Operational meaning of discord in terms of teleportation fidelity (original) (raw)
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The classical-quantum boundary for correlations: Discord and related measures
Reviews of Modern Physics, 2012
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 the correlations are amongst the most actively-studied topics of quantum information theory in the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior. Thus distinguishing quantum correlation other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half we review the mathematical properties of the measures of quantum correlation, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures quantum correlation identify and quantify the deviation from classicality in various quantum information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
The upper bound and continuity of quantum discord
Journal of Physics A: Mathematical and Theoretical, 2011
Quantum discord is viewed as the measure of quantum correlation which can be nonzero even when entanglement in the system is zero. We study two properties of quantum discord: the upper bound and the continuity. We prove the upper bound of quantum discord in terms of the coherent information for any quantum state and discuss the condition for the reachable upper bound. If two states are close to each other, then we find that quantum discord has little change and provides a bound with respect to this small change.
Theoretical and experimental aspects of quantum discord and related measures
2011
Correlations are a very important tool in the study of multipartite systems, both for classical and quantum ones. The discussion about the quantum nature of correlations permeates Physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Here we provide a short review about the quantum nature of correlations, discussing both its theoretical and experimental aspects. We focus on quantum discord and related measures. After discussing their fundamental aspects (theoretically and experimentally), we proceed by analysing the dynamical behaviour of correlations under decoherence as well as some applications in different scenarios, such as quantum computation and relativity, passing through critical and biological systems.
Quantum discord from system–environment correlations
Physica Scripta, 2014
In an initially uncorrelated mixed separable bi-partite system, quantum correlations can emerge under the action of a local measurement or local noise [1]. We analyze this counter-intuitive phenomenon using quantum discord as a quantifier. We then relate changes in quantum discord to system-environment correlations between the system in a mixed state and some purifying environmental mode using the Koashi-Winter inequality. On this basis, we suggest an interpretation of discord as a byproduct of transferring entanglement and correlations around the different subsystems of a global pure state.
Physical Review A, 2011
Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier [1] introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers exponential speed up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy, and identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
Comparison of different measures for quantum discord under non-Markovian noise
Journal of Physics A: Mathematical and Theoretical, 2011
Two measures for quantum correlations were proposed recently from a geometric perspective [Phys. Rev. Lett. 104, 080501 (2010); e-print arXiv:1004.0190]. We prove the the equivalence of the two geometric measures with respect to Bell-diagonal states, and demonstrate the similarities and differences for quantum correlation using the geometry-based measure and mutual-informationbased measure. Our study on critical point of sudden transition might be useful for keeping long time quantum correlation under decoherence.
Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. [Nature Phys. 6, 659 (2010)] have shown that the lower bound on the uncertainties of the measurement outcomes depends on the correlations between the observed system and an observer who possesses a quantum memory. If the system is maximally entangled with its memory, the outcomes of two incompatible measurements made on the system can be predicted precisely. Here, we obtain an uncertainty relation that tightens the lower bound of Berta et al. by incorporating an additional term that depends on the quantum discord and the classical correlations of the joint state of the observed system and the quantum memory. We discuss several examples of states for which our lower bound is tighter than the bound of Berta et al. On the application side, we discuss the relevance of our inequality for the security of quantum key distribution and show that it can be used to provide bounds on the distillable common randomness and the entanglement of formation of bipartite quantum states.
Quantum discord for a two-parameter class of states in 2⊗ d quantum systems
Journal of Physics A: Mathematical and Theoretical, 2010
Quantum discord witnesses the nonclassicality of quantum states even when there is no entanglement in these quantum states. This type of quantum correlation also has some interesting and significant applications in quantum information processing. Quantum discord has been evaluated explicitly only for certain class of two-qubit states. We extend the previous studies to 2 ⊗ d quantum systems and derive an analytical expression for quantum discord for a two-parameter class of states for d ≥ 3. We compare quantum discord, classical correlation, and entanglement for qubit-qutrit systems to demonstrate that different measures of quantum correlation are not identical and conceptually different.
Equivalence regimes for geometric quantum discord and local quantum uncertainty
Physical Review A, 2021
The concept of quantum discord aims at unveiling quantum correlations that go beyond those described by entanglement. Its original formulation [J. Phys. A 34, 6899 (2001); Phys. Rev. Lett 88, 017901 (2002)] is difficult to compute even for the simplest case of two-qubits systems. Alternative formulations have been developed to address this drawback, such as the geometric measure of quantum discord [Phys. Rev. A 87, 062303 (2013)] and the local quantum uncertainty [Phys. Rev. Lett 110, 240402 (2013)] that can be evaluated in closed form for some quantum systems, such as two-qubit systems. We show here that these two measures of quantum discord are equivalent for 2 × D dimensional bipartite quantum systems. By considering the relevant example of N00N states for phase estimation in lossy environments, we also show that both metrics of quantum discord quantify the decrease of quantum Fisher information of the phase estimation protocol. Given their ease of computation in 2 × D bipartite systems, the geometric measure of quantum discord and the local quantum uncertainty demonstrate their relevance as computable measures of quantum discord.
Linking Quantum Discord to Entanglement in a Measurement
Physical Review Letters, 2011
We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement, that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system. PACS numbers: 03.65.Ta, 03.67.Mn