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On Error Exponents in Quantum Hypothesis Testing

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Identification and Other Probabilistic Models

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 16))

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Abstract

In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching.

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Notes

  1. 1.

    Although the way to derive the operator inequality and the definition of v(σ n) are different from those of [6], it results in the same one as [6] in the case that both of ρ n and σ n are tensored states.

  2. 2.

    Comprehensible explanations of the monotonicity property are found in [1, Sec. 7.2] and [14].

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Ahlswede, R. (2021). On Error Exponents in Quantum Hypothesis Testing. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Identification and Other Probabilistic Models. Foundations in Signal Processing, Communications and Networking, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-65072-8_25

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