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arXiv:1207.7226 · Physical Review A

Operational meaning of discord in terms of teleportation fidelity

Satyabrata Adhikari, Subhashish Banerjee

Published Dec 14, 2012• 29 citations
arXivHTMLPDF

Abstract

Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of nonclassical correlations of an arbitrary quantum system based on its minimal distance from the set of classical states, in terms of teleportation fidelity for general two-qubit and ($d\ensuremath{\bigotimes}d$)-dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two-qubit state must violate Bell's inequality. This is illustrated by an open-system model of a dissipative two-qubit state. For the ($d\ensuremath{\bigotimes}d$)-dimensional states the lower bound of discord is shown to be obtainable from an experimentally measurable witness operator.

DOI
10.1103/physreva.86.062313

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Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of nonclassical correlations of an arbitrary quantum system based on its minimal distance from the set of classical states, in terms of teleportation fidelity for general two-qubit and (d\ensuremath⨂dd\ensuremath{\bigotimes}dd\ensuremath⨂d)-dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two-qubit state must violate Bell's inequality. This is illustrated by an open-system model of a dissipative two-qubit state. For the (d\ensuremath⨂dd\ensuremath{\bigotimes}dd\ensuremath⨂d)-dimensional states the lower bound of discord is shown to be obtainable from an experimentally measurable witness operator.
Abstract Quantum teleportation fundamentally depends on shared quantum correlations between spatially separated parties. Although entanglement is widely recognized as the primary resource enabling teleportation, quantum discord represents a more general form of nonclassical correlations that can persist even when entanglement is absent. We provide a thorough analysis combining analytical and numerical evaluations of quantum discord, negativity, and concurrence across varying noise parameters. The study includes simulations under both ide-alized and realistic noisy conditions, incorporating depolarizing noise models alongside experimentally relevant constraints. To improve quantum fidelity and accurately characterize quantum correlations in noisy environments, advanced error mitigation techniques—such as measurement error correction and zero-noise extrapolation—are applied. In this study, we focus on teleportation protocols utilizing two-qubit Werner states, which constitute a significant class of noisy mixed states modeling imperfect entanglement. We systematically examine how the teleportation fidelity varies as a function of the Werner mixing parameter λ and investigate its relationship with the corresponding quantum discord. Our findings indicate that quantum discord remains strictly greater than zero even in parameter regions where entanglement vanishes, emphasizing the role of discord in sustaining quantum advantages in teleportation schemes exposed to noise and imperfections. This highlights the importance of considering non-entanglement quantum correlations for a comprehensive understanding of teleportation resources in realistic settings.
We study quantum teleportation via Bell-diagonal mixed states of two qubits in the context of the intrinsic properties of the quantum discord. We show that when the quantum-correlated state of the two qubits is used for quantum teleportation, the character of the teleportation efficiency changes substantially depending on the Bell-diagonal-state parameters, which can be seen when the worst-case-scenario or best-case-scenario fidelity is studied. Depending on the parameter range, one of two types of single-qubit states is hardest/easiest to teleport. The transition between these two parameter ranges coincides exactly with the transition between the range of classical correlation decay and quantum correlation decay characteristic for the evolution of the quantum discord. The correspondence provides a physical interpretation for the prominent feature of the decay of the quantum discord.
Two-qubit X-state is a large class of quantum states which plays an important role in the quantification and dynamical study of quantum correlations. However, the corresponding quantification of quantum discord is still missing for bona fide discord measures, like original quantum discord, Bures distance of discord, and relative entropy of discord. In this paper, we consider the calculation of Bures distance of discord, which is a kind of correlation satisfying all criteria of a discord measure, for two-qubit X-states. Firstly, we derive an explicit expression for Bures distance of discord for a kind of five-parameters family of states. Moreover, for general two-qubit X-states, we not only calculate the Bures distance of discord for a subset of two-qubit X-states by classifying and analyzing the optimal local measurements and the optimal projection operators but also provide an analytic upper bound for the entirety.
The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.
We extend the geometric measure of quantum discord, introduced and computed for two-qubit states, to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.
By considering an arbitrary two-qubit state, it is shown that the Fisher information is intrinsically linked to the geometric discord which allows a measure for quantum correlations beyond entanglement. The complex amplitude of oscillations of the probability density function is upper bounded by the geometric discord which subsequently results in the Fisher information being bounded by the geometric discord. This gives an experimental observable which can be used to quantify quantum correlations beyond entanglement. This observable can be used to witness quantum correlations in an interferometry experiment, and provide another avenue for quantum technologies to continue to develop.