We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.
Abstract We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner–Yanase skew information. The variances in this uncertainty relation do not involve any classical mixing uncertainty, and is therefore purely of quantum mechanical nature. We show that a large class of mixed entangled states can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including two-qubit and two-qutrit Werner states and it turns out, for the states discussed in this paper, to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The relevant uncertainty relation reduces to the Schrodinger–Robertson inequality for pure states.