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arXiv:quant-ph/0506160 · International Journal of Quantum Information

MUTUAL INFORMATION OF BIPARTITE STATES AND QUANTUM DISCORD IN TERMS OF COHERENCE INFORMATION

Fedor Herbut

Published Dec 1, 2005• 6 citations
arXivHTMLPDF

Abstract

In relation to an observable and quantum state, the entity IC from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this paper, its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogating" the global state about the state of the opposite subsystem is derived with detailed entropy and information gain discussion. The apparent disappearance of discord in measurement is investigated, and it is shown that it is actually shifted from between subsystems 1 and 2 to between subsystems 1 and (2 + 3), where 3 is the measuring instrument. Finally, it is shown that the global coherence information IC(A2, ρ12) is shifted into the global coherence information [Formula: see text] in the final state [Formula: see text] of the measurement interaction.

DOI
10.1142/s021974990500150x

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In relation to an observable and quantum state, the entity IC from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this paper, its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogating" the global state about the state of the opposite subsystem is derived with detailed entropy and information gain discussion. The apparent disappearance of discord in measurement is investigated, and it is shown that it is actually shifted from between subsystems 1 and 2 to between subsystems 1 and (2 + 3), where 3 is the measuring instrument. Finally, it is shown that the global coherence information IC(A2, ρ12) is shifted into the global coherence information [Formula: see text] in the final state [Formula: see text] of the measurement interaction.
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem.
Quantum discord, as defined by Olliver and Zurek (2002 Phys. Rev. Lett. 88 017901) as the difference of two natural quantum extensions of the classical mutual information, plays an interesting role in characterizing quantumness of correlations. Inspired by this idea, we will study quantumness of bipartite states arising from different quantum analogs of the classical conditional entropy. Our approach is intrinsic, in contrast to the Olliver–Zurek method that involves extrinsic local measurements. For this purpose, we introduce two alternative variants of quantum conditional entropies via conditional density operators, which in turn are intuitive quantum extensions of equivalent classical expressions for the conditional probability. The significance of these quantum conditional entropies in characterizing quantumness of bipartite states is illustrated through several examples.
We extend the definition of quantum discord as a quantifier of nonClassical correlations in a quantum state to the case where weak measurements are performed on subsystem AAA of a bipartite system ABABAB. The properties of weak discord are explored for several families of quantum states. We find that in many cases weak quantum discord is identical to normal discord and in general the values of the two are very close to each other. Weak quantum discord reduces to discord in the appropriate limits as well. We also discuss the implications of these observations on the interpretations of quantum discord.
A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.
Quantum discord measures the fraction of the pair-wise mutual information that is locally inaccessible in a multipartite system. Nonzero quantum discord has interesting and significant applications because although non-zero entanglement guarantees the existence of quantum correlation in a bipartite quantum system, zero entanglement does not guarantee the absence of a quantum correlation. On the other hand, many quantum optics systems can be described as deformed quantum oscillators. In this work, we investigate the quantum discord of bipartite entangled nonlinear coherent states, in the context of the so-called f-deformed coherent states algebra. To calculate the quantum discord, we consider quasi- Werner mixed states bases on bipartite entangled f-deformed coherent states. Two explicit analytic expressions are derived for the quantum discord of two different nonlinear deformed coherent states. The first one considers deformed coherent states obtained as eigenstates of the annihilation deformed operator, and the second one is obtained by using a deformed displacement operator. We compare the quantum discord of those states, when the nonlinear deformation function is either associated with the SU(1,1) coherent states in the Gilmore-Perelomov or Barut-Girardello representations, respectively.
Abstract Quantum discord captures nonclassical correlations beyond entanglement and plays a piv-otal role in quantum communication, computation, and thermodynamics. Traditionally defined via entropy-based asymmetries in mutual information, discord remains conceptually rich but operationally opaque particularly in noisy or mixed-state regimes where entanglement vanishes yet quantum advantage persists. In this work, we introduce a novel formulation of discord based on Measurement-Induced Coherence Transfer (MICT). Rather than quantifying information imbalance, MICT discord measures the coherence gained in subsystem A when a projective measurement is performed on subsystem B. This directional, coherence-centric perspective reframes discord as a physically observable transfer process, firmly grounded in the resource theory of quantum coherence. Numerical simulations on Werner states validate the framework and reveal strong basis sensitivity: computational-basis measurements yield vanishing discord, whereas Hadamard-basis measurements consistently produce maximal coherence. This sharp divergence from standard discord measures underscores the operational significance of measurement choice in coherence-aware protocols. Finally, we discuss experimental feasibility, showing that MICT discord can be estimated via standard quantum state tomography and coherence monotones. Our results position MICT discord as a practical diagnostic and a new lens for interpreting quantum correlations, with potential applications in coherence-based benchmarking, quantum thermodynamics, and noise-resilient communication protocols.