Noiseless method for checking the Peres separability criterion by local operations and classical communication

Abstract

We present a method for checking Peres separability criterion in an arbitrary bipartite quantum state $\rho_{AB}$ within local operations and classical communication scenario. The method does not require the prior state reconstruction and the structural physical approximation. The main task for the two observers, Alice and Bob, is to estimate some specific functions. After getting these functions, they can determine the minimal eigenvalue of $\rho^{T_{B}}_{AB}$, which serves as an entanglement indicator in lower dimensions.