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 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
UR - http://hdl.handle.net/2160/43901
U2 - 10.1063/1.4936311
DO - 10.1063/1.4936311
M3 - Article
SN - 0022-2488
VL - 56
SP - 122104
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 12
ER -