Distillation of mixed-state continuous-variable entanglement by photon subtraction

TL;DR

This paper theoretically analyzes how to distill entanglement from mixed continuous-variable states using photon subtraction, even with channel losses, providing formulas and bounds for effective entanglement enhancement.

Contribution

It introduces explicit formulas for entanglement calculation and establishes a lower bound for photon-subtraction efficiency in lossy channels.

Findings

One-copy distillation remains feasible near typical fiber losses.

Explicit formulas for entanglement before and after distillation are provided.

A minimal transmission coefficient for photon subtraction is derived.

Abstract

We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beamsplitters and coherent photon-detection techniques, including conventional on-off detectors and photon number resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beamsplitter is derived, representing the minimal value that still allows to enhance the entanglement.