Comparing Energy Difference and Fidelity of Quantum States

Details Comparing Energy Difference and Fidelity of Quantum States Comparing Energy Difference and Fidelity of Quantum States

2011-12-18

arxiv.org/abs/1112.4200v1

Journal of Russian Laser Research, Volume 32, Number 5, p.412-421 (2011)

Physics

Quantum Physics

9 pages

Scientific paper

We look for upper bounds of the relative energy difference of two pure quantum states with a fixed fidelity between them or upper bounds of the fidelity for a fixed relative energy difference. The results depend on the concrete families of states chosen for the comparison. Exact analytical expressions are found for several popular sets of states: coherent, squeezed vacuum, binomial, negative binomial, and coherent phase states. Their consequence is that to guarantee, for example, the relative energy difference less than 10% for quite arbitrary (unknown) coherent states, the fidelity must exceed the level 0.995. For other kinds of states, the restrictions can be much stronger.

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