Quasifree stochastic calculus and quantum random walks

Alexander Belton; Michal Gnacik; J. Martin Lindsay; Ping Zhong

doi:10.1007/s10955-019-02273-9

Quasifree stochastic calculus and quantum random walks

Alexander Belton, Michal Gnacik, J. Martin Lindsay, Ping Zhong

School of Mathematics & Physics

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Abstract

The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.

Original language	English
Pages (from-to)	1-39
Number of pages	39
Journal	Journal of Statistical Physics
Volume	176
Issue number	1
Early online date	2 May 2019
DOIs	https://doi.org/10.1007/s10955-019-02273-9
Publication status	Published - Jul 2019

Keywords

Quantum stochastic calculus
quasifree representation
heat bath
repeated quantum interactions
toy Fock space
noncommutative Markov chain
quantum stochastic dilation
quantum dynamical semigroup
quantum Langevin equation

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Quasifree stochastic calculusFinal published version, 587 KBLicence: CC BY

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AU - Lindsay, J. Martin

AU - Zhong, Ping

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AB - The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.

KW - Quantum stochastic calculus

KW - quasifree representation

KW - heat bath

KW - repeated quantum interactions

KW - toy Fock space

KW - noncommutative Markov chain

KW - quantum stochastic dilation

KW - quantum dynamical semigroup

KW - quantum Langevin equation

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VL - 176

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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Quasifree stochastic calculus and quantum random walks

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Keywords

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