Separability of Mixed States: Necessary and Sufficient Conditions

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Abstract

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for \(2\times2\) and \(2\times3\) systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, it is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are considered.

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Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model.

Werner (1989)

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Conditional Quantum Dynamics and Logic Gates

, , … (2009)

Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting non--classical properties. We describe a simple quantum logic gate, the quantum controlled--NOT, and analyse some of its applications. We discuss two possible physical realisations of the gate; one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole--dipole interaction.