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Comparing energy difference and fidelity of quantum states

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Journal of Russian Laser Research Aims and scope

Abstract

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, a 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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Authors and Affiliations

  1. Instituto de Física, Universidade de Brasília Caixa Postal 04455, 70910-900, Brasília, DF, Brazil

    Victor V. Dodonov

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  1. Victor V. Dodonov
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Correspondence to Victor V. Dodonov.

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Dodonov, V.V. Comparing energy difference and fidelity of quantum states. J Russ Laser Res 32, 412–421 (2011). https://doi.org/10.1007/s10946-011-9230-2

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  • DOI: https://doi.org/10.1007/s10946-011-9230-2

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