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

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

7 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 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 픲(d) are provided.

Original language	English
Article number	122104
Pages (from-to)	122104-1-122104-21
Number of pages	21
Journal	Journal of Mathematical Physics
Volume	56
Issue number	12
DOIs	https://doi.org/10.1063/1.4936311
Publication status	Published - 2015
Externally published	Yes

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title = "Hamiltonian purification",

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 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 픲(d) are provided.",

author = "Davide Orsucci and Daniel Burgarth and Paolo Facchi and Hiromichi Nakazato and Saverio Pascazio and Kazuya Yuasa and Vittorio Giovannetti",

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T1 - Hamiltonian purification

AU - Orsucci, Davide

AU - Burgarth, Daniel

AU - Facchi, Paolo

AU - Nakazato, Hiromichi

AU - Pascazio, Saverio

AU - Yuasa, Kazuya

AU - Giovannetti, Vittorio

PY - 2015

Y1 - 2015

N2 - 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 픲(d) are provided.

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 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 픲(d) are provided.

U2 - 10.1063/1.4936311

DO - 10.1063/1.4936311

M3 - Article

SN - 0022-2488

VL - 56

SP - 122104-1-122104-21

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 12

M1 - 122104

ER -

Hamiltonian purification

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