Local operations and completely positive maps in algebraic quantum field theory

DOI10.1007/978-981-13-2487-1_3zbMATH Open1414.81148arXiv1704.01229OpenAlexW2607072805MaRDI QIDQ2418725

Publication date: 28 May 2019

Abstract: Einstein introduced the locality principle which states that all physical effect in some finite space-time region does not influence its space-like separated finite region. Recently, in algebraic quantum field theory, R'{e}dei captured the idea of the locality principle by the notion of operational separability. The operation in operational separability is performed in some finite space-time region, and leaves unchanged the state in its space-like separated finite space-time region. This operation is defined with a completely positive map. In the present paper, we justify using a completely positive map as a local operation in algebraic quantum field theory, and show that this local operation can be approximately written with Kraus operators under the funnel property.

Full work available at URL: https://arxiv.org/abs/1704.01229

zbMATH Keywords

algebraic quantum field theory completely positive maps local operations

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Operator spaces and completely bounded maps (46L07) Axiomatic quantum field theory; operator algebras (81T05) Quantum measurement theory, state operations, state preparations (81P15) Operator algebra methods applied to problems in quantum theory (81R15) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)