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Chinese Physics B

Quantifying coherence with dynamical discord*

Lian-Wu Yang, Yunjie Xia

Published Jul 22, 2021• 1 citation
Publisher

Abstract

Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.

DOI
10.1088/1674-1056/ac16d1

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Quantum coherence and discord are two kinds of manifestations of nonclassicality. By calculating the coherence and discord in the specific bipartite quantum systems, we show quantitative connections between the coherence and the discord in the bipartite quantum systems created from local systems with the help of incoherent operations. We show that the coherence bounds the dynamical discord, and under particular conditions of the initial quantum states, the coherence of single systems is equal to the dynamical discord. We extend these results to the multipartite quantum systems.
Coherent superposition and entanglement are two fundamental aspects of nonclassicality. Here we provide a quantitative connection between the two on the level of operations by showing that the dynamical coherence of an operation upper bounds the dynamical entanglement that can be generated from it with the help of additional incoherent operations. In case a particular choice of monotones based on the relative entropy is used for the quantification of these dynamical resources, this bound can be achieved. In addition, we show that an analog to the entanglement potential exists on the level of operations and serves as a valid quantifier for dynamical coherence.
Recent results in quantum information theory characterize quantum coherence in the context of resource theories. Here, we study the relation between quantum coherence and quantum discord, a kind of quantum correlation which appears even in nonentangled states. We prove that the creation of quantum discord with multipartite incoherent operations is bounded by the amount of quantum coherence consumed in its subsystems during the process. We show how the interplay between quantum coherence consumption and creation of quantum discord works in the preparation of multipartite quantum correlated states and in the model of deterministic quantum computation with one qubit.
Abstract Establishing quantum correlations between two remote parties by sending an information carrier is an essential step of many protocols in quantum information processing. We obtain trade-off relations between discords and coherence within a bipartite system. Then we study the distribution of coherence in a bipartite quantum state by using the relations of relative entropy and mutual information. We show that the increase of the relative entropy of discord between two remote parties is bounded by the nonclassical correlations quantified by the relative entropy of coherence between the carrier and two remote parties, providing an optimal protocol for discord distribution and showing that quantum correlations are the essential resource for such tasks.
We introduce measures of quantum coherence as the speed of evolution of a system under decoherence. That is, coherence is the ability to estimate a dephasing channel, quantified by the quantum Fisher information. We extend the analysis to interferometric noise estimation, proving that quantum discord is the minimum sensitivity to local dephasing. A physically motivated set of free operations for discord is proposed. The amount of discord created by strictly incoherent operations is upper bounded by the initial coherence.
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.