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 ø(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.
| Original language | English |
|---|---|
| Pages (from-to) | 833-840 |
| Number of pages | 8 |
| Journal | Journal of Modern Optics |
| Volume | 51-6 |
| Issue number | 7 |
| DOIs | |
| State | Published - 2004 |
| Externally published | Yes |
Bibliographical note
Funding Information:We thank Y. Aharonov, L. Vaidman and S. Popescu for helpful comments, J. I. Cirac for suggesting the analogy with ion chains in a trap, I. Klich for helpful ideas and A. Botero for many invaluable discussions. We acknowledge support from the Israel Science Foundation (Grant No. 62/01-1).