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DOE OSTI · 22479563

Hamiltonian purification

Orsucci, Davide·Burgarth, Daniel·Facchi, Paolo·Pascazio, Saverio·Nakazato, Hiromichi·Yuasa, Kazuya·Giovannetti, Vittorio
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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 non-commuting Hamiltonians (h{sub 1}, …, h{sub m}) operating on a d-dimensional quantum system ℋ{sub d}, the problem consists in identifying a set of commuting Hamiltonians (H{sub 1}, …, H{sub m}) operating on a larger d{sub E}-dimensional system ℋ{sub d{sub E}} which embeds ℋ{sub d} as a proper subspace, such that h{sub j} = PH{sub j}P with P being the projection which allows one to recover ℋ{sub d} from ℋ{sub d{sub E}}. 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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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSALGEBRAHAMILTONIANSMATHEMATICAL SOLUTIONSPURIFICATIONQUANTUM SYSTEMS

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Orsucci, Davide, Burgarth, Daniel, Facchi, Paolo, Pascazio, Saverio, Nakazato, Hiromichi, Yuasa, Kazuya, Giovannetti, Vittorio. 2015-12-15. Hamiltonian purification. https://doi.org/10.1063/1.4936311

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