### Abstract

The main subject of my talk will be investigation of the possibility of having high temperature entanglement in the macroscopic (thermodynamical) limit. I will first introduce the notions of entanglement and classical correlations for a general state involving any number of subsystems. I will then develop the theory for calculating both classical and quantum correlations for totally symmetric pure states of any number of qubits, as well as any subset and mixture of these. These states are important as they feature in some high T superconducting models. In the second half of the talk, I will be discussing the role of entanglement in macroscopic solid-state systems providing examples from simple models such as the Ising and Heisenberg one-dimensional spin chains. I will argue that these models cannot sustain high temperature entanglement – entanglement only exists close to the very low (critical) temperature. Then I will look at the electron pairing of Yang’s (in the Hubbard Model and related models) used in high T superconductivity. Electron pairing is described by totally symmetric states mentioned above and I plan to discuss the relationship between the existence of off diagonal long range order – which ensures typical superconducting behaviour - and the existence of entanglement and classical correlations. The question of having macroscopic entanglement at high temperature is not only important practically, for information processing, but also has a fundamental significance, which – I believe - may have a long term effect on fundamental physics.