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

We present a method for checking the Peres separability criterion in an arbitrary bipartite quantum state rho(AB) within local operations and classical communication scenario. The method does not require noise operation which is needed in making the partial transposition map physically implementable. The main task for the two observers, Alice and Bob, is to measure some specific functions of the partial transposed matrix. With these functions, they can determine the eigenvalues of rho(T)(AB)(B), among which the minimum serves as an entanglement witness.