Squashed Entanglement for Multipartite States and Entanglement Measures Based on the Mixed Convex Roof (original) (raw)
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Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero entanglement resources to start with. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of a geometric measure of entanglement and a related quantity. The results are compared with those for the negativity and the relative entropy of entanglement.
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We consider pure quantum states of N qubits and study the genuine N −qubit entanglement that is shared among all the N qubits. We introduce an information-theoretic measure of genuine N -qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle. 03.65.Ud, 73.43.Nq, 89.70.+c The nature of quantum entanglement is a fascinating topic in quantum mechanics since the famous Einstein-Podolsky-Rosen paper [1] in 1935. Recently, much interest has been focused on entanglement in quantum systems containing a large number of particles. On one hand, multipartite entanglement is valuable physical resource in large-scale quantum information processing . On the other hand, multipartite entanglement seems to play an important role in condensed matter physics [4], such as quantum phase transitions (QPT) and high temperature superconductivity . Therefore, how to characterize and quantify multipartite entanglement remains one of the central issues in quantum information theory.
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International Journal of Quantum Information, 2006
We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem. For qubits (or spin 1/2) the combs are automatically invariant under SL(2, C). This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five-and six-qubit entanglement.
ENTANGLEMENT MEASURE FOR A MULTIPARTITE PURE STATE
dti.unimi.it
This work concerns with the problem of quantifing entanglement in pure states of multipartite two-levels systems. We adopt an information theoretical approach using information entropy to quantify the degree of correlations existing between qubits. In this way the work may give some hints about the problems of generalizing usual entenglement measures from bipartite to multipartite systems.
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Based on the idea of measuring the factorizability of a given density matrix, we propose a pairwise analysis strategy for quantifying and understanding multipartite entanglement. The methodology proves very effective as it immediately guarantees, in addition to the usual entanglement properties, additivity and strong super additivity. We give a specific set of quantities that fulfill the protocol and which, according to our numerical calculations, make the entanglement measure an LOCC non-increasing function. The strategy allows a redefinition of the structural concept of global entanglement.
Physical Review A, 2008
We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of mixture of some permutation-invariant multi-qubit states. The results generalized to multi-qudit states are also shown to hold. The second family of states contain Dür's bound entangled states. Along the way, we have discussed the relation of REE to two other measures: robustness of entanglement and geometric measure of entanglement, slightly extending previous results.
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Physical Review A, 2006
We formalize and extend an operational multipartite entanglement measure introduced in T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006) through the generalization of global entanglement (GE) [ D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this new measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field being thus able to detect a quantum phase transition.