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Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs

J. Novotny·G. Alber·I. Jex
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Abstract

The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly.

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J. Novotny, G. Alber, I. Jex. 2006-03-21. Completely positive covariant two-qubit quantum processes and optimal quantum NOT operations for entangled qubit pairs. https://doi.org/10.1103/physreva.73.062311

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