Geometric quantum discord with Bures distance

Spehner, Dominique; Orszag, Miguel

doi:10.1088/1367-2630/15/10/103001

Cited by 116 publications

(177 citation statements)

References 52 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%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

386

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%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

386

416

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“…Most importantly for the aims of the present paper, the QIP is a monotonically decreasing function under the action of arbitrary local CPTP maps on the system a [39,40]. Furthermore, the QIP can be interpreted as the minimal global speed of evolution for the state ρ ab under all local unitary transformations on the ancilla b, as a consequence of the connection between the quantum Fisher information and the Bures metric [40,48,49].…”

Section: A Quantum Interferometric Powermentioning

confidence: 99%

Characterizing non-Markovianity via quantum interferometric power

2015

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Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamiołkowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.

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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%

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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Geometric quantum discord with Bures distance

Cited by 116 publications

References 52 publications

Measures and applications of quantum correlations

Measures and applications of quantum correlations

Characterizing non-Markovianity via quantum interferometric power

Sudden change of geometric quantum discord in finite temperature reservoirs

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