Geometric quantum discord with Bures distance: the qubit case

Spehner, Dominique; Orszag, Miguel

doi:10.1088/1751-8113/47/3/035302

Cited by 49 publications

(76 citation statements)

References 41 publications

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“…(45), that satisfy all of the five Requirements of Section 3.1 [35,27,127,128,129]. Indeed, D Bu is contractive, and for pure states |ψ AB it holds that…”

Section: Bures Distancementioning

confidence: 99%

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Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

370

416

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Abstract. Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations in composite states. We focus on various approaches to define and quantify general quantum correlations, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

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“…(45), that satisfy all of the five Requirements of Section 3.1 [35,27,127,128,129]. Indeed, D Bu is contractive, and for pure states |ψ AB it holds that…”

Section: Bures Distancementioning

confidence: 99%

“…An operational interpretation of Q G Bu A (ρ AB ) can be provided in terms of the optimal success probability of an ambiguous quantum state discrimination task [127], as discussed later in Section 4.2.2. Closed formulae for Q G Bu A (ρ AB ) have been supplied for Bell diagonal states of two qubits [27,128].…”

Section: Bures Distancementioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

370

416

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“…We adopt in this work three forms of the distance-based measures of GQDs [34][35][36][37][38][39][40][41][42]. They are defined via the minimal distance from ρ to Ω 0 , i.e.,…”

Section: Distanced-based Measures Of the Gqdsmentioning

confidence: 99%

“…They are all well defined and can avoid the problem for the GQD based on the Frobenius norm [43]. We concentrate in the following on a bipartite system AB described by the density operator ρ, and the three GQDs are defined respectively via the trace distance [34][35][36][37], the Hellinger distance [38,39], and the Bures distance [40][41][42]. To facilitate later description, we call them the TDD, HDD, and BDD for brevity.…”

Section: Distanced-based Measures Of the Gqdsmentioning

confidence: 99%

Sudden change of geometric quantum discord in finite temperature reservoirs

Sun

2015

Annals of Physics

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We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively.

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“…How many kinds of quantum correlation and how to characterize them are therefore quite fundamental questions. Entanglement and discord, as two kinds of quantum correlation, drawing strong attention, have been intensively studied, and still in active research (for examples see [3,4,5,6]). …”

Section: Introductionmentioning

confidence: 99%