Spectral properties of reduced fermionic density operators and parity superselection rule

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 $\Phi (\varrho )={\sum }_i{a}_i\varrho a_i^{†}$. We conjecture that spectra of ${\Phi }^p(\varrho )$ and conventional $p$-particle reduced density matrix ${\varrho }_p$ coincide. Nontrivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.

8 pages, a new section on particle-reduced density operators and generalized Pauli constraints, published version, Quantum Inf. Process. (2017) 16: 2

References in corpus (13)

• Reference frames, superselection rules, and quantum information
• Phenomenology with Massive Neutrinos
• Entanglement in fermionic systems
• Fermionic mode entanglement in quantum information
• Pinning of Fermionic Occupation Numbers
• Entanglement in fermion systems and quantum metrology
• Entanglement of Identical Particles
• Quantum teleportation with identical particles
• Quasipinning and selection rules for excitations in atoms and molecules
• Fermionic Quasi-free States and Maps in Information Theory
• Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state
• Quantifying Quantum Correlations in Fermionic Systems using Witness Operators
• Connecting the von Neumann and Renyi entropies for Fermions

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