High-temperature macroscopic entanglement

被引:112
作者
Vedral, V [1 ]
机构
[1] Univ London Imperial Coll Sci Technol & Med, Blackett Lab, Opt Sect, London SW7 2BZ, England
来源
NEW JOURNAL OF PHYSICS | 2004年 / 6卷
关键词
D O I
10.1088/1367-2630/6/1/102
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper, we intend to show that macroscopic entanglement is possible at high temperatures. We have analysed multipartite entanglement produced by the eta-pairing mechanism, which features strongly in the fermionic lattice models of high T-c superconductivity. This problem is shown to be equivalent to calculating multipartite entanglement in totally symmetric states of qubits. It is demonstrated that we can conclusively calculate the relative entropy of entanglement within any subset of qubits in the overall symmetric state. Three main results are then presented. First, the condition for superconductivity, namely existence of the off-diagonal long-range order (ODLRO), is dependent not on two-site entanglement but just classical correlations as the sites become more and more distant. Secondly, the entanglement that does survive in the thermodynamical limit is the entanglement of the total lattice and, at half-filling, it scales with the log of the number of sites. It is this entanglement that will exist at temperatures below the superconducting critical temperature, which can currently be as high as 160 K. Finally, it is proved that a complete mixture of symmetric states does not contain any entanglement in the macroscopic limit. On the other hand, a mixture of symmetric states possesses the same two qubit entanglement features as the pure states involved, in the sense that the mixing does not destroy entanglement for a finite number of qubits, albeit it does decrease it. Furthermore, maximal mixing of symmetric states does not destroy ODLRO and classical correlations. We discuss generalizations to the subsystems of any dimensionality (i.e. higher than spin-half).
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页码:1 / 19
页数:19
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