the coupling strength to be second order. Here we provide a rigorous treatment of joint weak measurement for all order of coupling, which allows us to reveal several unexplored features. We use the pointer state to be a two-dimensional Gaussian and show that the joint weak value can be extracted for any strength of the coupling. We further demonstrate an interesting result that, instead of joint pointer observables, single pointer displacement can provide the information of joint weak value, if at least fourth order expansion of the coupling is taken. This treatment is used to investigate Hardy paradox for any strength of coupling.

Quantum first passage time “speakable”? V. Ranjith School of Natural Sciences and Engineering, National Institute of Advanced Studies, Bangalore In collaboration with: N. Kumar

The time-instant at which an event happens for the first time is the First Passage Time (FPT) of the event. This notion is very intuitive and robust in classical physics. In principle, it can be helpfully generalized to define first passage probability distributions in time for (classical) stochastic processes. For example, a classical random walker would cross a certain well defined boundary for the first time at a certain instant of time (say t’) in a particular realization of the random walk. Replicating this process over several realizations, a FPT probability density can be operationally obtained. However, in quantum frameworks, in general, it is very problematic to define even a (Quantum) FPT probability distribu- tion. This is due to the well studied counter-intuitive features of quantum processes like interference. The present poster highlights the key features of the standard quantum mechanics that render the notion of QFPT “un- speakable”. Links to the quantum-measurement problem are also highlighted. Finally, a special scenario within the quantum framework is presented wherein the difficulties nicely drop out to render a “speakable” QFPT distribution. (Partly based on [arXiv:1302.4669]) References: [1] Kamal Sharma and N. Kumar, Phys. Rev. E 86 (2012) 032104; ibid. 87 (2013) 019904(E). [2] O. Lumpkin, Phys. Rev. A. 51 (1995) 2758. [3] J.J. Halliwell and J.M. Yearsley, Phys. Rev. D 86 (2012) 024016.

Enhancing bandwidth of Josephson parametric amplifier with impedence engineering Tanay Roy Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai In collaboration with: A.M. Vadiraj, Suman Kundu, Meghan Patankar, R. Vijayaraghavan

Superconducting Josephson parametric amplifiers (JPAs) have recently become a crucial component of superconducting quan- tum information processing systems because of their ability to measure single quantum objects with very high fidelity. In spite of their excellent noise performance, JPAs based on a single, driven non-linear oscillator suffer from two major drawbacks-- narrow bandwidth and saturation at very low signal powers and are thus suited to single qubit experiments only. With the rapid development of multi-qubit systems, there is a practical need to develop an amplifier with larger bandwidth and signal han- dling capacity, while maintaining quantum-limited noise performance. We will describe a method to enhance the bandwidth by engineering the impedance seen by the JPA and demonstrate its performance using numerical simulations. We observe a bandwidth increase of more than a factor of two without affecting the quality factor of the resonator. Though quantum-limited performance is still achieved, we observe a strong dependence of the noise performance on the biasing conditions. Finally, we will present some preliminary experimental results.

Quantum phase relations in superconducting charge qubit lattice Sujit Sarkar Poorna Prajna Institue of Scientific Research, Bangalore

Superconducting circuits, such as charge qubits, are macroscopic in size but have generic quantum properties. We present the analytical relations for different quantum phases and phase boundaries between the Josephson couplings and the interaction parameters of charge qubit lattice. These relations are not universal. To make the charge qubit lattice fully tunable, we also consider the presence of magnetic flux through d.c. SQUIDs. The magnetic flux shifts the quantum phases and phase boundaries, this effect is also non-uniform in quantum phase diagram. We also present the effect of site dependent Josephson coupling and interaction parameters of the system.

Applying Leggett-Garg inequality for device-independent quantum cryptography Akshata Shenoy Electrical Communication Engineering Department, Indian Institute of Science, Bangalore In collaboration with: S. Aravinda, R. Srikanth, Dipankar Home

Since the advent of Quantum Cryptography through the pioneering protocols known as BB84 [1] and E91 [2], their rigorous security proofs [3] and attempted experimental realizations [4], a particularly noteworthy development has been the notion of device-independent (DI) quantum cryptography [5]. This line of study arose because of the feature that cryptography based on the laws of quantum physics, even though unconditionally secure, can be rendered insecure due to flaws in the practical realizations, and because of the possibility of a malicious vendor tampering the relevant devices in a clever way. The usually implicit assumption that all devices used to establish secure communication are trusted and well-characterized, is not made in DI quantum cryptography, where one assumes only that quantum mechanics is a valid theory and that no unwanted signal leakage occurs from the devices used. The key element for ensuring security in such a scenario is the role played by Bell-type inequality (BI), which has been explored extensively in this context. In a nutshell, BB84-type protocols are insecure in the DI scenario, while sufficiently large violation of BI involving entanglement is considered to be necessary in order to ensure DI security. Against this backdrop, it is rather curious that no one has yet explored in the context of quantum cryptography, the possibility of an application of the temporal analogue of BI, known as the Leggett-Garg inequality (LGI) [6], which is violated by the relevant quantum mechanical results for the sequential measurements of a suitable observable on the same particle. Our present work fills this gap in the literature by showing that the use of an appropriate form of LGI enables to achieve, up to a considerable extent, the DI security for the BB84-type protocols without requiring entanglement. While the key generation is done by the usual BB84 method, the security check against a certain type of higher dimensional attack [7] is provided by testing the violation of the particular form of LGI used here. The amount of reduction in the observed violation of LGI due to eavesdropping determines the error rate that can be tolerated in our proposed protocol. [1] C.H. Bennett and G. Brassard, Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore (1984), p.175. [2] A.K. Ekert, Phys. Rev. Lett. 67 (1991) 661. [3] D.Mayers, J. Assn. Comput. Mac. 48 (2001) 351; P.W. Shor and J. Preskill, Phys. Rev. Lett. 85 (2000) 441. [4] N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, Rev. Mod. Phys. 74 (2002) 145 (2002). [5] L. Masanes, A. Acin and N. Gisin, Phys. Rev. A 73 (2006) 012112; J. Barrett, L. Hardy and A. Kent, Phys. Rev. Lett. 95 (2005) 010503; A. Acin, N. Gisin and L. Masanes, Phys. Rev. Lett. 97 (2006) 120405; S. Pironio, A. Acin, N. Brunner, N. Gisin, S. Massar and V. Scarani, New J. Phys. 11 (2009) 045021; C.C.W. Lim, C. Portmann, M. Tomamichel, R. Renner and N. Gisin, Phys. Rev. X 3 (2013) 031006. [6] A.J. Leggett and A. Garg, Phys. Rev. Lett. 54 (1985) 857; A.J. Leggett, Rep. Prog. Phys. 71 (2008) 022001. [7] A. Acin, N. Gisin and L. Masanes, Phys. Rev. Lett. 97 (2006) 120405.

Violation of entropic Leggett-Garg inequality in nuclear spins Abhishek Shukla Department of Physics and NMR Research Centre, Indian Institute of Science Education and Research, Pune In collaboration with: Hemant Katiyar, K. Rama Koteswara Rao, T.S. Mahesh

We present an experimental study of entropic Leggett-Garg inequality (ELGI) [1], formulated by Usha Devi et al. [2]. This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. We used a two qubit nuclear spin system to study ELGI. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the ideal negative result measurement procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we also demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities. [1] H. Katiyar, A. Shukla, K.R. Koteswara Rao and T.S. Mahesh, Phys. Rev. A 87 (2013) 052102. [2] A.R. Usha Devi, H.S. Karthik, Sudha and A.K. Rajagopal, Phys. Rev. A 87 (2013) 052103.

Complementarity in three slit interference Mohd. Asad Siddiqui Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi

The issue of interference and which-way information is studied in context of 3-slit interference experiments. An inequality is derived which puts a bound on how much fringe visibility and which-way information can be obtained simultaneously. Also we look at the same issue in 3-slit ghost interference, and find that it follows the same inequality with a nonlocal feature, which is different compared to 3-slit interference experiment. Quantum theory allows measurement of non-Hermitian operators Uttam Singh Physics, Harish-Chandra Research Institute, Allahabad

A physical observable in quantum theory is represented by a Hermitian operator as any measuring apparatus that is supposed to measure it should always yield a real number. However, reality of eigenvalue of some operator does not mean that it is necessarily Hermitian. There are examples of non-Hermitian operators which may admit real eigenvalues under some symmetry conditions. One may wonder if there is any way to measure a non-Hermitian operator, for example, the average of a non-Hermitian operator in a quantum state. We show that quantum theory allows direct measurement of any non-Hermitian operator via the weak measurement. The average of a non-Hermitian operator in a pure state is a complex multiple of the weak value of the positive semi-definite part of the non-Hermitian operator. We also prove a new uncertainty relation for any two non-Hermitian operators and illustrate this for the creation and annihilation operators, and the Kraus operators.

Quantum Measurements with Superconducting Circuits A.M. Vadiraj Quantum Measurement and Control Laboratory, Tata Institute of Fundamental Research, Mumbai In collaboration with: Tanay Roy, Cosmic Raj, Suman Kundu, Meghan Patankar, R. Vijayaraghavan

Superconducting circuit based devices are a promising test bed for an array of experiments in the field of quantum electrody- namics. With the development of ultra-low noise amplifiers, they provide an ideal setup for studying quantum measurement and back-action physics. In this poster, we present progress towards development of high-fidelity quantum measurements on a superconducting quantum bit using a Josephson Parametric Amplifier (JPA) [1]. The superconducting qubit is essentially an anharmonic oscillator consisting of a capacitively shunted Superconducting QUantum Interference Device (SQUID). The two lowest quantum levels of such an oscillator are used as a quantum bit. The qubit is coupled to a microwave cavity in the so called circuit QED architecture and implements a near ideal quantum measurement setup. The measurement is performed by using microwave signals to probe the cavity frequency which depends on the qubit state. The output signal is amplified using a JPA which enables real-time monitoring of the quantum state. We will also briefly describe a superconducting device com- prising of a doubly-clamped suspended aluminium beam resonator parametrically coupled to a JPA. The JPA will enable the detection of mechanical motion of the beam. The primary goal is to understand the back-action of the JPA on the mechanical beam under different operating conditions [2,3]. [1] M. Hatridge et al., Phys. Rev. B 83 (2011) 134501. [2] C. Laflamme et al., Phys. Rev. A 83 (2011) 033803. [3] C. Laflamme et al., Phys. Rev. Lett. 109 (2012) 123602.