  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.
