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Deterministic Quantum State Transformations

Anthony Chefles
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Abstract

We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for linearly-independent initial states. We also examine the issue of quantum coherence, that is, when such operations maintain the purity of superpositions. If, in any deterministic transformation from one linearly-independent set to another, even a single, complete superposition of the initial states maintains its purity, the initial and final states are related by a unitary transformation.

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Anthony Chefles. 2000-03-07. Deterministic Quantum State Transformations. https://doi.org/10.1016/s0375-9601(00)00291-7

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