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State Evolution and Trace-Preserving Completely Positive Maps

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Quantum Information Theory

Part of the book series: Graduate Texts in Physics ((GTP))

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Abstract

Until now, we have considered only quantum states and quantum measurement as quantum concepts. In order to prefer information processing with quantum systems, we should manipulate a wider class of state operations. This chapter examines what kinds of operations are allowed on quantum systems. The properties of these operations will also be examined.

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Notes

  1. 1.

    More precisely, we can implement only a finite number of unitary matrices in a finite amount of time. For a rigorous proof, we must approximate the respective TP-CP maps by a finite number of unitary matrices and evaluate the level of these approximations.

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Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, Aichi, Japan

    Masahito Hayashi

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  1. Masahito Hayashi
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Correspondence to Masahito Hayashi .

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Hayashi, M. (2017). State Evolution and Trace-Preserving Completely Positive Maps. In: Quantum Information Theory. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49725-8_5

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  • DOI: https://doi.org/10.1007/978-3-662-49725-8_5

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