Hamiltonian purification

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

doi:10.1063/1.4936311

Hamiltonian purification

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

School of Advanced Science and Engineering

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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, . . . , h_m} operating on a d-dimensional quantum system H_d, the problem consists in identifying a set of commuting Hamiltonians {H₁, . . . ,H_m} operating on a larger d_E-dimensional system H_{d_E} which embeds Hd as a proper subspace, such that h_j = PH_jP with P being the projection which allows one to recover H_d from H_{d_E}. The notions of spanning-set purification and generator purification of an algebra are also introduced and optimal solutions for u(d) are provided.

Original language	English
Article number	122104
Journal	Journal of Mathematical Physics
Volume	56
Issue number	12
DOIs	https://doi.org/10.1063/1.4936311
Publication status	Published - 2015 Dec 1

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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AU - Orsucci, Davide

AU - Burgarth, Daniel

AU - Facchi, Paolo

AU - Nakazato, Hiromichi

AU - Pascazio, Saverio

AU - Yuasa, Kazuya

AU - Giovannetti, Vittorio

PY - 2015/12/1

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AB - 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.

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Hamiltonian purification

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