Quantifying micro–macro entanglement of a single-photon entangled state by virtue of Wigner function method

Abstract

In this paper, using Wigner function (WF) method in phase space, we re-investigate micro–macro entanglement of a single-photon entangled state after one-sided amplification and de-amplification proposed by Simon’s group, and discuss the effects of the amplification and the loss. For the input–output process, we first build the relation between the input WF and the output WF. Next, the analytical expression of the output WF is derived related to the factors of the amplification and the loss. Finally, based on the above results, using the trace rule we also obtain the exact expressions of the detected probability and concurrence to quantify micro–macro entanglement, and analyze numerically the results. The results show that it is possible to detect micro–macro photon-number entanglement for reasonable values of photon loss.