TY - JOUR
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 - 2015/12/1
Y1 - 2015/12/1
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 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84951974274&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84951974274&partnerID=8YFLogxK
U2 - 10.1063/1.4936311
DO - 10.1063/1.4936311
M3 - Article
AN - SCOPUS:84951974274
VL - 56
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 12
M1 - 122104
ER -