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arXiv:1802.05877

Exact analytical solution of Entanglement of Formation and Quantum Discord for Werner state and Generalized Werner-Like states

S. Díaz-Solórzano, E. Castro

Published Feb 16, 2018• 3 citations
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Abstract

We obtained analytical expressions for Entangled of Formation (EoF) and Quantum Discord (QD) of Werner states and Generalized Werner-Like states. The optimization problem involved under the exact analytical form is obtained for both quantities. In order to illustrate the importance of our results we studied the EoF and the QD of these states. Using discrete formulation of continue states with the $f-$deformed coherent states obtained as deformed annihilation operator coherent states and as deformed displacement operator coherent states. The EoF and QD of bipartite Werner-Like states $f-$deformed coherent states are studied for the Pöschl-Teller, Morse and quantum dot deformed potentials. The result obtained are compared with the case of bipartite Werner-Like coherent states.

DOI
10.48550/arxiv.1802.05877

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We obtained analytical expressions for Entangled of Formation (EoF) and Quantum Discord (QD) of Werner states and Generalized Werner-Like states. The optimization problem involved under the exact analytical form is obtained for both quantities. In order to illustrate the importance of our results we studied the EoF and the QD of these states. Using discrete formulation of continue states with the f−f-f−deformed coherent states obtained as deformed annihilation operator coherent states and as deformed displacement operator coherent states. The EoF and QD of bipartite Werner-Like states f−f-f−deformed coherent states are studied for the Pöschl-Teller, Morse and quantum dot deformed potentials. The result obtained are compared with the case of bipartite Werner-Like coherent states.
The Generalized Werner-Like states (GWLs) are a class of non--X states in which the exchange operator is replaced for a generic one-rank projector in the Werner states. We obtained an exact analytical expression of Quantum Discord for these states. The optimization problem involved is solved by giving an analytical expression, in exact form for the conditional entropy. We compared the Quantum Discord (QD) with the Entanglement of Formation (EoF) for the same states. The pure states of GWLs with equal concurrence have the same QD and EoF.
Recently, the authors [arXiv quant-ph 1209.3706] studied quantum discord for Werner mixed states based on the four entangled coherent states, which are used for quantum teleportation of single qubit information encoded in superposed coherent state and compared it with entanglement of formation. In the present paper, we consider two more general bipartite superposed coherent states and get two quasi-Werner states. We study quantum discord and entanglement of formation for these states and compare them.
Quantum discord measures the fraction of the pair-wise mutual information that is locally inaccessible in a multipartite system. Nonzero quantum discord has interesting and significant applications because although non-zero entanglement guarantees the existence of quantum correlation in a bipartite quantum system, zero entanglement does not guarantee the absence of a quantum correlation. On the other hand, many quantum optics systems can be described as deformed quantum oscillators. In this work, we investigate the quantum discord of bipartite entangled nonlinear coherent states, in the context of the so-called f-deformed coherent states algebra. To calculate the quantum discord, we consider quasi- Werner mixed states bases on bipartite entangled f-deformed coherent states. Two explicit analytic expressions are derived for the quantum discord of two different nonlinear deformed coherent states. The first one considers deformed coherent states obtained as eigenstates of the annihilation deformed operator, and the second one is obtained by using a deformed displacement operator. We compare the quantum discord of those states, when the nonlinear deformation function is either associated with the SU(1,1) coherent states in the Gilmore-Perelomov or Barut-Girardello representations, respectively.
Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord (QD) and entanglement of formation (EOF) are two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of characterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in arbitrary-dimensional bipartite quantum systems in terms of Hurwitz's theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of arbitrary-dimensional bipartite quantum states via purification, and the relationship between QD and EOF.
Quantum Discord of fff-Deformed Bipartite Entangled Oscillators
Quantum correlations in compound systems are of great importance, and they are fundamental resource for the development of quantum computation protocols and quantum information. In this work we construct bipartite pure coherent states using the fff-deformed oscillator formalism and the Barut-Girardello deformation function. Also we construct the extension of these systems to mixed states using Werner like states. For the states constructed, we study the dependence of the entanglement and quantum discord upon the deformation and mixed parameters.
Abstract Using the single-mode approximation we study the quantum correlations of a free Dirac field on the Werner state in the noninertial frame. We present analytical quantum discord D and its geometric measurement D G . We notice that the quantum discord still exists for the system ρ ARI even in the acceleration limit. We also calculate the entanglement of formation (EOF) and the geometric measure of entanglement ( E G ) to compare the behaviors of the entanglement with the quantum discord. The entanglement is nonzero for the fidelity of the Werner state with a Bell state F > 0.5, while the quantum discord is equal to zero only for F = 0.25. We also observe that the quantum discord is more robust to the change of acceleration than the entanglement, which is more sensitive to the acceleration.