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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