Tight lower bound on geometric discord of bipartite states

Rana, Swapan; Parashar, Preeti

doi:10.1103/physreva.85.024102

Cited by 63 publications

(73 citation statements)

References 17 publications

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“…Luo and Fu evaluated the geometric measure of quantum discord for an arbitrary state and gave a tight lower bound for geometric discord of arbitrary bipartite states [29]. Recently, a different tight lower bound for geometric discord of arbitrary bipartite states was given by S. Rana et al [30], and Ali Saif M. Hassan et al [31] independently. Alternatively, D. girolami et al found an explicit expression of geometric discord for two-qubit system and extended it to 2 ⊗ d dimensional systems [32].…”

Section: Brief Review Of Geometric Measure Of Quantum Discordmentioning

confidence: 99%

Geometric quantum discord of a Jaynes–Cummings atom and an isolated atom

Qiang

Zhang

2015

J. Phys. B: At. Mol. Opt. Phys.

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Abstract.We studied the geometric quantum discord of a quantum system consisted of a JaynesCummings atom, a cavity and an isolated atom. The analytical expressions of the geometric quantum discord for two atoms, every atom with cavity and the total system were obtained. We showed that the geometric quantum discord is not always zero when entanglement fall in death for two-atom subsystem; the geometric measurement of quantum discord of the total system developed periodically with a single frequency if the initial state of two atoms was not entangled, otherwise, it oscillates with two or four frequencies according to the cavity is initially empty or not, respectively.

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Section: Brief Review Of Geometric Measure Of Quantum Discordmentioning

confidence: 99%

Geometric quantum discord of a Jaynes–Cummings atom and an isolated atom

Qiang

Zhang

2015

J. Phys. B: At. Mol. Opt. Phys.

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“…For a general bipartite state of d 1 × d 2 dimensions, the density matrix can be written as The lower bound [28,50] of the GD has been derived as…”

Section: B Gdmentioning

confidence: 99%

“…As a variant of quantum discord, geometric discord (GD) was introduced by Dakic and coworkers [27]. Due to its simplicity in calculation, it has attracted a lot of research interests [28,29].…”

Section: Introductionmentioning

confidence: 99%

Quantum Correlations in Qutrit-Qutrit Systems under Local Quantum Noise Channels

2014

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Due to decoherence, realistic quantum systems inevitably interact with the environment when quantum information is processed, which causes the loss of quantum properties. As a fundamental issue of quantum properties, quantum correlations have attracted a lot of interests in recent years. Because of the importance of high dimensional systems in quantum information, in this work, we study the quantum correlations affected by the Markovian environment by considering the quantum correlations of qutrit-qutrit quantum systems measured by the negativity and the geometric discord. The local noise channels covered in this work includes dephasing, tritflip, trit-phase-flip, and depolarising channels. We have also investigated the cases where the local decoherence channels of two sides are identical and non-identical.

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“…(5) fail to be projectors, leading to difficulties in analytic calculations. However we note that these operators originated from a particular choice of unitary and there may be other measurements (corresponding to different choices of unitaries) which would saturate the bound [11]. Indeed it turns out that the projection operators Π k = |p k p k |, k = 1, 2 with…”

mentioning

confidence: 99%

“…, µ m 2 −1 ) t with µ i being the generators of SU (m) and similarly for ν [10]. Then a lower bound on GD is given by [11,12] …”

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confidence: 99%

Geometric discord and measurement-induced nonlocality for well known bound entangled states

Rana

Parashar

2013

Quantum Inf Process

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We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's (2 ⊗ 4, 3 ⊗ 3 and 4 ⊗ 4 dimensional) bound entangled states and that of Bennett et al.'s in 3 ⊗ 3 dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the 4 ⊗ 4 bound entangled state of Benatti et al.and the 2 ⊗ 8 state having the same matrix representation (in computational basis) is same. Coincidently, the 2m ⊗ 2m Werner and isotropic states also exhibit the same property, when seen as 2 ⊗ 2m 2 dimensional states.

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Tight lower bound on geometric discord of bipartite states

Cited by 63 publications

References 17 publications

Geometric quantum discord of a Jaynes–Cummings atom and an isolated atom

Geometric quantum discord of a Jaynes–Cummings atom and an isolated atom

Quantum Correlations in Qutrit-Qutrit Systems under Local Quantum Noise Channels

Geometric discord and measurement-induced nonlocality for well known bound entangled states

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