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Journal of the Korean Physical Society

Entanglement Dynamics of Multipartite States under an XY Quantum-CriticalEnvironment

XIAO SAN MA, An Min Wang

Published Dec 15, 2009• 1 citation
Publisher
DOI
10.3938/jkps.55.2317

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It has been shown that, for the two-qubit Heisenberg XY model, anisotropy and magnetic field may together be used to produce entanglement for any finite temperature by adjusting the external magnetic field beyond some finite critical strength. This interesting result arises from an analysis employing the Wootters concurrence, a computable measure of entanglement for two-qubit states. Recently, Mintert {\em et al.} proposed generalizations of Wootters concurrence for multipartite states. These MKB concurrences possess a mathematical property that enables one to understand the origin of this characteristic behavior. Here, we first study the effect of anisotropy and magnetic field on the multipartite thermal entanglement of a four-qubit Heisenberg XY chain using the MKB concurrences. We show that this model exhibits characteristic behavior similar to that of the two-qubit model. In addition, we show that this can again be understood using the same mathematical property. Next, we show that the six-qubit Heisenberg XY chain possesses properties necessary for it to have the characteristic behavior too. Most importantly, it is possible to directly measure the multipartite MKB concurrences of pure states. This may provide an experimental verification of our conjecture that for a Heisenberg XY chain of any even number of qubits, it is always possible to obtain non-zero genuine multipartite entanglement at any finite temperature by applying a sufficiently large magnetic field.

arXiv:0704.1368•Apr 11, 2007•0 citations
Recently, Mintert et al (MKB) (2005 Phys. Rev. Lett. 95 260502) proposed generalizations of the Wootters concurrence for multipartite quantum systems, which can be evaluated efficiently for arbitrary mixed states. In this paper, we study in detail the origin of the robustness of multipartite thermal entanglement in N -qubit XY models with N = 2, 4 and 6 using the MKB concurrences. For N = 2, we establish the principle for the occurrence of robust bipartite thermal entanglement (Kamta and Starace 2002 Phys. Rev. Lett. 88 107901). We show explicitly that similar robust multipartite thermal entanglement can be found in the N = 4 case, and how this can be explained employing the same principle. It is then deduced that the six-qubit XY model also possesses robust multipartite thermal entanglement like the N = 2 case. More generally, our work spells out the characteristic properties for a given realistic model to have robust multipartite thermal entanglement like that in the two-qubit XY model.
It has been shown that, for the two-qubit Heisenberg XY model, anisotropy and magnetic field may together be used to produce entanglement for any finite temperature by adjusting the external magnetic field beyond some finite critical strength. This interesting result arises from an analysis employing the Wootters concurrence, a computable measure of entanglement for two-qubit states. Recently, Mintert {\em et al.} proposed generalizations of Wootters concurrence for multipartite states. These MKB concurrences possess a mathematical property that enables one to understand the origin of this characteristic behavior. Here, we first study the effect of anisotropy and magnetic field on the multipartite thermal entanglement of a four-qubit Heisenberg XY chain using the MKB concurrences. We show that this model exhibits characteristic behavior similar to that of the two-qubit model. In addition, we show that this can again be understood using the same mathematical property. Next, we show that the six-qubit Heisenberg XY chain possesses properties necessary for it to have the characteristic behavior too. Most importantly, it is possible to directly measure the multipartite MKB concurrences of pure states. This may provide an experimental verification of our conjecture that for a Heisenberg XY chain of any even number of qubits, it is always possible to obtain non-zero genuine multipartite entanglement at any finite temperature by applying a sufficiently large magnetic field.