Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
- URL: http://arxiv.org/abs/2211.08351v2
- Date: Thu, 17 Nov 2022 18:51:35 GMT
- Title: Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
- Authors: Frederik vom Ende
- Abstract summary: We investigate Stinespring dilations of quantum-dynamical semigroups.
In particular this characterizes the generators of quantum-dynamical semigroups via Stinespring dilations.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work we investigate Stinespring dilations of quantum-dynamical
semigroups, which are known to exist by means of a constructive proof given by
Davies in the early 70s. We show that if the semigroup describes an open
system, that is, if it does not consist of only unitary channels, then the
evolution of the dilated closed system has to be generated by an unbounded
Hamiltonian; subsequently the environment has to correspond to an
infinite-dimensional Hilbert space, regardless of the original system.
Moreover, we prove that the second derivative of Stinespring dilations with a
bounded total Hamiltonian yields the dissipative part of some quantum-dynamical
semigroup -- and vice versa. In particular this characterizes the generators of
quantum-dynamical semigroups via Stinespring dilations.
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