The are several nonequivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map $\Lambda_t$ is CP divisible if and only if the second tensor power $\LAmbda_t ⊗ \Lambda_t$ is CP divisible as well. Moreover, the P divisibility of the map $\Lambda_t ⊗ \Lambda_t$ is equivalent to the CP divisibility of the map $\Lambda_$t . Interestingly, the latter property is no longer true if we replace the P divisibility of $\Lambda_t ⊗ \Lambda_t$ by simple positivity and the CP divisibility of $\Lambda_t$ by complete positivity. That is, unlike when $\Lambda_t$ has a time-independent generator, positivity of $\Lambda_t ⊗ \Lambda_t$ does not imply complete positivity of $\Lambda_t$ .

Tensor power of dynamical maps and positive versus completely positive divisibility

BENATTI, FABIO;CHRUSCINSKI, DARIUSZ HILARY;
2017

Abstract

The are several nonequivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map $\Lambda_t$ is CP divisible if and only if the second tensor power $\LAmbda_t ⊗ \Lambda_t$ is CP divisible as well. Moreover, the P divisibility of the map $\Lambda_t ⊗ \Lambda_t$ is equivalent to the CP divisibility of the map $\Lambda_$t . Interestingly, the latter property is no longer true if we replace the P divisibility of $\Lambda_t ⊗ \Lambda_t$ by simple positivity and the CP divisibility of $\Lambda_t$ by complete positivity. That is, unlike when $\Lambda_t$ has a time-independent generator, positivity of $\Lambda_t ⊗ \Lambda_t$ does not imply complete positivity of $\Lambda_t$ .
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https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.012112
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2895722
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