Bounds of concurrence and their relation with fidelity and frontier states

The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper-lower bound are determined analytically

Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems

It is shown that for a given bipartite density matrix and by choosing a suitable separable set (instead of product set) on the separable-entangled boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via optimization for a generic entangled density matrix. Based on this, We obtain optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and $2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters basis, iso-concurrence decomposable states, states obtained from BD states via one parameter and three parameters local operations and classical communications (LOCC), $d\otimes d$ Werner and isotropic states, and a one parameter $3\otimes 3$ state. We also obtain the optimal decomposition for multi partite isotropic state. It is shown that in all $2\otimes 2$ systems considered here the average concurrence of the decomposition is equal to the concurrence. We also show that for some $2\otimes 3$ Bell decomposable states the average concurrence of the decomposition is equal to the lower bound of the concurrence of state presented recently in [Buchleitner et al, quant-ph/0302144], so an exact expression for concurrence of these states is obtained. It is also shown that for $d\otimes d$ isotropic state where decomposition leads to a separable and an entangled pure state, the average I-concurrence of the decomposition is equal to the I-concurrence of the state. Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition, Concurrence, Bell decomposable states, LOCC} PACS Index: 03.65.UdComment: 31 pages, Late

Entanglement dynamics of three-qubit states in noisy channels

We study entanglement dynamics of the three-qubit system which is initially prepared in pure Greenberger-Horne- Zeilinger (GHZ) or W state and transmitted through one of the Pauli channels $\sigma_z, \, \sigma_x, \, \sigma_y$ or the depolarizing channel. With the help of the lower bound for three-qubit concurrence we show that the W state preserves more entanglement than the GHZ state in transmission through the Pauli channel $\sigma_z$. For the Pauli channels $\sigma_x, \, \sigma_y$ and the depolarizing channel, however, the entanglement of the GHZ state is more resistant against decoherence than the W-type entanglement. We also briefly discuss how the accuracy of the lower bound approximation depends on the rank of the density matrix under consideration.Comment: 2 figures, 32 reference

Speed of disentanglement in multi-qubit systems under depolarizing channel

We investigate the speed of disentanglement in the multiqubit systems under the local depolarizing channel, in which each qubit is independently coupled to the environment. We focus on the bipartition entanglement between one qubit and the remaining qubits constituting the system, which is measured by the negativity. For the two-qubit system, the speed for the pure state completely depends on its entanglement. The upper and lower bounds of the speed for arbitrary two-qubit states, and the necessary conditions for a state achieving them, are obtained. For the three-qubit system, we study the speed for pure states, whose entanglement properties can be completely described by five local-unitary-transformation invariants. An analytical expression of the relation between the speed and the invariants is derived. The speed is enhanced by the the three-tangle which is the entanglement among the three qubits, but reduced by the the two-qubit correlations outside of the concurrence. The decay of the negativity can be restrained by the other two negativity with the coequal sense. The unbalance between two qubits can reduce speed of disentanglement of the remaining qubit in the system, even can retrieve the entanglement partially. For the k-qubit systems in an arbitrary superposition of GHZ state and W state, the speed depends almost entirely on the amount of the negativity when k increases to five or six. An alternative quantitative definition for the robustness of entanglement is presented based on the speed of disentanglement, with comparison to the widely studied robustness measured by the critical amount of noise parameter where the entanglement vanishes. In the limit of large number of particles, the alternative robustness of the GHZ-type states is inversely proportional to k, and the one of the W states approaches 1/\sqrt{k}.Comment: 14 pages, 5 figures. to appear in Annals of Physic

Nonlocality threshold for entanglement under general dephasing evolutions: A case study

Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic system where the two qubits are locally affected by a quantum environment with an Ohmic class spectrum. We show that steady entanglement can be achieved and provide the lower bound of initial state purity such that this stationary entanglement is above the nonlocality threshold thus guaranteeing the maintenance of nonlocal correlations.Comment: 7 pages, 4 figures. Revised versio