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ABSTRACT: We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. Comment: 5 pages, 2 figures
01/2010;
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ABSTRACT: Many of the properties of the partial transposition are not clear so far. Here the number of the negative eigenvalues of K(T)(the partial transposition of K) is considered carefully when K is a two-partite state. There are strong evidences to show that the number of negative eigenvalues of K(T) is N(N-1)/2 at most when K is a state in Hilbert space N*N. For the special case, 2*2 system(two qubits), we use this result to give a partial proof of the conjecture sqrt(K(T))(T)>=0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of K(T) or the negative entropy of K.
10/2006;
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ABSTRACT: The maximally connected state (MCS) which was first introduced by Briegel and Raussendorf Phys. Rev. Lett. 86 910 (2001)] has many interesting properties in quantum information theory. Many important states that we are focusing on currently are included in this special set of states. To decide whether a state is a MCS or not is the main problem concerned in this paper. In this paper, (1) we give a general criterion for MCS; (2) when the ranks of all of the two-qubit reduced density matrices are two, we give a convenient criterion.
Phys. Rev. A. 12/2005; 72(6).
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ABSTRACT: To find the criterion of a set of positive-definite matrices which can be written as reduced density matrices of a multipartite matrix is a hard and important problem. When the problem is concerned with multiparty density matrices, it is much more significant for computational many-body physics and many-body quantum entanglement which is one of the focuses of current quantum information theory. We give several results on the necessary compatibility relations between a set of two-party reduced density matrices and a global state in Hilbert space NA×NB×NC where NA, NB, and NC are arbitrary.
Phys. Rev. A. 11/2005; 72(5).
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ABSTRACT: It is a hard and important problem to find the criterion of a set of positive-definite matrices which can be written as reduced density operators of a multipartite global quantum state. This problem is closely related to the study of many-body quantum entanglement, which is one of the focuses of current quantum-information theory. We give several results on the necessary compatibility relations between a set of reduced and global density matrices, including (i) compatibility conditions for the one-party reduced density matrices of any (NA×NB)-dimensional bipartite mixed quantum state, (ii) compatibility conditions for the one-party reduced matrices of any M-partite quantum states with the dimension N⊗M, and (iii) compatibility conditions for the two-party reduced density matrixes of (2×2×2)-dimensional tripartite mixed quantum state.
Phys. Rev. A. 05/2005; 71(5).
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ABSTRACT: To find whether a set of reduced density matrices comes from a common multiparty state is a hard and important problem. In this paper, we do the following. (i) We introduce a method to find out some polytopes in one-party eigenvalue space which are sufficient conditions of this problem. (ii) We point out that there are some relations between the compatible conditions and the entanglement of pure states. And we show this idea more clearly in the three-qubit case. (iii) We investigate the relations between the compatibility problem and the invariants of a matrix set under some groups. Furthermore, we show that it is one of the reasons why the compatibility problems which involve the multiparty density matrices are much more difficult than the one-party case.
Phys. Rev. A. 10/2004; 70(4).
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ABSTRACT: We consider a two-qubit unitary operation along with arbitrary local unitary operations acts on a two-qubit pure state, whose entanglement is C_0. We give the conditions that the final state can be maximally entangled and be non-entangled. When the final state can not be maximally entangled, we give the maximal entanglement C_max it can reach. When the final state can not be non-entangled, we give the minimal entanglement C_min it can reach. We think C_max and C_min represent the entanglement changing power of two-qubit unitary operations. According to this power we define an order of gates. Comment: 11 pages
03/2004;
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ABSTRACT: We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state. Comment: 6 pages
07/2003;
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ABSTRACT: Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found and could be viewed as a special state-dependent quantum cloner which has no information about the states. In this paper, we investigate the state-dependent cloning when the state-set contains more than two states. We get some bounds of the global fidelity for these processes. This method is not dependent on the number of the states contained in the state-set. It is also independent of the numbers of copying. Comment: 13 pages, 1 figure, to appear in Phys. Rev. A
09/2002;
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ABSTRACT: We propose an experimentally feasible scheme to demonstrate quantum nonlocality, using Greenberger-Horne-Zeilinger (GHZ) and $W$ entanglement between atomic ensembles generated by a new developed method based on laser manipulation and{} single-photon detection. Comment: 10 pages, 4 figures
08/2002;
