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Title: Hamiltonian purification

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.
Authors:
 [1] ;  [2] ; ;  [3] ;  [4] ; ;  [5] ;  [6]
  1. Scuola Normale Superiore, I-56126 Pisa (Italy)
  2. Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ (United Kingdom)
  3. Dipartimento di Fisica and MECENAS, Università di Bari, I-70126 Bari (Italy)
  4. (Italy)
  5. Department of Physics, Waseda University, Tokyo 169-8555 (Japan)
  6. NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa (Italy)
Publication Date:
OSTI Identifier:
22479563
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; HAMILTONIANS; MATHEMATICAL SOLUTIONS; PURIFICATION; QUANTUM SYSTEMS