Maximal entanglement increase with single-photon subtraction

TL;DR

This paper proves that single-photon subtraction can increase bipartite entanglement in Gaussian states by at most log 2, establishing a universal upper bound valid for all such states.

Contribution

It introduces a rigorous proof that the entanglement increase from single-photon subtraction is capped at log 2 for all Gaussian states.

Findings

Entanglement increase is bounded by log 2.

The bound applies universally to all Gaussian input states.

Photon subtraction cannot exceed this entanglement increase.

Abstract

Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the R\'enyi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.