A lower bound on ground state entanglement between two regions for a free field

Author： Reznik Benni Retzker Alex Silman Jonathan

ISSN： 1362-3044

Source： Journal of Modern Optics, Vol.51, Iss.6-7, 2004-05, pp. : 833-840

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

In discrete models, such as spin chains, the entanglement between a pair of particles in a chain has been shown to vanish beyond a certain separation. In the continuum, a quantum field &phis;(x) at a point represents a single degree of freedom, thus at a region of finite size there are infinite separate degrees of freedom. We show that as a consequence, in contrast to discrete models, the ground state of a free, quantized and relativistic field exhibits entanglement between any pair of arbitrarily separated finite regions. We also provide a lower bound on the decay rate of the entanglement as a function of the separation length between the regions and briefly discuss the physical reasons behind this different behaviour of discrete and continuous systems.