dorsal/arxiv
View SchemaHigh Temperature Macroscopic Entanglement
| Authors | Vlatko Vedral |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405102 |
| URL | https://arxiv.org/abs/quant-ph/0405102 |
| DOI | 10.1088/1367-2630/6/1/102 |
| Journal | New J. Phys. 6, 102 (2004) |
Abstract
In this paper I intend to show that macroscopic entanglement is possible at high temperatures. I analyze 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. I demonstrate that we can conclusively calculate the relative entropy of entanglement within any subset of qubits in an overall symmetric state. Three main results then follow. First, I show that the condition for superconductivity, namely the existence of the off diagonal long range order (ODLRO), is not dependent on two-site entanglement, but on 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 Kelvin. Thirdly, I prove that a complete mixture of symmetric states does not contain any entanglement in the macroscopic limit. On the other hand, the same 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 finite number of qubits, albeit it does decrease it. Maximal mixing of symmetric states also does not destroy ODLRO and classical correlations. I discuss various other inequalities between different entanglements as well as generalizations to the subsystems of any dimensionality (i.e. higher than spin half).
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"abstract": "In this paper I intend to show that macroscopic entanglement is possible at\nhigh temperatures. I analyze multipartite entanglement produced by the $\\eta$\npairing mechanism which features strongly in the fermionic lattice models of\nhigh $T_c$ superconductivity. This problem is shown to be equivalent to\ncalculating multipartite entanglement in totally symmetric states of qubits. I\ndemonstrate that we can conclusively calculate the relative entropy of\nentanglement within any subset of qubits in an overall symmetric state. Three\nmain results then follow. First, I show that the condition for\nsuperconductivity, namely the existence of the off diagonal long range order\n(ODLRO), is not dependent on two-site entanglement, but on just classical\ncorrelations as the sites become more and more distant. Secondly, the\nentanglement that does survive in the thermodynamical limit is the entanglement\nof the total lattice and, at half filling, it scales with the log of the number\nof sites. It is this entanglement that will exist at temperatures below the\nsuperconducting critical temperature, which can currently be as high as 160\nKelvin. Thirdly, I prove that a complete mixture of symmetric states does not\ncontain any entanglement in the macroscopic limit. On the other hand, the same\nmixture of symmetric states possesses the same two qubit entanglement features\nas the pure states involved, in the sense that the mixing does not destroy\nentanglement for finite number of qubits, albeit it does decrease it. Maximal\nmixing of symmetric states also does not destroy ODLRO and classical\ncorrelations. I discuss various other inequalities between different\nentanglements as well as generalizations to the subsystems of any\ndimensionality (i.e. higher than spin half).",
"arxiv_id": "quant-ph/0405102",
"authors": [
"Vlatko Vedral"
],
"categories": [
"quant-ph"
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"doi": "10.1088/1367-2630/6/1/102",
"journal_ref": "New J. Phys. 6, 102 (2004)",
"title": "High Temperature Macroscopic Entanglement",
"url": "https://arxiv.org/abs/quant-ph/0405102"
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