Hamiltonian purification

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians {h1, …, hm} operating on a d-dimensional quantum system ℋd, the problem consists in identifying a set of commuting...

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Bibliographic Details
Published in:Journal of mathematical physics 2015-12, Vol.56 (12), p.1
Main Authors: Orsucci, Davide, Burgarth, Daniel, Facchi, Paolo, Nakazato, Hiromichi, Pascazio, Saverio, Yuasa, Kazuya, Giovannetti, Vittorio
Format: Article
Language:English
Subjects:
ALGEBRA
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Commuting
Embedded systems
HAMILTONIANS
MATHEMATICAL SOLUTIONS
Physics
PURIFICATION
Quantum physics
QUANTUM SYSTEMS
Quantum theory
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Summary:The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians {h1, …, hm} operating on a d-dimensional quantum system ℋd, the problem consists in identifying a set of commuting Hamiltonians {H1, …, Hm} operating on a larger dE-dimensional system ℋdE which embeds ℋd as a proper subspace, such that hj = PHjP with P being the projection which allows one to recover ℋd from ℋdE. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for (d) are provided.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4936311