Decomposition of quantum Markov chains and its applications

Guan, Ji

Decomposition of quantum Markov chains and its applications

Guan, Ji

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Publication Type:: Thesis
Issue Date:: 2018

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Field	Value	Language
dc.contributor.author	Guan, Ji
dc.date.accessioned	2018-10-09T00:14:56Z
dc.date.available	2018-10-09T00:14:56Z
dc.date.issued	2018
dc.identifier.uri	http://hdl.handle.net/10453/127999
dc.description	University of Technology Sydney. Faculty of Engineering and Information Technology.	en_AU
dc.description.abstract	Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a crucial role in reachability analysis and model-checking of Markov chains. (Discrete-time) Quantum Markov chains have been introduced as a model of quantum communicating systems and also a semantic model of quantum programs. The BSCC (Bottom Strongly Connected Component) and stationary coherence decompositions of quantum Markov chains were introduced in. This thesis presents a new decomposition technique, namely periodic decomposition, for quantum Markov chains. This decomposition further helps us find sufficient and necessary conditions for limiting states of quantum Markov chains. To confirm the power of these decomposition techniques, we apply them to characterizing the one-shot zero-error capacity of quantum channels, finding the structure of quantum decoherence-free subsystems against quantum noises and super-activating quantum memory with entanglement via modeling the underlying quantum systems by quantum Markov chains.	en_AU
dc.format	Thesis (PhD)
dc.language.iso	en_AU	en_AU
dc.relation	https://opus.lib.uts.edu.au/bitstream/10453/127999/2/02whole.pdf
dc.rights	The author owns the copyright in this thesis including all reproduction and reuse rights for the work. The work may not be altered without the permission of the copyright owner. Attribution is essential when quoting or paraphrasing from this thesis.
dc.rights	au.edu.uts.lib/ppc
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Markov chains.	en_AU
dc.subject	Decomposition techniques.	en_AU
dc.subject	Dynamical semigroups.	en_AU
dc.subject	Stochastic processes.	en_AU
dc.subject	Stationary states.	en_AU
dc.title	Decomposition of quantum Markov chains and its applications	en_AU
dc.type	Thesis	en_AU
utslib.copyright.status	open_access

Abstract:

Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a crucial role in reachability analysis and model-checking of Markov chains. (Discrete-time) Quantum Markov chains have been introduced as a model of quantum communicating systems and also a semantic model of quantum programs. The BSCC (Bottom Strongly Connected Component) and stationary coherence decompositions of quantum Markov chains were introduced in. This thesis presents a new decomposition technique, namely periodic decomposition, for quantum Markov chains. This decomposition further helps us find sufficient and necessary conditions for limiting states of quantum Markov chains. To confirm the power of these decomposition techniques, we apply them to characterizing the one-shot zero-error capacity of quantum channels, finding the structure of quantum decoherence-free subsystems against quantum noises and super-activating quantum memory with entanglement via modeling the underlying quantum systems by quantum Markov chains.

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http://hdl.handle.net/10453/127999