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

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