Quantum Operations in an Information Theory for Fermions
arXiv:2102.09074 · doi:10.1103/PhysRevA.104.032411
Abstract
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to have a superposition between even and odd parity fermionic states. It thereby characterizes the set of physically allowed fermionic quantum states. Here we introduce the physically allowed quantum operations, in congruence with the parity super-selection rule, that map the set of allowed fermionic states onto itself. We first introduce unitary and projective measurement operations of the fermionic states. We further extend the formalism to general quantum operations in the forms of Stinespring dilation, operator-sum representation, and axiomatic completely-positive-trace-preserving maps. We explicitly show the equivalence between these three representations of fermionic quantum operations. We discuss the possible implications of our results in characterization of correlations in fermionic systems.
8+20 pages, 2 figures
References in corpus (10)
- General criterion for the entanglement of two indistinguishable particles
- Fermionic mode entanglement in quantum information
- Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions
- Entanglement in fermion systems and quantum metrology
- Pairing in fermionic systems: A quantum information perspective
- Computable Measures for the Entanglement of Indistinguishable Particles
- Classical simulation of fermionic linear optics augmented with noisy ancillas
- Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state
- Quantumness of Correlations in Fermionic Systems
- Coffman-Kundu-Wootters inequality for fermions