ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 08 Dec 2019 12:07:25 GMT2019-12-08T12:07:25Z50231- Observing the operational significance of discord consumptionhttps://scholarbank.nus.edu.sg/handle/10635/116489Title: Observing the operational significance of discord consumption
Authors: Gu, M.; Chrzanowski, H.M.; Assad, S.M.; Symul, T.; Modi, K.; Ralph, T.C.; Vedral, V.; Lam, P.K.
Abstract: Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this quantum advantage'. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. No entanglement exists at any point of this experiment. Thus we introduce and demonstrate an operational method to use discord as a physical resource. © 2012 Macmillan Publishers Limited. All rights reserved.
Sat, 01 Sep 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1164892012-09-01T00:00:00Z
- Unified view of quantum and classical correlationshttps://scholarbank.nus.edu.sg/handle/10635/116020Title: Unified view of quantum and classical correlations
Authors: Modi, K.; Paterek, T.; Son, W.; Vedral, V.; Williamson, M.
Abstract: We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states. © 2010 The American Physical Society.
Mon, 22 Feb 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1160202010-02-22T00:00:00Z
- The classical-quantum boundary for correlations: Discord and related measureshttps://scholarbank.nus.edu.sg/handle/10635/116627Title: The classical-quantum boundary for correlations: Discord and related measures
Authors: Modi, K.; Brodutch, A.; Cable, H.; Paterek, T.; Vedral, V.
Abstract: One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information- processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones. © 2012 American Physical Society.
Mon, 26 Nov 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1166272012-11-26T00:00:00Z
- Unification of witnessing initial system-environment correlations and witnessing non-Markovianityhttps://scholarbank.nus.edu.sg/handle/10635/116669Title: Unification of witnessing initial system-environment correlations and witnessing non-Markovianity
Authors: Rodríguez-Rosario, C.A.; Modi, K.; Mazzola, L.; Aspuru-Guzik, A.
Abstract: We show the connection between a witness that detects dynamical maps with initial system-environment correlations and a witness that detects non-Markovian open quantum systems. Our analysis is based on studying the role that state preparation plays in witnessing violations of contractivity of open-quantum-system dynamics. Contractivity is a property of some quantum processes where the trace distance of density matrices decrease with time. From this, we show how a witness of initial correlations is an upper bound to a witness of non-Markovianity. We discuss how this relationship shows further connections between initial system-environment correlations and non-Markovianity, at an instance of time, in open quantum systems. Copyright © EPLA, 2012.
Sun, 01 Jul 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1166692012-07-01T00:00:00Z
- Linear assignment maps for correlated system-environment stateshttps://scholarbank.nus.edu.sg/handle/10635/112457Title: Linear assignment maps for correlated system-environment states
Authors: Rodríguez-Rosario, C.A.; Modi, K.; Aspuru-Guzik, A.
Abstract: Assignment maps are mathematical operators that describe initial system-environment states for open quantum systems. We re-examine the notion of assignments that account for correlations between the system and the environment and show that these maps can be made linear at the expense of giving up positivity or consistency of the map. We study the role of positivity and consistency of the map and show the effects of relaxing these. Finally, we establish a connection between the violation of the positivity of linear assignments and the no-broadcasting theorem. © 2010 The American Physical Society.
Wed, 20 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124572010-01-20T00:00:00Z
- Positivity in the presence of initial system-environment correlationhttps://scholarbank.nus.edu.sg/handle/10635/112485Title: Positivity in the presence of initial system-environment correlation
Authors: Modi, K.; Rodríguez-Rosario, C.A.; Aspuru-Guzik, A.
Abstract: The constraints imposed by the initial system-environment correlation can lead to nonpositive dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models. © 2012 American Physical Society.
Wed, 12 Dec 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124852012-12-12T00:00:00Z
- Quantum Correlations in Mixed-State Metrologyhttps://scholarbank.nus.edu.sg/handle/10635/116547Title: Quantum Correlations in Mixed-State Metrology
Authors: Modi, K.; Cable, H.; Williamson, M.; Vedral, V.
Abstract: We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated single-qubit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits) and time (number of gates) requirements, we introduce mixedness as a key constraint of the experiment.We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives ffiffiffiffi N p enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1165472011-01-01T00:00:00Z
- Vanishing quantum discord is not necessary for completely positive mapshttps://scholarbank.nus.edu.sg/handle/10635/116673Title: Vanishing quantum discord is not necessary for completely positive maps
Authors: Brodutch, A.; Datta, A.; Modi, K.; Rivas, A.; Rodríguez-Rosario, C.A.
Abstract: The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment state. We reexamine the connections between complete positivity and quantum discord within two different sets of assumptions about the relevant family of initial states. We present an example of a system-environment state with nonvanishing quantum discord that leads to a completely positive map. This invalidates an earlier claim about the necessity of vanishing quantum discord for completely positive maps. In our final remarks, we discuss the physical validity of each approach. © 2013 American Physical Society.
Mon, 01 Apr 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1166732013-04-01T00:00:00Z
- Dynamical role of system-environment correlations in non-Markovian dynamicshttps://scholarbank.nus.edu.sg/handle/10635/112422Title: Dynamical role of system-environment correlations in non-Markovian dynamics
Authors: Mazzola, L.; Rodríguez-Rosario, C.A.; Modi, K.; Paternostro, M.
Abstract: We analyze the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer, we unveil a fundamental connection between non-Markovian behavior and dynamics of system-environment correlations. We derive an upper bound to the rate of change of the distinguishability between different states of the system that explicitly depends on the establishment of correlations between system and environment. We illustrate our results using a fully solvable spin-chain model, which allows us to gain insight into the mechanisms triggering non-Markovian evolution. © 2012 American Physical Society.
Mon, 30 Jul 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124222012-07-30T00:00:00Z
- Relation between nonlocality and contextuality for a biphotonhttps://scholarbank.nus.edu.sg/handle/10635/53134Title: Relation between nonlocality and contextuality for a biphoton
Authors: Soeda, A.; Kurzyński, P.; Ramanathan, R.; Modi, K.; Kaszlikowski, D.
Abstract: We investigate the set of qutrit states in terms of symmetric states of two qubits that violate the minimal contextual inequality, namely the Klyachko-Can-Binicoglu-Shumovsky (KCBS) inequality. The physical system that provides a natural framework for this problem is a biphoton, which consists of two photons in the same spatiotemporal mode and whose effective polarization behaves as a three-level quantum system. The relationship between the KCBS contextual inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality is investigated. We find that every biphotonic state that is contextual with respect to KCBS is nonlocal as per the CHSH test when the two photons are apart, but the converse is not true. © 2013 American Physical Society.
Mon, 25 Feb 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/531342013-02-25T00:00:00Z
- Operational approach to open dynamics and quantifying initial correlationshttps://scholarbank.nus.edu.sg/handle/10635/112477Title: Operational approach to open dynamics and quantifying initial correlations
Authors: Modi, K.
Abstract: A central aim of physics is to describe the dynamics of physical systems. Schrödinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most general form, has proved to be difficult because the dynamics is dependent on the state of the environment and the correlations with it. For discrete processes, such as quantum gates or chemical reactions, quantum process tomography provides the complete description of the dynamics, provided that the initial states of the system and the environment are independent of each other. However, many physical systems are correlated with the environment at the beginning of the experiment. Here, we give a prescription of quantum process tomography that yields the complete description of the dynamics of the system even when the initial correlations are present. Surprisingly, our method also gives quantitative expressions for the initial correlation.
Sun, 01 Jan 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124772012-01-01T00:00:00Z
- Classical to quantum in large-number limithttps://scholarbank.nus.edu.sg/handle/10635/116260Title: Classical to quantum in large-number limit
Authors: Modi, K.; Fazio, R.; Pascazio, S.; Vedral, V.; Yuasa, K.
Abstract: We construct a quantumness witness following the work of Alicki & van Ryn (AvR). We reformulate the AvR test by defining it for quantum states rather than for observables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness, the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that, in the large-number limit, quantum systems become classical, whereas the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. However, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large-number limit that resembles nuclear magnetic resonance (NMR) systems. We make several conclusions about detecting quantumness in NMR-like systems. © 2012 The Royal Society.
Sat, 13 Oct 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1162602012-10-13T00:00:00Z
- Unification of quantum and classical correlations and quantumness measureshttps://scholarbank.nus.edu.sg/handle/10635/116800Title: Unification of quantum and classical correlations and quantumness measures
Authors: Modi, K.; Vedral, V.
Abstract: We give a pedagogical introduction to quantum discord and discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy. This allows us to put all correlations on an equal footing. Entanglement and dissonance jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We finally show, using relative entropy, how different notions of quantum correlations are related to each other. This gives a single theory that incorporates all correlations, quantum and classical, and different methods of quantifying them. © 2011 American Institute of Physics.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1168002011-01-01T00:00:00Z
- Role of preparation in quantum process tomographyhttps://scholarbank.nus.edu.sg/handle/10635/115919Title: Role of preparation in quantum process tomography
Authors: Modi, K.; Sudarshan, E.C.G.
Abstract: It was recently pointed out how differences in preparation procedures for quantum experiments can lead to nontrivial differences in the results of the experiment. The differences arise from the initial correlations between the system and the environment. Therefore, any quantum experiment that is prone to influences from the environment must be prepared carefully. We study quantum-process tomography in light of this. We suggest several experimental setups, where preparation of the initial state plays a role in the final outcome of the experiment. By studying the linearity and the positivity of the resulting maps, the experimenter can determine the nature of the initial correlations between the system and the environment. © 2010 The American Physical Society.
Thu, 27 May 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159192010-05-27T00:00:00Z
- Detecting multipartite classical states and their resemblanceshttps://scholarbank.nus.edu.sg/handle/10635/112414Title: Detecting multipartite classical states and their resemblances
Authors: Chen, L.; Chitambar, E.; Modi, K.; Vacanti, G.
Abstract: We study various types of multipartite states lying near the quantum-classical boundary. The so-called classical states are precisely those in which each party can perfectly identify a locally held state without disturbing the global state, a task known as nondisruptive local state identification (NDLID). We show NDLID to be closely related local broadcasting, and we introduce a class of states called generalized classical states which allow for both NDLID and multipartite broadcasting when the most general quantum measurements are permitted. Simple analytical methods and a physical criterion are given for detecting whether a multipartite state is classical or generalized classical. For deciding the latter, a semidefinite programming algorithm is presented which may find use in other fields such as signal processing. © 2011 American Physical Society.
Tue, 15 Feb 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124142011-02-15T00:00:00Z
- Preparation of states in open quantum mechanicshttps://scholarbank.nus.edu.sg/handle/10635/116535Title: Preparation of states in open quantum mechanics
Authors: Modi, K.
Abstract: We study preparation of states for open quantum mechanics. For non-Markovian systems that are initially correlated with the environment, the effects of the preparation procedure are nontrivial. This is due to the indirect effects on the state of the environment induced via the correlations with the system and the act of preparation on the system. We give three concrete examples of preparation procedure to elucidate our claims. © 2011 World Scientific Publishing Company.
Thu, 01 Sep 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1165352011-09-01T00:00:00Z
- Coherent and incoherent contents of correlationshttps://scholarbank.nus.edu.sg/handle/10635/116265Title: Coherent and incoherent contents of correlations
Authors: Modi, K.; Gu, M.
Abstract: We examine bipartite and multipartite correlations within the construct of unitary orbits. We show that the set of product states is a very small subset of set of all possible states, while all unitary orbits contain classically correlated states. Using this we give meaning to degeneration of quantum correlations due to a unitary interactions, which we call coherent correlations. The remaining classical correlations are called incoherent correlations and quantified in terms of the distance of the joint probability distributions to its marginals. Finally, we look at how entanglement looks in this picture for the two-qubit case. © 2013 World Scientific Publishing Company.
Wed, 30 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1162652013-01-30T00:00:00Z
- Operational interpretations of quantum discordhttps://scholarbank.nus.edu.sg/handle/10635/112478Title: Operational interpretations of quantum discord
Authors: Cavalcanti, D.; Aolita, L.; Boixo, S.; Modi, K.; Piani, M.; Winter, A.
Abstract: Quantum discord quantifies nonclassical correlations beyond the standard classification of quantum states into entangled and unentangled. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first information-theoretic operational meaning in terms of entanglement consumption in an extended quantum-state-merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding. © 2011 American Physical Society.
Thu, 31 Mar 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124782011-03-31T00:00:00Z
- Quantum discord bounds the amount of distributed entanglementhttps://scholarbank.nus.edu.sg/handle/10635/116548Title: Quantum discord bounds the amount of distributed entanglement
Authors: Chuan, T.K.; Maillard, J.; Modi, K.; Paterek, T.; Paternostro, M.; Piani, M.
Abstract: The ability to distribute quantum entanglement is a prerequisite for many fundamental tests of quantum theory and numerous quantum information protocols. Two distant parties can increase the amount of entanglement between them by means of quantum communication encoded in a carrier that is sent from one party to the other. Intriguingly, entanglement can be increased even when the exchanged carrier is not entangled with the parties. However, in light of the defining property of entanglement stating that it cannot increase under classical communication, the carrier must be quantum. Here we show that, in general, the increase of relative entropy of entanglement between two remote parties is bounded by the amount of nonclassical correlations of the carrier with the parties as quantified by the relative entropy of discord. We study implications of this bound, provide new examples of entanglement distribution via unentangled states, and put further limits on this phenomenon. © 2012 American Physical Society.
Thu, 16 Aug 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1165482012-08-16T00:00:00Z
- Witnessing the quantumness of a single system: From anticommutators to interference and discordhttps://scholarbank.nus.edu.sg/handle/10635/116674Title: Witnessing the quantumness of a single system: From anticommutators to interference and discord
Authors: Fazio, R.; Modi, K.; Pascazio, S.; Vedral, V.; Yuasa, K.
Abstract: We introduce a method to witness the quantumness of a system. The method relies on the fact that the anticommutator of two classical states is always positive. By contrast, we show that there is always a nonpositive anticommutator due to any two quantum states. We notice that interference depends on the trace of the anticommutator of two states, and it is therefore operationally more suitable to detect quantumness by looking at anticommutators of states rather than their commutators. © 2013 American Physical Society.
Thu, 23 May 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1166742013-05-23T00:00:00Z
- Quantum locking of classical correlations and quantum discord of classical-quantum stateshttps://scholarbank.nus.edu.sg/handle/10635/116552Title: Quantum locking of classical correlations and quantum discord of classical-quantum states
Authors: Boixo, S.; Aolita, L.; Cavalcanti, D.; Modi, K.; Winter, A.
Abstract: A locking protocol between two parties is as follows: Alice gives an encrypted classical message to Bob which she does not want Bob to be able to read until she gives him the key. If Alice is using classical resources, and she wants to approach unconditional security, then the key and the message must have comparable sizes. But if Alice prepares a quantum state, the size of the key can be comparatively negligible. This effect is called quantum locking. Entanglement does not play a role in this quantum advantage. We show that, in this scenario, the quantum discord quantifies the advantage of the quantum protocol over the corresponding classical one for any classical-quantum state. © 2011 World Scientific Publishing Company.
Sat, 01 Oct 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1165522011-10-01T00:00:00Z
- Operational significance of discord consumptionhttps://scholarbank.nus.edu.sg/handle/10635/116766Title: Operational significance of discord consumption
Authors: Symul, T.; Chrzanowski, H.M.; Assad, S.; Lam, P.K.; Ralph, T.C.; Gu, M.; Modi, K.; Vedral, V.
Abstract: For many years, the notion of quantum correlations was equated with the notion of quantum entanglement. The wide range of quantum protocols whose extra-powers over classical protocol were shown to originate from quantum entanglement mostly motivated this. For example, it was shown that for certain class of problems, a quantum computer could provide exponential speed-up over its classical counterpart, given that it relied on quantum entangled resources. Recently, however, the requirement of possessing entanglement to perform efficient quantum computation has been questioned both theoretically [1] and experimentally [2]. It appears that a non-classical quantity called quantum discord [3] is all that is required. © 2013 IEEE.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1167662013-01-01T00:00:00Z
- Criteria for measures of quantum correlationshttps://scholarbank.nus.edu.sg/handle/10635/115048Title: Criteria for measures of quantum correlations
Authors: Brodutch, A.; Modi, K.
Abstract: Entanglement does not describe all quantum correlations and several authors have shown the need to go beyond entanglement when dealing with mixed states. Various different measures have sprung up in the literature, for a variety of reasons, to describe bipar- tite and multipartite quantum correlations; some are known under the collective name quantum discord. Yet, in the same sprit as the criteria for entanglement measures, there is no general mechanism that determines whether a measure of quantum and classical correlations is a proper measure of correlations. This is partially due to the fact that the answer is a bit muddy. In this article we attempt tackle this muddy topic by writing down several criteria for a "good" measure of correlations. We breakup our list into necessary, reasonable, and debatable conditions. We then proceed to prove several of these conditions for generalized measures of quantum correlations. However, not all conditions are met by all measures; we show this via several examples. The reasonable conditions are related to continuity of correlations, which has not been previously discussed. Continuity is an important quality if one wants to probe quantum correlations in the laboratory. We show that most types of quantum discord are continuous but none are continuous with respect to the measurement basis used for optimization. © Rinton Press.
Sat, 01 Sep 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1150482012-09-01T00:00:00Z