Spectral properties of reduced fermionic density operators and parity superselection rule

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• 作者：Grigori G. Amosov ; Sergey N. Filippov
• 关键词：Fermionic state ; Reduced density matrix ; Tracing out modes ; Tracing out particles ; Spectrum ; Equispectrality ; Superselection rule ; Generalized Pauli constraints
• 刊名：Quantum Information Processing
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：16
• 期：1
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics;
• 出版者：Springer US
• ISSN：1573-1332
• 卷排序：16

文摘

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.