Quantum Bochner's theorem for phase spaces built on projective representations

Dangniam, N; Ferrie, C

Quantum Bochner's theorem for phase spaces built on projective representations

Dangniam, N Ferrie, C

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Publication Type:: Journal Article
Citation:: Journal of Physics A: Mathematical and Theoretical, 2015, 48 (11)
Issue Date:: 2015-03-20

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Field	Value	Language
dc.contributor.author	Dangniam, N	en_US
dc.contributor.author	Ferrie, C https://orcid.org/0000-0003-2736-9943	en_US
dc.date.issued	2015-03-20	en_US
dc.identifier.citation	Journal of Physics A: Mathematical and Theoretical, 2015, 48 (11)	en_US
dc.identifier.issn	1751-8113	en_US
dc.identifier.uri	http://hdl.handle.net/10453/119360
dc.description.abstract	© 2015 IOP Publishing Ltd. Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the necessary and sufficient conditions on a function such that it is a quantum characteristic function of a valid (and possibly mixed) quantum state and such that its Fourier transform is a true probability density. We extend this theorem to discrete phase space representations which possess enough symmetry. More precisely, we show that discrete phase space representations that are built on projective unitary representations of abelian groups, with a slight restriction on admissible two-cocycles, enable a quantum Bochner's theorem.	en_US
dc.relation.ispartof	Journal of Physics A: Mathematical and Theoretical	en_US
dc.relation.isbasedon	10.1088/1751-8113/48/11/115305	en_US
dc.subject.classification	Mathematical Physics	en_US
dc.title	Quantum Bochner's theorem for phase spaces built on projective representations	en_US
dc.type	Journal Article
utslib.citation.volume	11	en_US
utslib.citation.volume	48	en_US
utslib.for	020603 Quantum Information, Computation and Communication	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access
pubs.issue	11	en_US
pubs.publication-status	Published	en_US
pubs.volume	48	en_US

Abstract:

© 2015 IOP Publishing Ltd. Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the necessary and sufficient conditions on a function such that it is a quantum characteristic function of a valid (and possibly mixed) quantum state and such that its Fourier transform is a true probability density. We extend this theorem to discrete phase space representations which possess enough symmetry. More precisely, we show that discrete phase space representations that are built on projective unitary representations of abelian groups, with a slight restriction on admissible two-cocycles, enable a quantum Bochner's theorem.

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http://hdl.handle.net/10453/119360