On the fidelity of two pure states

Details On the fidelity of two pure states On the fidelity of two pure states

2000-11-13

arxiv.org/abs/quant-ph/0011053v1

J. Phys. A: Math. Gen., vol. 34(35), pp 7095-7101, 2001.

Physics

Quantum Physics

LaTeX2e, 8 pages, submitted to J. Phys. A: Math. and Gen

Scientific paper

10.1088/0305-4470/34/35/333

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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