Recovering Entanglement by Local Operations

We show that any quantification of the bipartite entanglement of mixed states uniquely based on the density operator may lead to a paradoxical increase of entanglement under purely local operations. This apparent paradox is solved in the physical ensemble description of the system state by introducing the concept of "hidden" entanglement, which measures the amount of entanglement that may be recovered without the help of any non-local operation. For two noninteracting qubits under a low-frequency stochastic noise, we show that entanglement can be recovered by local pulses only. We also discuss how hidden entanglement may provide new insights about entanglement revivals in non-Markovian dynamics. We finally propose a simple quantum information scheme, implementable by all-optical setups, which gives evidence of the concept of hidden entanglement.