Quantum Discord for Multipartite Coherent States Interpolating Between Werner and Greenberger–horne–zeilinger States

Daoud, Mohammed; Laamara, R. Ahl

doi:10.1142/s0219749912500608

Cited by 22 publications

(20 citation statements)

References 65 publications

(86 reference statements)

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“…It is the minimum Hilbert-Schmidt distance between the given state and the zero discord state [20]. From an analytical point of view, the calculation of this geometric measure requires a simpler minimization process compared to the entropic QD [21,22]. Despite this remarkable feature, the GMQD cannot be considered as a faithful quantifier of non-classical correlations [23].…”

Section: Introductionmentioning

confidence: 99%

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

et al. 2019

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Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system [S. Kim et al., Phys. Rev. A. 97, 032326 (2018)]. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.

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Section: Introductionmentioning

confidence: 99%

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

et al. 2019

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“…The state |GHZ k (α, m) (33) has rank two reduced density matrices (37) and (38). For these two qubit states, the Koashi-Winter relation which provides the connection between the quantum discord and the entanglement of formation, can be exploited to obtain the relevant pairwise quantum correlations.…”

Section: Bipartite Measures Of Quantum Discordmentioning

confidence: 99%

“…One may quote for instance entanglement properties in GHZ (Greenberger-Horne-Zeilinger), W (Werner) states discussed in [22,23] and entangled coherent state extensions of cluster qubits investigated in [24,25,26]. To quantify quantum correlations beyond entanglement in coherent states systems, measures such as quantum discord [27,28] and its geometric variant [29] were used.Explicit results were derived for quantum discord [30,31,32,33,34,35,36,37] and geometric quantum discord [38,39,40,41] for some special sets of coherent states.On the other hand, decoherence is a crucial process to understand the emergence of classicality in quantum systems. It describes the inevitable degradation of quantum correlations due to experimental and environmental noise.…”

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confidence: 99%

Quantum Discord in Photon-Added Glauber Coherent States of GHZ-Type

Daoud

Kaydi

Hadfi

2015

Open Syst. Inf. Dyn.

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We investigate the influence of photon excitations on quantum correlations in tripartite Glauber coherent states of Greenberger-Horne-Zeilinger type. The pairwise correlations are measured by means of the entropy-based quantum discord. We also analyze the monogamy property of quantum discord in this class of tripartite states in terms of the strength of Glauber coherent states and the photon excitation order. 1In the context of information processing and transmission, several theoretical and experimental results confirm the advantages of quantum protocols compared to their classical counterparts (see for instance [1,2,3]). Quantum technology exploiting the intriguing phenomena of quantum world, such as entanglement, offers secure ways for communication [4,5] and potentially powerful algorithms in quantum computation [6]. Originally, quantum information processing focused on discrete (finitedimensional) entangled states like the polarizations of a photon or discrete levels of an atom. But, the extension from discrete to continuous variables has been also proven beneficial in coding and manipulating efficiently quantum information. Coherent states, which constitute the prototypical instance of continuous-variables states, are expected to play a central role in this context. They are appealing for their mathematical elegance (continuity and over-completion property) and closeness to classical physical states (minimization of Heisenberg uncertainty relation). Implementing a logical qubit encoding by treating entangled coherent states as qubits in a two dimensional Hilbert space has been shown a promising strategy in performing successfully various quantum tasks such as quantum teleportation [7,8], quantum computation [9, 10, 11], entanglement purification [12] and errors correction [13]. In view of these potential applications, a special attention was paid, during the last years, to the identification, characterization and quantification of quantum correlations in bipartite coherent states systems (see for instance the papers [14,15,16] and references therein). The bipartite treatment was extended to superpositions of multimode coherent states [17,18,19,20,21] which exhibit multipartite entanglement. One may quote for instance entanglement properties in GHZ (Greenberger-Horne-Zeilinger), W (Werner) states discussed in [22,23] and entangled coherent state extensions of cluster qubits investigated in [24,25,26]. To quantify quantum correlations beyond entanglement in coherent states systems, measures such as quantum discord [27,28] and its geometric variant [29] were used.Explicit results were derived for quantum discord [30,31,32,33,34,35,36,37] and geometric quantum discord [38,39,40,41] for some special sets of coherent states.On the other hand, decoherence is a crucial process to understand the emergence of classicality in quantum systems. It describes the inevitable degradation of quantum correlations due to experimental and environmental noise. Various decoherence models were investigated and in particular the ph...

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“…We discuss first the situation where the classical state is given by χ − ρ (49). Remark that χ − ρ possesses parity and exchange symmetries.…”

Section: Classical Correlationsmentioning

confidence: 99%

Unified scheme for correlations using linear relative entropy

Daoud

Laamara²,

Kaydi³

2014

Physics Letters A

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A linearized variant of relative entropy is used to quantify in a unified scheme the different kinds of correlations in a bipartite quantum system. As illustration, we consider a two-qubit state with parity and exchange symmetries for which we determine the total, classical and quantum correlations. We also give the explicit expressions of its closest product state, closest classical state and the corresponding closest product state. A closed additive relation, involving the various correlations quantified by linear relative entropy, is derived.

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Quantum Discord for Multipartite Coherent States Interpolating Between Werner and Greenberger–horne–zeilinger States

Cited by 22 publications

References 65 publications

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Quantum Discord in Photon-Added Glauber Coherent States of GHZ-Type

Unified scheme for correlations using linear relative entropy

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