Survival of entanglement in thermal states

¹  Department of Physics, Graduate School of Science, University of Tokyo - Tokyo 113-0033, Japan
²  Quantum Information Technology Lab, Department of Physics, National University of Singapore 117542 Singapore, Singapore
³  The School of Physics and Astronomy, University of Leeds - Leeds LS2 9JT, UK
⁴  PRESTO, JST - Kawaguchi, Saitama 332-0012, Japan
⁵  Institute for Theoretical Physics, University of Innsbruck - Technikerstraße 25, A-6020 Innsbruck, Austria
⁶  Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences - Innsbruck, Austria

Received: 17 July 2007
Accepted: 18 December 2007

Abstract

We present a general sufficiency condition for the presence of multipartite entanglement in thermal states stemming from the ground-state entanglement. The condition is written in terms of the ground-state entanglement and the partition function and it gives transition temperatures below which entanglement is guaranteed to survive. It is flexible and can be easily adapted to consider entanglement for different splittings, as well as be weakened to allow easier calculations by approximations. Examples where the condition is calculated are given. These examples allow us to characterize a minimum gapping behavior for the survival of entanglement in the thermodynamic limit. Further, the same technique can be used to find noise thresholds in the generation of useful resource states for one-way quantum computing.