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[en] In this paper, a new entanglement measure called EMM (the entanglement measure based on minors) has been constructed by the convex roof method and proved to be a good entanglement measure according to the axiomatic point of view. Computation of EMM can be finished directly by the two-order minors of a coefficient matrix, instead of the eigenvalues of the density operator required by most of the other entanglement measures, so it is very fast and very easy. On the other hand, EMM(|ψ)) is related to the modified Bures distance between |ψ) and the closest separable state, so it has geometry meaning. We also investigate the relations between EMM and the entanglement of formation, negativity and logarithmic negativity, and discover that EMM is always smaller than or equal to them. EMM is equivalent to concurrence. However, their definitions and methods of proof are completely different. EMM will improve the efficiency of searching for maximally entangled multipartite states

[en] In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and some sufficient separability criteria from entanglement-breaking channels are given.

[en] We demonstrate a general procedure to construct entanglement witnesses for any entangled state. This procedure is based on the trace inequality and a general form of entanglement witnesses, which is in the form W=ρ-c_ρI, where ρ is a density matrix, c_ρ is a non-negative number related to ρ, and I is the identity matrix. The general form of entanglement witnesses is deduced from Choi-Jamiolkowski isomorphism, that can be reinterpreted as that all quantum states can be obtained by a maximally quantum entangled state pass through certain completely positive maps. Furthermore, we provide the necessary and sufficient condition of the entanglement witness W=ρ-c_ρI in operation, as well as in theory.

[en] Since the first quantum secret sharing protocol based on Greenberger–Horne–Zeilinger (GHZ) states was presented by Hillery et al, dozens of quantum secret sharing protocols based on different entangled states (e.g. Bell states, d-level Bell states and GHZ states, etc) and product states have been developed. In this paper, we present a quantum secret sharing protocol, in which the genuinely maximally entangled six-qubit states, which was found recently by Borras et al, are used. An ordinary entangled state such as a Bell state or a GHZ state, etc can be used to share at most only one bit. However, according to our protocol, Alice can share three bits among three parties by a six-qubit state, which shows that our protocol is more efficient than any previous protocol. (paper)

[en] In an arbitrated quantum signature scheme, the signatory signs the message and the receiver verifies the signature's validity with the assistance of the arbitrator. We present an arbitrated quantum signature scheme using two-particle entangled Bell states similar to the previous scheme using three-particle entangled Greenberger-Horne-Zeilinger states [G. H. Zeng and C. H. Keitel, Phys. Rev. A 65, 042312 (2002)]. The proposed scheme can preserve the merits in the original scheme while providing a higher efficiency in transmission and reducing the complexity of implementation.

[en] Secret sharing is a procedure for sharing a secret among a number of participants such that only the qualified subsets of participants have the ability to reconstruct the secret. Even in the presence of eavesdropping, secret sharing can be achieved when all the members are quantum. So what happens if not all the members are quantum? In this paper, we propose two semiquantum secret sharing protocols by using maximally entangled Greenberger-Horne-Zeilinger-type states in which quantum Alice shares a secret with two classical parties, Bob and Charlie, in a way that both parties are sufficient to obtain the secret, but one of them cannot. The presented protocols are also shown to be secure against eavesdropping.