Characterizing and quantifying the incompatibility of quantum instruments

Abstract

Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information theoretic tasks. In this work, we focus on the less well-explored question of the incompatibility of quantum instruments, that is, devices that describe the measurement process in its entirety, accounting for both the classical measurement outcome and the quantum post-measurement state. In particular, we focus on the recently introduced notion of parallel compatibility of instruments, which has been argued to be a natural notion of instrument compatibility. We introduce -- similarly to the case of measurements and channels -- the incompatibility robustness of quantum instruments and derive universal bounds on it. We then prove that post-processing of quantum instruments is a free operation for parallel compatibility. Last, we provide families of instruments for which our bounds are tight, and families of compatible indecomposable instruments.

10 pages, typos fixed, minor issues fixed

References in corpus (4)

• All sets of incompatible measurements give an advantage in quantum state discrimination
• Incompatibility of quantum channels
• Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality
• Incompatibility of observables, channels and instruments in information theories

Cited by in corpus (6)

• Thermodynamic Approach to Quantifying Incompatible Instruments
• Incompatibility of quantum instruments
• Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
• One-shot manipulation of coherence in dynamic quantum resource theory
• A Theory of Quantum Instruments
• Multi-object operational tasks for measurement incompatibility