Detection of a mixed bipartite entangled state in arbitrary dimension via a structural physical approximation of partial transposition

Abstract

It is very crucial to know that whether the quantum state generated in the experiment is entangled or not. In the literature, this topic was studied extensively and researchers proposed different approaches for the detection of mixed bipartite entangled state in arbitrary dimension. Proceeding in this line of research, we also propose three different criteria for the detection of mixed bipartite negative partial transpose (NPT) entangled state in arbitrary dimension. Our criteria is based on the method of structural physical approximation (SPA) of partial transposition (PT). We have shown that the proposed criteria for the detection of NPT entangled state can be realized experimentally. Two of the proposed criteria is given in terms of the concurrence of the given state in arbitrary dimension so it is essential to find out the concurrence. Thus, we provide new lower and upper bound of concurrence of the quantum state under investigation in terms of average fidelity of two quantum states and hence these bounds can be realized experimentally. Moreover, we have shown how to perform SPA map on qutrit-qubit system and then explicitly calculated the matrix elements of the density matrix describing the SPA-PT of the qutrit-qubit system. We then illustrate our criteria for the detection of entanglement by considering a class of qubit-qubit system and a class of qutrit-qubit system.