Tight lower bound to the geometric measure of quantum discord

Hassan, Ali Saif M.; Lari, Behzad; Joag, Pramod S.

doi:10.1103/physreva.85.024302

Cited by 85 publications

(78 citation statements)

References 51 publications

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“…A (ρ AB ) have been carried out [103,104,105,106] and lower bounds provided [107,108,109]. The two-sided quantifier Q G 2 AB was defined in [110].…”

Section: Geometric Measuresmentioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

388

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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“…A (ρ AB ) have been carried out [103,104,105,106] and lower bounds provided [107,108,109]. The two-sided quantifier Q G 2 AB was defined in [110].…”

Section: Geometric Measuresmentioning

confidence: 99%

Measures and applications of quantum correlations

Adesso¹,

Bromley²,

Cianciaruso³

2016

J. Phys. A: Math. Theor.

388

416

View full text Add to dashboard Cite

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“…Following the treatment method in [4], the authors of Ref. [35] and [36] derived a tight lower bound to the geometric discord of arbitrary m ⊗ n states…”

Section: Notations and Definitionsmentioning

confidence: 99%

Quantum discord in quantum random access codes and its connection to dimension witnesses

Yao

Zou

et al. 2012

Phys. Rev. A

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We exploit quantum discord (and geometric discord) to detect quantum correlations present in a well-known communication model called quantum random access codes (QRACs), which has a variety of applications in quantum information theory. In spite of the fact that there is no entanglement between the two parts involved in this model, analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be regarded as a figure of merit to characterize the quantum feature of QRACs, since this model has no classical counterparts. To gain further insight, we also investigate the dynamical behavior of quantum discord under some specific state rotations. In two-state case, the connection between quantum discord and dimension witness is graphically discussed and intriguingly our results illustrate that these two quantities are monotonically related to each other. For state encodings in real |0 − |1 plane, we derive an explicit analytical expression of the geometric discord and find that geometric discord reaches the maximal value for the optimal encoding strategy. However, for arbitrary state encodings in Bloch sphere, our numerical simulations reveal that maximal geometric discord could not coincide with optimal 2 → 1 QRAC.

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“…To characterize the quantum correlations in the system we use the geometric quantum discord measure [32][33][34][35], which is easier to obtain instead of original quantum discord measure (which involves an optimization procedure [36]), and it has been proved to be a necessary and sufficient condition for non-zero quantum discord [32].…”

Section: E Geometric Quantum Discordmentioning

confidence: 99%

“…Additionally, the lower bound of the GQD is calculated using the density operator, which is defined on a bipartite system (belonging to H a ⊗ H b , with dim H a = m and dim H b = n) [32][33][34][35] as: …”

Section: E Geometric Quantum Discordmentioning

confidence: 99%

Bath-induced correlations in an infinite-dimensional Hilbert space

Nizama

Cáceres

2017

Eur. Phys. J. B

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Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T > 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

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Tight lower bound to the geometric measure of quantum discord

Cited by 85 publications

References 51 publications

Measures and applications of quantum correlations

Measures and applications of quantum correlations

Quantum discord in quantum random access codes and its connection to dimension witnesses

Bath-induced correlations in an infinite-dimensional Hilbert space

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