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Quantum Discord has local and nonlocal quantumness

Pankaj Agrawal, Indranil Chakrabarty, Sk Sazim, Arun Kumar Pati

Published Feb 3, 2015• 1 citation
OpenAlex

Abstract

It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by quantum discord, but not by the conventional measure of entanglement. We argue that a state displays quantumness that can be of and nonlocal origin. The physical quantity such as the quantum discord probes not only the nonlocal quantumness but also the quantumness, such as the local superposition. This can be a reason why such measures are non-zero when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of quantumness, nonlocal quantumness, and classical mixedness of a state.

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It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by quantum discord, but not by the conventional measure of entanglement. We argue that a state displays quantumness that can be of and nonlocal origin. The physical quantity such as the quantum discord probes not only the nonlocal quantumness but also the quantumness, such as the local superposition. This can be a reason why such measures are non-zero when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of quantumness, nonlocal quantumness, and classical mixedness of a state.
It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by information theoretic quantities such as quantum discord, but not by the conventional measures of entanglement. We argue that a state displays quantumness, that can be of local and nonlocal origin. Information theoretic measures not only characterize the nonlocal quantumness, but also the local quantumness, such as the “local superposition”. This can be a reason, why such measures are nonzero, when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness and classical mixedness of a state.
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.
In this didactic article we explore the concept of quantum correlations beyond entanglement. We begin by introducing and motivating the classically correlated states and then showing how to quantify the quantum correlations using an entropic approach, arriving at a well known measure called the quantum discord. Quantum correlations and discord are then operationally linked with the task of local broadcasting. We conclude by providing some alternative perspectives on quantum correlations and how to measure them.
Correlations may arise in quantum systems through various means, of which the most remarkable one is quantum entanglement. Additionally, there are systems that exhibit nonclassical correlations even in the absence of entanglement. Quantum dissonance refers to how Quantum Discord (QD) — the difference between the total correlation and the classical correlation in a given quantum state — appears as a nonclassical correlation in a system without entanglement. It could be said that QD has the potential to provide a more inclusive viewpoint for discerning the nonclassical correlations. In this paper, we address the problem of manipulating the QD between two subsystems through local operations. We propose two explicit procedures for obtaining separable Werner states, a type of mixed state with nonzero QD. Both approaches involve performing local operations on classically correlated states and offers a step-by-step method for obtaining separable Werner states with nonzero discord, providing an alternative (explicit and user-friendly) to existing methods.
Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.
The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present a direct measure of quantum correlation by revealing the difference between the structures of classically and quantum correlated states. Our measure explicitly includes the contributions of the inseparability and local nonorthogonality of the eigenvectors of a density matrix. Besides its relatively easy computability, our measure can provide a unified understanding of quantum correlation of all the present versions.