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.
arXiv commentaccepted version
References in corpus (34)
- Noncommuting mixed states cannot be broadcast
- General Entanglement Breaking Channels
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
- An Invitation to Quantum Incompatibility
- Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
- Quantifying quantum resources with conic programming
- All sets of incompatible measurements give an advantage in quantum state discrimination
- Incompatible measurements in quantum information science
- Quantum Incompatibility Witnesses
- Notes on Joint Measurability of Quantum Observables
- Non-disturbing quantum measurements
- Commutative POVMs and Fuzzy Observables
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- Incompatibility of quantum channels
- Quantum random access codes and incompatibility of measurements
- 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
- Necessary and sufficient condition for contextuality from incompatibility
- Radon-Nikodym derivatives of quantum operations
- Witnessing incompatibility of quantum channels
- Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
- Approximate simulation of quantum channels
- Jordan products of quantum channels and their compatibility
- Qualitative Noise-Disturbance Relation for Quantum Measurements
- Completely positive maps on modules, instruments, extremality problems, and applications to physics
- Incompatibility of observables, channels and instruments in information theories
- Compatibility of covariant quantum channels with emphasis on Weyl symmetry
- Quantum incompatibility of channels with general outcome operator algebras
- On the compatibility of quantum instruments
- Post-processing of quantum instruments
- Characterizing and quantifying the incompatibility of quantum instruments
- A general theory of comparison of quantum channels (and beyond)
- Random access test as an identifier of nonclassicality