Spectral properties of reduced fermionic density operators and parity superselection rule

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Abstract

We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that spectra of mode-reduced states are not identical in general and fully characterize pure states with equispectral mode-reduced states. Such states are related via local unitary operations with states satisfying the parity superselection rule. Thus, valid purifications for fermionic density operators are found. To get particle-reduced operators for a general system, we introduce the operation \(\varPhi (\varrho ) = \sum _i a_i \varrho a_i^{\dag }\). We conjecture that spectra of \(\varPhi ^p(\varrho )\) and conventional p-particle reduced density matrix \(\varrho _p\) coincide. Non-trivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.

Keywords

Fermionic state Reduced density matrix Tracing out modes Tracing out particles Spectrum Equispectrality Superselection rule Generalized Pauli constraints 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.V. A. Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Institute of Physics and TechnologyRussian Academy of SciencesMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyMoscow RegionRussia
  4. 4.P. N. Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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