Witnessed entanglement and the geometric measure of quantum discord

Debarba, Tiago; Maciel, Thiago O.; Vianna, Reinaldo O.

doi:10.1103/physreva.86.024302

Cited by 83 publications

(64 citation statements)

References 36 publications

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“…(45) [122,123,80,78,124]. Because D p is only contractive for p = 1, the trace distance based geometric measure, alias "trace distance discord", is the only one of its class that directly obeys Requirements (ii), (iv), and (v), hence emerging as the most suitable choice out of all the Schatten D p norm induced geometric measures.…”

Section: Trace Distancementioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

362

402

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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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Section: Trace Distancementioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

362

402

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“…Such disturbance could be quantified as the distance between the original state and the measured one [14,15,22,23]. In this way we define the multipartite relative entropy of quantumness [14,24]: Definition 1 (Multipartite Relative Entropy of Quantumness-MREQ).…”

Section: Quantumness Of Correlationsmentioning

confidence: 99%

“…Our own efforts in this problem started with the proposal of entanglement witnesses for systems of indistinguishable particles [10], followed by appropriate adaptations of entropy of entanglement and negativity [11]. More recently, extending the concept of quantumness of correlations [12][13][14][15] to the realm of indistinguishable particles, we introduced the concept of quantumness of correlations of indistinguishable particles [16], which allowed us to devise a measurement procedure (dubbed an activation protocol) [17,18] that determines the class * Electronic address: debarba@utfpr.edu.br † Electronic address: fernandoiemini@gmail.com of states without quantumness of correlations. In this activation protocol the quantumness of correlations of the system manifests itself as the smallest amount of bipartite entanglement created between system and measurement ancilla, during the local measurement protocol.…”

Section: Introductionmentioning

confidence: 99%

Quantumness of correlations in fermionic systems

2017

Self Cite

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We present a new approach for the quantification of quantumness of correlations in fermionic systems. We study the Multipartite Relative Entropy of Quantumness in such systems, and show how the symmetries in the states can be used to obtain analytical solutions. Numerical evidences about the uniqueness of such solutions are also presented. Supported by these results, we show that the minimization of the Multipartite Relative Entropy of Quantumness, over certain choices of its modes multipartitions, reduces to the notion of Quantumness of Indistinguishable Particles. By means of an activation protocol, we characterize the class of states without quantumness of correlations. As an example, we calculate the dynamics of quantumness of correlations for a purely dissipative system, whose stationary states exhibit interesting topological non-local correlations.

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“…Moreover, it has turned out that among all geometric quantum discords based on the Schatten p-norms [18] only geometric quantum discord based on the Schatten 1-norm is a meaningful measure of quantum correlations [17].…”

Section: Introductionmentioning

confidence: 99%

On the Brodutch and Modi method of constructing geometric measures of classical and quantum correlations

Walczak

Wintrowicz

2017

Quantum Inf Process

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Recently, Brodutch and Modi proposed a general method of constructing meaningful measures of classical and quantum correlations. We systematically apply this method to obtain geometric classical and quantum correlations based on the Bures and the trace distances for two-qubit Bell diagonal states. Moreover, we argue that in general the Brodutch and Modi method may provide non-unique results, and we show how to modify this method to avoid this issue.

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Witnessed entanglement and the geometric measure of quantum discord

Cited by 83 publications

References 36 publications

Measures and applications of quantum correlations

Measures and applications of quantum correlations

Quantumness of correlations in fermionic systems

On the Brodutch and Modi method of constructing geometric measures of classical and quantum correlations

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