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On the fidelity of two pure states

Andreas Winter
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Abstract

The fidelity of two pure states (also known as transition probability) is a symmetric function of two operators, and well-founded operationally as an event probability in a certain preparation-test pair. Motivated by the idea that the fidelity is the continuous quantum extension of the combinatorial equality function, we enquire whether there exists a symmetric operational way of obtaining the fidelity. It is shown that this is impossible. Finally, we discuss the optimal universal approximation by a quantum operation.

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Andreas Winter. 2000-11-13. On the fidelity of two pure states. https://doi.org/10.1088/0305-4470%2F34%2F35%2F333

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