Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

Namkung, Min; Chang, Jinho; Shin, Jaehee; Kwon, Younghun

doi:10.1007/s10773-015-2573-7

Cited by 15 publications

(15 citation statements)

References 31 publications

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“…(43) and (44) are the same, the intermediate subdomain Q θ is absent and the quantum discord is given by analytical expressions. On the other hand, instead of rough conditions (34) and (35), the inequalities S cond (0) ≤ 0 and S cond (π/2) ≤ 0 define now the complete subdomains Q 0 and Q π/2 , respectively.…”

Section: Equations For the Boundariesmentioning

confidence: 99%

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On the quantum discord of general X states

Yurischev

2015

Quantum Inf Process

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Quantum discord Q is a function of density matrix elements. The domain of such a function in the case of two-qubit system with X density matrix may consist of three subdomains at most: two ones where the quantum discord is expressed in closed analytical forms (Q_{\pi/2} and Q_0) and an intermediate subdomain for which, to extract the quantum discord Q_\theta, it is required to solve in general numerically a one-dimensional minimization problem to find the optimal measurement angle \theta\in(0,\pi/2). Hence the quantum discord is given by a piecewise-analytic-numerical formula Q=\min{Q_{\pi/2}, Q_\theta, Q_0}. Equations for determining the boundaries between these subdomains are obtained. The boundaries consist of bifurcation points. The Q_{\theta} subdomains are discovered in the generalized Horodecki states, in the dynamical phase flip channel model, in the anisotropic spin systems at thermal equilibrium, in the heteronuclear dimers in an external magnetic field. We found that transitions between Q_{\theta} subdomain and Q_{\pi/2} and Q_0 ones occur suddenly but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher derivatives of discord function.Comment: 23 pages, 12 figures. arXiv admin note: text overlap with arXiv:1404.573

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Section: Equations For the Boundariesmentioning

confidence: 99%

“…There exists a statement that classical correlations of binary states are optimized via projective positive operator valued measurements (projective POVMs):[29][30][31][32][33][34]. See also[21,38].…”

mentioning

confidence: 99%

On the quantum discord of general X states

Yurischev

2015

Quantum Inf Process

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“…Beyond X-states, recent studies in this direction reveal that for a large majority of two-qubit states, an optimal measurement is among the eigenstates of σ x , σ y , and σ z , and very small errors persist for the states which do not minimize on the aforementioned sets [235,244,245]. Motivated by these observations and the error analysis for the X-states, QD has been considered for different restricted classes of measurements, and the general term, "constrained QD", has been used to identify them [246].…”

Section: A Qubit Systemsmentioning

confidence: 99%

Quantum discord and its allies: a review of recent progress

Bera¹,

Das²,

Sadhukhan³

et al. 2017

Rep. Prog. Phys.

207

162

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“…This is supported by the argument of deterministic quantum computation with one-qubit (DQC1) [ 17 ]. Further, A. Datta et al [ 18 ] insisted that quantum discord [ 19 , 20 , 21 ] can contribute to DQC1. It has been shown that quantum discord can be related not only to quantum computation [ 22 , 23 ], but also to quantum protocols such as quantum state merging [ 24 ], remote state preparation [ 25 ], and assisted optimal state discrimination [ 26 , 27 , 28 , 29 ].…”

Section: Introductionmentioning

confidence: 99%

Coherence and Entanglement Dynamics in Training Variational Quantum Perceptron

Namkung

Kwon

2020

Entropy

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In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv:1809.06056 (2018). In detail, we show that in the first part of the training of the variational quantum perceptron, the quantum coherence of the total system is concentrated in the index register and in the second part, the Grover algorithm consumes the quantum coherence in the index register. This implies that the quantum coherence distribution and the quantum coherence depletion are required in the training of variational quantum perceptron. In addition, we investigate the behavior of entanglement during the training of variational quantum perceptron. We show that the bipartite concurrence between feature and index register decreases since Grover operation is only performed on the index register. Also, we reveal that the concurrence between the two qubits of index register increases as the variational quantum perceptron is trained.

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Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

Abstract: In this article, we investigate the error bound of quantum discord, obtained by the analytic formula of Ali et al.[Phys. Rev. A 81(2010)

Cited by 15 publications

References 31 publications

On the quantum discord of general X states

On the quantum discord of general X states

Quantum discord and its allies: a review of recent progress

Coherence and Entanglement Dynamics in Training Variational Quantum Perceptron

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