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arXiv:quant-ph/0202100 · Physical Review A

Description of entanglement in terms of quantum phase

Luis Lorenzo Sánchez-Soto, Julián Delgado, A. B. Klimov, Gunnar G. Bjork

Published Oct 21, 2002• 12 citations
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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.

DOI
10.1103/physreva.66.042112

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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.
We explore the role played by the quantum relative phase in a well-known model of atom-field interaction, namely, the Dicke model. We introduce an appropriate polar decomposition of the atom-field relative amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties, as we demonstrate by studying the positive operator-valued measure derived from it. We find the probability distribution for this relative phase and, by resorting to a numerical procedure, we study its time evolution.