Efficiency of Entanglement Concentration by Photon Subtraction

The most used states in continuous variable quantum information processing are Gaussian states, such as coherent states, squeezed states, or Einstein-Podolsky-Rosen like states [1]. The latter type of entangled states are two mode squeezed vacuum and represents a common source for most quantum communication protocols, such as quantum teleportation [2], quantum key distribution [3], quantum dense coding [4], etc. However due to the exponential decay of the entanglement over the length of quantum communication channels [5], protocols such as entanglement concentration are needed to ensure faithful quantum communication [6]. They deserve to enhance the amount of entanglement by using local operations (exploiting ancillary systems) and eventually classical communication. Entanglement concentration involves several copies of bipartite states each having a low amount of entanglement and aims at producing a smaller number of copies possessing a higher amount of entanglement [6]. However, it could also work on a single copy of a bipartite entangled state [7], but unfortunately it cannot be realized within continuous variable by Gaussian operations [8]. Hence methods like “photon subtraction” have been proposed [9, 10], where nonGaussian operations are realized by photon number measurements after beam splitter transforms with ancillary modes. However the photon subtraction protocol is probabilistic since its success depends on the probability of getting ‘good’ measurement outcomes. Hence in characterizing it one should take into account both entanglement enhancement and probability of success. To this end we introduce here a measure of efficiency for the photon subtraction protocol and show that iterating it does not lead to higher efficiency than a single application. In order to overcome this limit we present an adaptive version of the protocol able to greatly enhance its efficiency. We restrict our analysis to the case of weak fields so to consider only few relevant measurements outcomes.