Gaussian Geometric Discord

Adesso, Gerardo; Girolami, Davide

doi:10.1142/s0219749911008192

Cited by 55 publications

(64 citation statements)

References 35 publications

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“…(7) with the restriction that the measurement of A is a general single-mode Gaussian POVM (Adesso and Datta, 2010;. These measurements are all executable using linear optics and homodyne detection (Giedke and Cirac, 2002).…”

Section: H Continuous-variable Discordmentioning

confidence: 99%

The classical-quantum boundary for correlations: Discord and related measures

et al. 2012

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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 correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations 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 correlations, 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 identify and quantify the deviation from classicality in various quantuminformation-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.

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Section: H Continuous-variable Discordmentioning

confidence: 99%

The classical-quantum boundary for correlations: Discord and related measures

et al. 2012

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“…We also have investigated the CV geometric discord [19], comparing the Gaussian and non-Gaussian cases. We have shown that the behavior of geometric discord is completely different from that of quantum discord.…”

Section: Discussionmentioning

confidence: 99%

“…Clearly D G = 0 iff D = 0, since both measures vanish on the set of classically correlated states. In particular, it has been be proven that D G can be seen a measure of the discrepancy between a state before and after a local measurement on subsystem B [34]: Analogous to the case of Gaussian discord, a Gaussian version of the geometric discord can be defined by restricting to Gaussian measurements [19]. Again, it can be analytically computed for two-mode Gaussian states.…”

Section: Geometric Discordmentioning

confidence: 99%

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Quantum discord for Gaussian states with non-Gaussian measurements

2012

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In recent years the paradigm based on entanglement as the unique measure of quantum correlations has been challenged by the rise of new correlation concepts, such as quantum discord, able to reveal quantum correlations that are present in separable states. It is in general difficult to compute quantum discord, because it involves a minimization over all possible local measurements in a bipartition. In the realm of continuous variable (CV) systems, a Gaussian version of quantum discord has been put forward upon restricting to Gaussian measurements. It is natural to ask whether non-Gaussian measurements can lead to a stronger minimization than Gaussian ones. Here we focus on two relevant classes of two-mode Gaussian states: squeezed thermal states (STS) and mixed thermal states (MTS), and allow for a range of experimentally feasible non-Gaussian measurements, comparing the results with the case of Gaussian measurements. We provide evidence that Gaussian measurements are optimal for Gaussian states.

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“…When applied to two-mode Gaussian states in Refs. [27,28], the definition (1.2) was modified by allowing general local measurements (POVMs).…”

Section: Introductionmentioning

confidence: 99%

Hellinger distance as a measure of Gaussian discord

Marian¹,

Marian²

2015

J. Phys. A: Math. Theor.

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Abstract. Especially investigated in recent years, the Gaussian discord can tentatively be quantified by a distance between a given two-mode Gaussian state and the set of all the zero-discord two-mode Gaussian states. However, as this set consists only of product states, such a distance captures all the correlations (quantum and classical) between modes. Therefore it is merely un upper bound for the geometric discord, no matter which is the employed distance. In this work we choose for this purpose the Hellinger metric that is known to have many beneficial properties recommending it as a good measure of quantum behaviour. In general, this metric is determined by affinity, a relative of the Uhlmann fidelity with which it shares many important features. As a first step of our work, the affinity of a pair of n-mode Gaussian states is written. Then, in the two-mode case, we succeeded in determining exactly the closest Gaussian product state and computed the Gaussian discord accordingly. The obtained general formula is remarkably simple and becomes still friendlier in the significant case of symmetric two-mode Gaussian states. We then analyze in detail two special classes of two-mode Gaussian states of theoretical and experimental interest as well: the squeezed thermal states and the mode-mixed thermal ones. The former are separable under a well-known threshold of squeezing, while the latter are always separable. It is worth stressing that for symmetric states belonging to either of these classes, we find consistency between their geometric Hellinger discord and the originally defined discord in the Gaussian approach. At the same time, the Gaussian Hellinger discord of such a state turns out to be a reliable measure of the total amount of its cross correlations.

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Gaussian Geometric Discord

Cited by 55 publications

References 35 publications

The classical-quantum boundary for correlations: Discord and related measures

The classical-quantum boundary for correlations: Discord and related measures

Quantum discord for Gaussian states with non-Gaussian measurements

Hellinger distance as a measure of Gaussian discord

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