Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High Temperature Macroscopic Entanglement   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).

7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math