Hamiltonian Purification
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 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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