1RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
2Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic
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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.
Featured image: Input-output devices $mathcal{D}_A$ and $mathcal{D}_B$ are compatible, denoted by $mathcal{D}_A$ $circhskip{-1mm}circ$ $mathcal{D}_B$, if and only if there exists a joint device $mathcal{D}_{AB}$ which produces an output for both original devices simultaneously with a single input in each use of the joint device.
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Cited by
[1] Stan Gudder, “Multi-Observables and Multi-Instruments”, arXiv:2307.11223, (2023).
[2] Stanley Gudder, “A Theory of Quantum Instruments”, arXiv:2305.17584, (2023).
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