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arXiv:1604.06870

Comparison of quantum discord and fully entangled fraction of two classes of $d\otimes d^2$ states

Javad Behdani, Seyed Javad Akhtarshenas, Mohsen Sarbishaei

Published Apr 23, 2016• 0 citations
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Abstract

The quantumness of a generic state is the resource of many applications in quantum information theory and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the $d\otimes d$ Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.

DOI
10.48550/arxiv.1604.06870

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Comparison of quantum discord and fully entangled fraction of two classes of d⊗d2d\otimes d^2d⊗d2 states
The quantumness of a generic state is the resource of many applications in quantum information theory and it is interesting to survey the measures which are able to detect its trace in the properties of the state. In this work we study the quantum discord and fully entangled fraction of two classes of bipartite states and compare their behaviors. These classes are complements to the d⊗dd\otimes dd⊗d Werner and isotropic states, in the sense that each class possesses the same purification as the corresponding complemental class of states. Our results show that maximally entangled mixed states are also maximally discordant states, leading to a generalization of the well-known fact that all maximally entangled pure states have also maximum quantum discord. Moreover, it is shown that the separability-entanglement boundary of a Werner or isotropic state is manifested as an inflection point in the diagram of quantum discord of the corresponding complemental state.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers exponential speed up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy, and identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
In this paper, we investigate comparatively the behaviors of quantum discord and concurrence for Werner states based on two bipartite entangled squeezed states. The maximally entangled squeezed states are regarded as a perfect-Werner states, while the non-maximally entangled squeezed states are called quasi-Werner states. We show that, the behavior of the quantum correlations keep unchanged for these two types of states. However, the quantum correlations amount presents in perfect-Werner states is very higher than that presents in quasi-Werner ones. Furthermore, we show that for large values of squeezed parameter the quasi-Werner states approaches the perfect-Werner states qualitatively and quantitatively.
In this article, we focus on tridiagonal Toeplitz Hermitian matrices, which fulfill the requirement of a valid Hamiltonian often used in Quantum Information. We investigate the behavior of such matrices to pursue the dynamics of quantum correlations (entanglement and quantum discord) for bipartite Werner state and maximally entangled mixed states. We have found interesting results that the main diagonal terms in the Toeplitz matrices never affect the quantum correlations in both quantum states. However, super-diagonal and sub-diagonal terms play the important role in the dynamics. We investigate the phenomenon of entanglement sudden death and also observe the presence of quantum discord in the absence of entanglement. Most importantly it is found that MEMS is more sensitive in comparison to the Werner state.
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.
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.