Incompatibility of quantum instruments
arXiv:2212.11225 · doi:10.22331/q-2024-02-12-1246
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.
accepted version
References in corpus (13)
- All sets of incompatible measurements give an advantage in quantum state discrimination
- Incompatible measurements in quantum information science
- Notes on Joint Measurability of Quantum Observables
- Non-disturbing quantum measurements
- Commutative POVMs and Fuzzy Observables
- Incompatibility of quantum channels
- All measurements in a probabilistic theory are compatible if and only if the state space is a simplex
- Realization schemes for quantum instruments in finite dimensions
- Radon-Nikodym derivatives of quantum operations
- Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
- Incompatibility of observables, channels and instruments in information theories
- Characterizing and quantifying the incompatibility of quantum instruments
- Random access test as an identifier of nonclassicality