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

### Citation:

B Reznik, A Retzker, and J Silman. 7/6/2004. “A lower bound on ground state entanglement between two regions for a free field.” Journal of Modern Optics, 51, 6-7, Pp. 833-840. Publisher's Version

### 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 ⊘(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.