Non-commutative Markov chains and multi-analytic operators

Rolf Gohm

doi:10.48550/arXiv.0902.3445

Non-commutative Markov chains and multi-analytic operators

Rolf Gohm

Department of Physics

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Abstract

We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

Original language	English
Pages (from-to)	275-288
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	364
Issue number	1
DOIs	https://doi.org/10.48550/arXiv.0902.3445 https://doi.org/10.1016/j.jmaa.2009.11.021
Publication status	Published - 01 Apr 2010

Keywords

Repeated interaction
Open quantum system
Non-commutative Markov chain
Multivariate operator theory
Row contraction
Outgoing Cuntz scattering system
Transfer function
Multi-analytic operator
Input–output formalism
Linear system
Quantum control
Observability
Scattering theory
Characteristic function

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10.48550/arXiv.0902.3445
10.1016/j.jmaa.2009.11.021Licence: Unclear 1

Non-commutative Markov chains and multi-analytic operatorsFinal published version, 267 KBLicence: Unclear 2

http://hdl.handle.net/2160/3976

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Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains
Gohm, R.
Engineering and Physical Sciences Research Council
01 Jun 2009 → 31 May 2012
Project: Externally funded research

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title = "Non-commutative Markov chains and multi-analytic operators",

abstract = "We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.",

keywords = "Repeated interaction, Open quantum system, Non-commutative Markov chain, Multivariate operator theory, Row contraction, Outgoing Cuntz scattering system, Transfer function, Multi-analytic operator, Input–output formalism, Linear system, Quantum control, Observability, Scattering theory, Characteristic function",

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N2 - We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

AB - We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input–output formalism with a transfer function corresponding to a multi-analytic operator, in the sense of multivariate operator theory. Finally we show that observability for this system is closely related to the scattering theory of non-commutative Markov chains.

KW - Repeated interaction

KW - Open quantum system

KW - Non-commutative Markov chain

KW - Multivariate operator theory

KW - Row contraction

KW - Outgoing Cuntz scattering system

KW - Transfer function

KW - Multi-analytic operator

KW - Input–output formalism

KW - Linear system

KW - Quantum control

KW - Observability

KW - Scattering theory

KW - Characteristic function

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M3 - Article

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VL - 364

SP - 275

EP - 288

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Non-commutative Markov chains and multi-analytic operators

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Keywords

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Quantum Control : Approach Based on Scattering Theory for Non-commutative Markov Chains

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