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Title: Inequalities for quantum marginal problems with continuous variables

We consider a mixed continuous-variable bosonic quantum system and present inequalities which must be satisfied between principal values of the covariances of a complete set of observables of the whole system and the principal values of the covariances of a complete set of observables of a subsystem. We use several classical results for the proof: the Courant-Fischer-Weyl min-max theorem for Hermitian operators and its consequence, the Cauchy interlacing theorem, and prove their analogues in the symplectic setting. For the case of passive transformations of Gaussian mixed states we also prove that the obtained inequalities are, in a sense, the best possible. The obtained mathematical results are applied to the system of n uncorrelated thermal modes of the electromagnetic field. Finally, we present the results of numerical simulations of the problem, suggesting avenues of further research.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno (Czech Republic)
  2. Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic and Department of Computer Science, Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno (Czech Republic)
  3. Department of Computer Science, Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno (Czech Republic)
Publication Date:
OSTI Identifier:
22306207
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 6; Other Information: (c) 2014 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; BOSONS; COMPUTERIZED SIMULATION; ELECTROMAGNETIC FIELDS; HERMITIAN OPERATORS; HILBERT SPACE; MIXED STATES; QUANTUM MECHANICS