A note on entanglement of formation and generalized concurrence

Fei, Shao-Ming; Zhao, Hui

doi:10.1016/j.physleta.2004.07.030

Cited by 35 publications

(19 citation statements)

References 17 publications

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“…The results can be generalized to the case that AA { has n > 3 different non-zero eigenvalues [19]. Let l 1 , l 2 , …, l n , each with degeneracy m, mn ( N, be the non-zero eigenvalues of AA { .…”

Section: Eof For a Special Class Of Mixed Statesmentioning

confidence: 98%

“…(18) and (19), the quantum states with the measure of entanglement characterized by D are generally entangled. They are separated when n 5 1, l 1 R 1 (l 2 R 0) or m 5 1, l 2 R 1 (l 1 R 0).…”

Section: Eof For a Special Class Of Mixed Statesmentioning

confidence: 99%

“…In the higher dimensional case, due to the extremizations involved in the calculation, only a few explicit analytic formulae for EOF and concurrence have been found for some special symmetric states [16][17][18][19][20]. Some progress, in particular in the form of practical algorithms, has been obtained on possible lower bounds of the EOF and concurrence for qubit-qudit systems [21][22][23] and for bipartite systems in arbitrary dimensions [24][25][26] using numerical optimization over a large number of free parameters.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement of formation and concurrence for mixed states

Gao

Albeverio

Chen

et al. 2008

Front. Comput. Sci. China

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We review some results on analytical computations of the measures for quantum entanglement: entanglement of formation and concurrence. We introduce some estimations of the lower bounds for the entanglement of formation in bipartite mixed states, and of lower bounds for the concurrence in bipartite and tripartite systems. The results on lower bounds for the concurrence are also generalized to arbitrary multipartite systems.

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Section: Eof For a Special Class Of Mixed Statesmentioning

confidence: 98%

Section: Eof For a Special Class Of Mixed Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entanglement of formation and concurrence for mixed states

Gao

Albeverio

Chen

et al. 2008

Front. Comput. Sci. China

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“…For the two-qubit case, EoF is a monotonically increasing function of the concurrence, and an analytical formula of concurrence has been derived [33]. For the general high-dimensional case, due to the extremizations involved in the computation, only a few analytic formulas have been obtained for isotropic states [34] and Werner states [35] for EoF, and for some special symmetric states [36][37][38] for concurrence.…”

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confidence: 99%

From Quantum Discord and Quantum Entanglement to Local Hidden Variable Models

Fei

2014

Int J Theor Phys

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We revisit the quantum discord, quantum entanglement and local hidden variable models in quantum mechanics, and present a kind of understanding of quantum states from the view of correlations given by the probability distributions of local measurements outcomes.Keywords Quantum discord · Quantum entanglement · LHV modelThe correlations among the subsystems of a multipartite system play significant roles in many information processing tasks and physical processes. The types of correlations existed in a system depend on the state of the system. The evolution of the states results in the evolution of the correlations. It is of importance to learn and classify the states according to the correlations contained in a system. Physically, to get information from a system one needs to measure the system. Hence the kind of correlations in a state can be determined in terms of the probability distributions of the measurement outcomes. By revisiting the quantum discord, quantum entanglement and local hidden variable models in quantum mechanics, we attend to present a kind of understanding of quantum states from the view of correlations.Let us begin with the classical correlations between two random variables. If X is a random variable which has value x with probability p(x), then the information content S(X) of X is defined to be the information you would gain if you learned the value of X, given by the Shannon entropy,S is a function of the probability distribution of the values of X. The information is maximum when our prior knowledge of X is minimum. If X can take N different values, the information content (or entropy) of X is maximized when the probability distribution p is flat, with every p(x) = 1/N . And the maximum information which could in principle be stored by a variable which can take on N different values is log 2 (N ). When X can take two values with

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“…The construction of such kinds of states is presented in [10]. In [11], the results are generalized to the more general case: relations like Eq. (7) hold for states with ρ A having more nonzero eigenvalues such that all these eigenvalues are functions of two independent parameters.…”

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confidence: 99%