# Spectral properties of reduced fermionic density operators and parity superselection rule

Spectral properties of reduced fermionic density operators and parity superselection rule 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 $$\varPhi (\varrho ) = \sum _i a_i \varrho a_i^{\dag }$$ Φ ( ϱ ) = ∑ i a i ϱ a i † . We conjecture that spectra of $$\varPhi ^p(\varrho )$$ Φ p ( ϱ ) and conventional p-particle reduced density matrix $$\varrho _p$$ ϱ p coincide. Non-trivial generalized Pauli constraints are derived for states satisfying the parity superselection rule. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Spectral properties of reduced fermionic density operators and parity superselection rule

Quantum Information Processing, Volume 16 (1) – Dec 8, 2016
16 pages

/lp/springer_journal/spectral-properties-of-reduced-fermionic-density-operators-and-parity-aCclWZqsto
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1467-9
Publisher site
See Article on Publisher Site

### 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 $$\varPhi (\varrho ) = \sum _i a_i \varrho a_i^{\dag }$$ Φ ( ϱ ) = ∑ i a i ϱ a i † . We conjecture that spectra of $$\varPhi ^p(\varrho )$$ Φ p ( ϱ ) and conventional p-particle reduced density matrix $$\varrho _p$$ ϱ p coincide. Non-trivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 8, 2016

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