Scattering theory of plasmon-assisted entanglement transfer and distillation

Abstract

We analyze the quantum-mechanical limits to the plasmon-assisted entanglement transfer observed by Altewischer, van Exter, and Woerdman [Nature 418, 304 (2002)]. The maximal violation S of Bell's inequality at the photodetectors behind two linear media (such as the perforated metal films in the experiment) can be described by two ratio's ${\ensuremath{\tau}}_{1},$ ${\ensuremath{\tau}}_{2}$ of polarization-dependent transmission probabilities. A fully entangled incident state is transferred without degradation for ${\ensuremath{\tau}}_{1}={\ensuremath{\tau}}_{2},$ but a relatively large mismatch of ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ can be tolerated with a small reduction of S. We predict that fully entangled Bell pairs can be distilled out of partially entangled radiation if ${\ensuremath{\tau}}_{1}$ and ${\ensuremath{\tau}}_{2}$ satisfy a pair of inequalities.