Hamiltonian purification

Davide Orsucci, Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, Kazuya Yuasa, Vittorio Giovannetti

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Abstract

The problem of Hamiltonian purification introduced by Burgarth et al. [Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of noncommuting 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 u(d) are provided.

Original languageEnglish
Article number122104
JournalJournal of Mathematical Physics
Volume56
Issue number12
DOIs
Publication statusPublished - 2015 Dec 1

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Orsucci, D., Burgarth, D., Facchi, P., Nakazato, H., Pascazio, S., Yuasa, K., & Giovannetti, V. (2015). Hamiltonian purification. Journal of Mathematical Physics, 56(12), [122104]. https://doi.org/10.1063/1.4936311