DOCSLIB.ORG

Experimentally Witnessing the Quantumness of Correlations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Experimentally Witnessing the Quantumness of Correlations Experimentally witnessing the quantumness of correlations R. Auccaise,1 J. Maziero,2 L. C. C´eleri,2 D. O. Soares-Pinto,3 E. R. deAzevedo,3 T. J. Bonagamba,3 R. S. Sarthour,4 I. S. Oliveira,4 and R. M. Serra2, ∗ 1Empresa Brasileira de Pesquisa Agropecu´aria, Rua Jardim Botˆanico 1024, 22460-000 Rio de Janeiro, Rio de Janeiro, Brazil 2Centro de Ciˆencias Naturais e Humanas, Universidade Federal do ABC, R. Santa Ad´elia 166, 09210-170 Santo Andr´e, S˜ao Paulo, Brazil 3Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, Caixa Postal 369, 13560-970 S˜ao Carlos, S˜ao Paulo, Brazil 4Centro Brasileiro de Pesquisas F´ısicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil The quantification of quantum correlations (other than entanglement) usually entails laboured numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compare the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement. PACS numbers: 03.67.-a, 03.65.Ta, 03.67.Ac, 03.65.Ud Nonlocality [1] and entanglement [2] of composed sys- tems are distinguishing features of the quantum domain. dimHa dimHb Nevertheless, it is the possibility of locally broadcasting ρcc = pi,j |αiihαi| ⊗ |βj ihβj |, (1) [3] the state of a multiparticle system that broadly de- X X i=1 j=1 fines the nature of its correlations. Remarkably, even separable (nonentangled) states can be quantum corre- where {|αii} and {|βj i} are orthonormal basis for the lated. This kind of quantumness has an important role subsystems state spaces Ha and Hb, respectively, and that is not only related to fundamental physical aspects {pi,j} is a probability distribution. but also concerning applications in quantum information The class of states in equation (1) is contained in the processing [4–7] and communication [3, 8], thermody- set of separable states —those states that can be gen- namics [9], quantum phase transitions[10], and biological erated via local operations coordinated by communicat- systems [11]. ing classical bits—whose more general form is ρsep = a b i piρi ⊗ρi , where {pi} is a probability distribution and Pa b There are several unique aspects of quantum physics ρi (ρi ) is a valid density operator for the subsystem a(b). that discern it from classical theories. One of particular There are separable states that cannot be cast in terms relevance to quantum information science is the impossi- of orthogonal local basis as those given in equation (1) bility of creating a perfect copy of an unknown quantum and, therefore, present non-classical correlations. Un- state [12]. This fact is employed in some quantum crypto- derneath such states lies a non-classicality beyond the graphic protocols [12] and, when extended to multipartite entanglement-separability paradigm, which can be quan- mixed states [3], can be used to classify the aspects of cor- tified by a departure between classical and quantum ver- relations in a composed system as classical or quantum. sions of information theory. One of the most popular Let us consider a bipartite system described by the den- measures for this kind of non-classicality is the quantum sity operator ρ and shared by parts a and b, with respec- discord [13]. This quantifier has been receiving a great tive Hilbert spaces Ha and Hb. The correlations in state deal of attention [6–8, 14]. And it was proposed as a arXiv:1104.1596v2 [quant-ph] 9 Aug 2011 ρ are said to be locally broadcast if there are auxiliary figure of merit for the quantum advantage in some com- systems Ha1 , Ha2 , Hb1 , Hb2 and local operations (com- putational models without or with little entanglement pletely positive, trace-preserving linear maps) Λa : Ha → [4, 5]. Ha1 ⊗Ha2 and Λb : Hb → Hb1 ⊗Hb2 such that ρa1a2b1b2 = In general, measures of non-classical correlations in- Λa ⊗ Λb(ρ) with I(ρa1b1 )= I(ρa2b2 ), where the quantum volve complete knowledge of the system’s state followed mutual information—I(ρxy) = S(ρx)+ S(ρy) − S(ρxy), by extremization procedures. In the laboratory, the x xy S(ρ) = −tr(ρ log2 ρ), and ρ = try(ρ )—quantifies all first task is implemented by quantum state tomographic the correlations between the systems x and y. It turns methods and the second one is carried out by additional out that the correlations in a bipartite system can be lo- numerical manipulations. These procedures are demand- cally broadcast, and therefore have a classical nature, if ing and propagate the unavoidable experimental errors. and only if the system’s state can be written as [3] This observation motivates the search for alternatives 2 also a necessary condition for the absence of quantumness (a) Correlation in the correlations of the composite system (in this case Witness 1 hO4iρ = 0 [15]). We can easily verify that the observ- H (θ ) bd k n k ables in equation (2) can be written in terms of one com- x state ponent of the magnetization in one subsystem as hOiiρ = preparation a Ib † hσ1 ⊗ iξi , with ξi = Ua→b Rni (θi)ρRni (θi) Ua→b, 13 C a b a(b) (θ ) where Rni (θi) = Rni (θi) ⊗ Rni (θi), and Rni (θi) is a k nk local rotation by an angle θi around direction ni, with θ1 = 0, θ2 = θ3 = π/2, n2 = y, and n3 = z. Ua→b is the (b) |11> State Preparation pseudo (θ ) C Read-out controlled-NOT gate with the subsystem a as control. k n k NOT EPR x xy y x x yxy ρ ρ (a) ρQC CC T 1H Acq. x y x y x x y y xyxy n ,θ33 1 1 1 1 3 13 C 4J 4J 2J 2J 2J n ,θ22 Gradient n ,θ11 200 1000 -100 -200 200 1000 -100 -200 200 1000 -100 -200 Hz Hz Hz FIG. 1. (Color online) (a) Schematic representation of the op- (b) eration sequence used to witness the non-classical nature of 3 correlations. (b) Equivalent pulse sequence employed in our experiment. The thicker filled bars represent π/2 pulses, the 2 thinner bars indicate π/4 pulses, and the grey bars indicate Witness π/6 pulses with the phases as shown (negative pulse phases 1 are described by a bar over the symbol). The pulses rep- resented as unfilled dashed bars are modified to achieve the 0 ρ ρ ρ different rotations necessary for the witness protocol. The QC CC T dashed gradient pulse is applied to obtain the classically cor- (c) 1 3 1 related Bell-diagonal state. The time periods 2J , 2J , and 4J 6 represent free evolutions under the J coupling [18]. 4 regarding the classification of correlations in quantum Correlations 2 states. Once the nature of these correlations somehow de- 0 termines what can and cannot be done with a given sys- ρ ρ ρ tem, it is sometimes enough to know whether the correla- QC CC T tions in that system have a classical or a quantum nature. 1 FIG. 2. (Color online) (a) The H spectra (normalized by To accomplish this last task it is convenient to have an the thermal equilibrium state spectrum) obtained after the observable witness for the quantumness of correlations in witness circuit execution (with rotations Rn1 , Rn2 , and Rn3 ), the system. However, as the state space of classical cor- (b) witness expectation value, (c) quantum discord (light blue related systems is not convex, a linear witness cannot be columns) and classical correlation (dark blue columns) mea- used in general, and we have to take advantage of a non- sured in three different initial states, ρQC quantum correlated, linear witness. For a wide class of two-qubit systems, ρ = ρCC classically correlated, and ρT thermal equilibrium state. ab 3 a b a b a b The dashed line represents the experimental error bound for I + (Aiσ ⊗ I + BiI ⊗ σ + Ciσ ⊗ σ ) /4, a Pi=1 i i i i determination of classically correlated (zero discord) states. sufficient condition for classicality of correlations is [15] The witness was measured directly performing the circuit de- picted in Fig 1 (a), while the classical correlation and the 3 4 symmetric quantum discord was computed after full QST and Wρ = |hOiiρhOj iρ| =0, (2) numerical extremization procedures. The correlations are dis- X X 2 i=1 j=i+1 played in units of (ε / ln 2)bit [18]. a b 3 a with Oi = σi ⊗ σi for i =1, 2, 3 and O4 = i=1(ziσi ⊗ a b P We experimentally implemented the aforementioned Ib + w Ia ⊗ σb). The σ ( ) is the ith component of the i i i witness using the room temperature nuclear magnetic Pauli operator in subsystem a(b). A , B ,z , w ∈ ℜ i i i i resonance (NMR) system. In this scenario the qubits with z , w randomly chosen and constrained such that i i (quantum bits) are encoded in nuclear spins and they z2 = w2 = 1. For the so-called Bell-diagonal class Pi i Pi i are manipulated by radio-frequency (rf) pulses. Unitary Iab 3 a b of states, ρbd = + i=1 Ciσi ⊗ σi /4, Wρbd = 0 is operations are achieved by suitable choice of pulse am- P 3 (a) Re(Δρ ) Im(Δρ ) after the aforementioned pulse sequence.
Load more

Recommended publications
  • Quantum Correlations in Separable Multi-Mode States and in Classically Entangled Light
    Quantum correlations in separable multi-mode states and in classically entangled light N. Korolkova1 and G. Leuchs2 1 School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife, KY16 9SS, Scotland 2 Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany; Institute of Optics, Information and Photonics, University of Erlangen-Nuremberg, Staudtstraße 7/B2, Erlangen, Germany E-mail: [email protected]; [email protected] Abstract. In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum technologies. We briefly define the genuinely quantum concepts of entanglement and steering. We then move to the boarder line between classical and quantum world introducing quantum discord, a more general concept of quantum coherence, and finally a controversial notion of classical entanglement. To unveil the quantum aspects of often classically perceived systems, we focus more in detail on quantum discordant correlations between the light modes and on nonseparability properties of optical vector fields leading to entanglement between different degrees of freedom of a single beam. To illustrate the aptitude of different types of correlated systems to act as quantum or quantum-like resource, entanglement activation from discord, high- precision measurements with classical entanglement and quantum information tasks using intra-system correlations are discussed. The common themes behind the versatile quantum properties of seemingly classical light are coherence, polarization and inter and intra{mode quantum correlations. arXiv:1903.00469v1 [quant-ph] 27 Feb 2019 QUANTUM CORRELATIONS IN \CLASSICAL" LIGHT 2 Quantum correlations in \classical" light 1 Introduction 2 2 Definitions 3 2.1 Quantum correlations in nonseparable and separable states .
    [Show full text]
  • Quantum Computing a New Paradigm in Science and Technology
    Quantum computing a new paradigm in science and technology Part Ib: Quantum computing. General documentary. A stroll in an incompletely explored and known world.1 Dumitru Dragoş Cioclov 3. Quantum Computer and its Architecture It is fair to assert that the exact mechanism of quantum entanglement is, nowadays explained on the base of elusive A quantum computer is a machine conceived to use quantum conjectures, already evoked in the previous sections, but mechanics effects to perform computation and simulation this state-of- art it has not impeded to illuminate ideas and of behavior of matter, in the context of natural or man-made imaginative experiments in quantum information theory. On this interactions. The drive of the quantum computers are the line, is worth to mention the teleportation concept/effect, deeply implemented quantum algorithms. Although large scale general- purpose quantum computers do not exist in a sense of classical involved in modern cryptography, prone to transmit quantum digital electronic computers, the theory of quantum computers information, accurately, in principle, over very large distances. and associated algorithms has been studied intensely in the last Summarizing, quantum effects, like interference and three decades. entanglement, obviously involve three states, assessable by The basic logic unit in contemporary computers is a bit. It is zero, one and both indices, similarly like a numerical base the fundamental unit of information, quantified, digitally, by the two (see, e.g. West Jacob (2003). These features, at quantum, numbers 0 or 1. In this format bits are implemented in computers level prompted the basic idea underlying the hole quantum (hardware), by a physic effect generated by a macroscopic computation paradigm.
    [Show full text]
  • Quantum Discord and Entanglement of Quasi-Werner States Based on Bipartite Entangled Coherent States
    QUANTUM DISCORD AND ENTANGLEMENT OF QUASI-WERNER STATES BASED ON BIPARTITE ENTANGLED COHERENT STATES Manoj K Mishra 1, Ajay K Maurya 1 and Hari Prakash 1,2 1Physics Department, University of Allahabad, Allahabad, India 2Indian Institute of Information Technology, Allahabad, India email: [email protected] ,[email protected] , [email protected] , [email protected] ABSTRACT: Present work is an attempt to compare quantum discord and quantum entanglement of Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, two based on maximally ECS are exactly similar to the perfect Werner state, while the rest two, based on non-maximally ECS, which are called quasi-Werner states behave in somewhat different ways and their quantum discord and entanglement depends on the coherent amplitude and the measurement basis. I. INTRODUCTION Quantum correlations have been comprehensively accepted as the main resource for different quantum information processing tasks. Einstein et al [1] and Schrödinger et al [2] at the outset introduced the concept of quantum correlation exhibited in a non-separable bipartite quantum state and this was called quantum entanglement (QE). Concurrence [3], Entanglement of formation [3], Tangle [4] and Negativity [5], defined by various researchers, quantify the entanglement existing in a bipartite or multipartite quantum state. Significant number of theoretical and experimental schemes [6-12] have been proposed for generating the entangled states based on photonic [6], atomic [7-9] and coherent state [10-12] qubits. Motivation behind all these works related to entanglement is due to its fundamental nature and its application in quantum information processing tasks like quantum computation [13], quantum teleportation [14], quantum dense coding [15], and quantum cryptography [16].
    [Show full text]
  • Entanglement Distribution and Quantum Discord
    Entanglement distribution and quantum discord 1, 2 2 Alexander Streltsov, ∗ Hermann Kampermann, and Dagmar Bruß 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, D-14195 Berlin, Germany 2Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany Establishing entanglement between distant parties is one of the most important problems of quan- tum technology, since long-distance entanglement is an essential part of such fundamental tasks as quantum cryptography or quantum teleportation. In this lecture we review basic properties of en- tanglement and quantum discord, and discuss recent results on entanglement distribution and the role of quantum discord therein. We also review entanglement distribution with separable states, and discuss important problems which still remain open. One such open problem is a possible advantage of indirect entanglement distribution, when compared to direct distribution protocols. P I. INTRODUCTION where pij are probabilities with i;j pij = 1. The set of all separable states will be denoted by . Any separable S This lecture presents an overview of the task of estab- state can be produced with local operations and classical lishing entanglement between two distant parties (Alice communication (LOCC). An entangled state cannot be and Bob) and its connection to quantum discord [1–5]. written as in Eq. (1). In order to produce an entangled Surprisingly, it is possible for the two parties to perform state, a non-local operation is needed. In SectionII we this task successfully by exchanging an ancilla which will review different ways to quantify the amount of has never been entangled with Alice and Bob.
    [Show full text]
  • The Freezing Rènyi Quantum Discord Xiao-Yu Li1, Qin-Sheng Zhu 2, Ming-Zheng Zhu1, Hao Wu2, Shao-Yi Wu2 & Min-Chuan Zhu2
    www.nature.com/scientificreports OPEN The freezing Rènyi quantum discord Xiao-Yu Li1, Qin-Sheng Zhu 2, Ming-Zheng Zhu1, Hao Wu2, Shao-Yi Wu2 & Min-Chuan Zhu2 As a universal quantum character of quantum correlation, the freezing phenomenon is researched by Received: 18 March 2019 geometry and quantum discord methods, respectively. In this paper, the properties of Rènyi discord is Accepted: 18 September 2019 studied for two independent Dimer System coupled to two correlated Fermi-spin environments under Published: xx xx xxxx the non-Markovian condition. We further demonstrate that the freezing behaviors still exist for Rènyi discord and study the efects of diferent parameters on this behaviors. As an important part of the quantum theory, the quantum correlation has aroused extensive attention in lots of physical felds, such as quantum information1–3, condensed matter physics4,5 and gravitation wave6 due to some unimaginable properties in a composite quantum system which can not be reproduced by a classical system. In the past twenty years, entanglement was considered as the quantum correlation and gradually understood. But, the quantum discord concept has been put forward by Ollivier and Zurek7,8 and Henderson and Vedral9 with the deep understanding of quantum correlation. It was clearly demonstrated that entanglement represents only a portion of the quantum correlations and can entirely cover the latter only for a global pure state10. Later, many eforts have been devoted to quantify quantum correlation from the view of geometry10–20 and entropy7–9,21–29. Since the systematic correlation contains two parts: the classical correlations and quantum correlation, Maziero et al.30 found the frozen behavior of the classical correlations for phase-fip, bit-fip, and bit-phase fip channels.
    [Show full text]
  • Geometric Quantum Discord of Heisenberg Model with Dissipative Terms Jin Liang* & Chengwei Zhang
    www.nature.com/scientificreports OPEN Geometric quantum discord of Heisenberg model with dissipative terms Jin Liang* & Chengwei Zhang In this paper, we study a system with two interacting qubits described by the Heisenberg model with dissipative terms, and analyze decay dynamics and the steady-state of geometric quantum discords. Our results indicate that we can ignore the interaction force in the z-direction and adjust the parameters to change the loss of quantum correlation with time when the initial state satisfes some conditions. Moreover, we show that after a long enough period of time, unlike other parameters, the energy and the intensity of the non-uniform magnetic feld do not afect the steady-state. Quantum theory has received extensive attention in recent years due to its wide usage in a large number of new technologies1–4. Quantum correlation, as one of the basic questions in quantum theory 5, has a great develop- ment in recent years 6–8. Quantum correlation has multiple levels, such as nonlocal 9, steerable10 or entangled11, and a framework for measuring the quantum system has been built. Afer quantum discord was frstly proposed by Ollivier and Zurek2 and by Henderson and Vedral12 respectively, a series of discord-like quantum correla- tions were proposed which exhibit diferent properties when characterizing the dynamics of the same quantum system and have become important resources in quantum theory. As one of discord-like quantum correlations, the geometric quantum discord, which will be used in this paper, has been widely concerned because it is easier to calculate and useful. To gain a deeper understanding of the similarities and diferences between such discord-like quantum cor- relations, we will use a model which can be solved exactly—the Heisenberg model in contact with a thermal reservoir.
    [Show full text]
  • Correlaciones En Mecánica Cuántica: Entrelazamiento Y Quantum Discord Como Recursos Para Realizar Procesos En Información Cuántica
    UNIVERSIDAD DE CONCEPCIÓN FACULTAD DE CIENCIAS FÍSICAS Y MATEMÁTICAS DEPARTAMENTO DE FÍSICA Correlaciones en Mecánica Cuántica: Entrelazamiento y Quantum Discord como Recursos para Realizar Procesos en Información Cuántica Tesis para optar al grado académico de Doctor en Ciencias Físicas por Marcelo Javier Alid Vaccarezza Concepción, Chile Septiembre 2012 UNIVERSIDAD DE CONCEPCIÓN FACULTAD DE CIENCIAS FÍSICAS Y MATEMÁTICAS DEPARTAMENTO DE FÍSICA Correlaciones en Mecánica Cuántica: Entrelazamiento y Quantum Discord como Recursos para Realizar Procesos en Información Cuántica Tesis para optar al grado académico de Doctor en Ciencias Físicas por Marcelo Javier Alid Vaccarezza Director de Tesis : Dr. Luis Roa Oppliger Comisión : Dra. M. Loreto Ladrón de Guevara Dr. Gustavo Lima Concepción, Chile Septiembre 2012 Resumen. En la teoría cuántica de la información las correlaciones cuánticas son esenciales. Por ejemplo, el entrelazamiento, un fenómeno sin contraparte clásica, es fundamental tanto desde el punto de vista teórico como para el desarrollo tecnológico futuro que esté basado en la computación cuántica. Además del entrelazamiento existen otros tipos de correlaciones, presentes sólo entre sis- temas cuánticos, que también han despertado el interés entre los investigadores. El quantum discord y la disonancia son algunos de ellos. En esta tesis se estudia, clasifica y cuantifica el entrelazamiento, el quantum discord y la disonancia necesarios para llevar a cabo con éxito los protocolos de discriminación asistida de estados no ortogonales. Además, se estudia la dependencia que existe entre éstas correlaciones y los estados de los sistemas utilizados para tales procesos, logrando caracterizar la cantidad de entrelazamiento y quantum discord en términos de los parámetros que definen a los estados utilizados.
    [Show full text]
  • Quantum Discord As a Resource for Quantum Cryptography
    OPEN Quantum discord as a resource for SUBJECT AREAS: quantum cryptography QUANTUM Stefano Pirandola INFORMATION QUANTUM OPTICS Department of Computer Science, University of York, York YO10 5GH, United Kingdom. INFORMATION THEORY AND COMPUTATION Quantum discord is the minimal bipartite resource which is needed for a secure quantum key distribution, being a cryptographic primitive equivalent to non-orthogonality. Its role becomes crucial in Received device-dependent quantum cryptography, where the presence of preparation and detection noise 13 August 2014 (inaccessible to all parties) may be so strong to prevent the distribution and distillation of entanglement. The Accepted necessity of entanglement is re-affirmed in the stronger scenario of device-independent quantum 20 October 2014 cryptography, where all sources of noise are ascribed to the eavesdropper. Published 7 November 2014 ne of the hot topics in the quantum information theory is the quest for the most appropriate measure and quantification of quantum correlations. For pure quantum states, this quantification is provided by quantum entanglement1 which is the physical resource at the basis of the most powerful protocols of O 2–4 quantum communication and computation . However, we have recently understood that the characterization of Correspondence and quantum correlations is much more subtle in the general case of mixed quantum states5,6. requests for materials There are in fact mixed states which, despite being separable, have correlations so strong to be irreproducible by should be addressed to any classical probability distribution. These residual quantum correlations are today quantified by quantum 7 S.P. (stefano. discord , a new quantity which has been studied in several contexts with various operational interpretations and 8 9,10 11 [email protected].
    [Show full text]
  • Redalyc.Quantum Discord in Nuclear Magnetic Resonance Systems At
    Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Maziero, J.; Auccaise, R.; Céleri, L. C.; Soares-Pinto, D. O.; deAzevedo, E. R.; Bonagamba, T. J.; Sarthour, R. S.; Oliveira, I. S.; Serra, R. M. Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature Brazilian Journal of Physics, vol. 43, núm. 1-2, abril, 2013, pp. 86-104 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46425766006 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Braz J Phys (2013) 43:86–104 DOI 10.1007/s13538-013-0118-1 GENERAL AND APPLIED PHYSICS Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature J. Maziero · R. Auccaise · L. C. Céleri · D. O. Soares-Pinto · E. R. deAzevedo · T. J. Bonagamba · R. S. Sarthour · I. S. Oliveira · R. M. Serra Received: 10 December 2012 / Published online: 26 February 2013 © Sociedade Brasileira de Física 2013 Abstract We review the theoretical and the experi- Previous theoretical analysis of quantum discord deco- mental researches aimed at quantifying or identifying herence had predicted the time dependence of the dis- quantum correlations in liquid-state nuclear magnetic cord to change suddenly under the influence of phase resonance (NMR) systems at room temperature. We noise. The experiment attests to the robustness of the first overview, at the formal level, a method to deter- effect, sufficient to confirm the theoretical prediction mine the quantum discord and its classical counterpart even under the additional influence of a thermal envi- in systems described by a deviation matrix.
    [Show full text]
  • Quantum-Discord.Pdf
    Quantum mechanics governs the submicroscopic realm of photons, electrons, and atoms. In principle, its equations are valid for an object of any size, but a large object (and large, in this context, could mean anything bigger than 10 or 20 atoms) cannot effectively be isolated from its environment because it undergoes incessant interactions with the matter and radiation surrounding it. A process called decoherence ensues: information describing the object’s complex quantum state disperses into the environment, forcing the object into simpler states without the quantum features of its pre-decoherence state. Thus, even as the combined whole—object plus environment—adheres to the quantum rules of behavior, the object alone no longer exhibits any of the telltale signatures of quantumness and, in effect, “goes classical.” The border territory between quantum and classical is becoming increasingly important for applications, and Los Alamos National Laboratory Fellow Wojciech Zurek is making inroads into this regime. Zurek has dedicated much of his career to an elusive line of research into the foundations of quantum physics. How does the quantum behavior of the microscopic world give way to the classical behavior of the macroscopic world? Why do electrons behave differently than baseballs? settle on a particular state—up or down and not both. But if Just where does that transition lie, and what rules emerge avoiding a disturbance means perfectly isolating the qubits from it? What aspects of the world are irreducibly quantum? from the environment to prevent decoherence (decoherence Most of Zurek’s work is foundational in nature, but which would, at best, turn the quantum computer into a just like the advent of quantum theory itself, which long poorly performing classical computer), then actually building preceded its many practical applications, his pure research a quantum computer would be nearly impossible.
    [Show full text]
  • Sharma-Mittal Quantum Discord
    Sharma-Mittal Quantum Discord Souma Mazumdar,∗ Supriyo Duttay, Partha Guha z Depertment of Theoretical Sciences S. N. Bose National Centre for Basic Sciences Block - JD, Sector - III, Salt Lake City, Kolkata - 700 106 Abstract We demonstrate a generalization of quantum discord using a general- ized definition of von-Neumann entropy, which is Sharma-Mittal entropy; and the new definition of discord is called Sharma-Mittal quantum discord. Its analytic expressions are worked out for two qubit quantum states as well as Werner, isotropic, and pointer states as special cases. The R´enyi, Tsallis, and von-Neumann entropy based quantum discords can be ex- pressed as limiting case for of Sharma-Mittal quantum discord. We also numerically compare all these discords and entanglement negativity. Keywords: Quantum discord, Sharma-Mittal entropy, R´enyi entropy, Tsallis entropy, Werner state, isotropic state, pointer state. 1 Introduction Entropy is a measure of information generated by random variables. In classical information theory [1], we use Shannon entropy as a measure of information. In quantum information theory, the von-Neumann entropy is the generaliza- tion of classical Shannon entropy. In resent years, a number of entropies has been proposed to measure information, for instance the R´enyi entropy [2], and Tsallis entropy [3], in different contexts. The R´enyi entropy is a generaliza- tion of the Hartley entropy, the Shannon entropy, the collision entropy and the min-entropy. Also, the Tsallis entropy is a generalization of Boltzmann-Gibbs entropy. The Sharma-Mittal entropy generalizes both R´enyi entropy and Tsallis entropy. Further generalizations of entropy functions are also available in the arXiv:1812.00752v2 [quant-ph] 15 May 2019 literature [4], [5].
    [Show full text]
  • A Unified Approach to Local Quantum Uncertainty and Interferometric
    entropy Article A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information Paolo Gibilisco 1,*, Davide Girolami 2 and Frank Hansen 3 1 Department of Economics and Finance, University of Rome “Tor Vergata”, Via Columbia 2, 00133 Rome, Italy 2 Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy; [email protected] 3 Department of Mathematical Sciences, University of Copenaghen, Universitetsparken 5, DK-2100 Copenhagen, Denmark; [email protected] * Correspondence: [email protected] Abstract: Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen. Keywords: fisher information; operator monotone functions; matrix means; quantum Fisher infor- mation; metric adjusted skew information; local quantum uncertainty; interferometric power 1. Introduction Citation: Gibilisco, P.; Girolami, D.; Hansen, F. A Unified Approach to One of the key traits of many-body quantum systems is that the full knowledge Local Quantum Uncertainty and of their global configurations does not imply full knowledge of their constituents. The Interferometric Power by Metric impossibility of reconstructing the local wave functions jy1i, jy2i (pure states) of two Adjusted Skew Information. Entropy interacting quantum particles from the wave function of the whole system, jy12i 6= jy1i ⊗ 2021, 23, 263. https://doi.org/ jy2i, is due to the existence of entanglement [1]. Investigating open quantum systems, 10.3390/23030263 whose (mixed) states are described by density matrices r12 = ∑i pijyii12hyij, revealed that the boundary between the classical and quantum worlds is more blurred than we thought.
    [Show full text]