A description of entanglement in terms of quantum phase

Abstract

We explore the role played by the phase in an accurate description of the entanglement of bipartite systems. We first present an appropriate polar decomposition that leads to a truly Hermitian operator for the phase of a single qubit. We also examine the positive operator-valued measures that can describe the qubit phase properties. When dealing with two qubits, the relative phase seems to be a natural variable to understand entanglement. In this spirit, we propose a measure of entanglement based on this variable.