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arXiv · 1411.0316

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. [D. K. 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 H_{dE} which embeds H_d 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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Davide Orsucci, Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, Kazuya Yuasa, Vittorio Giovannetti. 2014-11-02. Hamiltonian Purification. https://doi.org/10.1063/1.4936311

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