Incompatibility of quantum instruments

• URL: http://arxiv.org/abs/2212.11225v2
• Date: Fri, 2 Feb 2024 12:49:00 GMT
• Title: Incompatibility of quantum instruments
• Authors: Leevi Lepp\"aj\"arvi and Michal Sedl\'ak
• Abstract summary: Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. We derive implications of instrument compatibility for the induced POVMs and channels. We prove equivalence between instrument compatibility and postprocessing of certain instruments, which we term complementary instruments.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum instruments describe outcome probability as well as state change induced by measurement of a quantum system. Incompatibility of two instruments, i. e. the impossibility to realize them simultaneously on a given quantum system, generalizes incompatibility of channels and incompatibility of positive operator-valued measures (POVMs). We derive implications of instrument compatibility for the induced POVMs and channels. We also study relation of instrument compatibility to the concept of non-disturbance. Finally, we prove equivalence between instrument compatibility and postprocessing of certain instruments, which we term complementary instruments. We illustrate our findings on examples of various classes of instruments.

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