Strongly Incompatible Quantum Devices

Abstract

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.

27 pages (AMSart), 6 figures

References in corpus (4)

• Non-disturbing quantum measurements
• Radon-Nikodym derivatives of quantum operations
• Coexistence and Joint Measurability in Quantum Mechanics
• Coexistence of quantum operations

Cited by in corpus (29)

• Incompatible measurements in quantum information science
• Robustness of incompatibility for quantum devices
• Incompatibility breaking quantum channels
• Incompatibility of quantum channels
• Quantification of quantum dynamics with input-output games
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
• Unified picture for spatial, temporal and channel steering
• Measurement incompatibility and quantum advantage in communication
• Qualitative Noise-Disturbance Relation for Quantum Measurements
• Universality of Sequential Quantum Measurements
• Incompatibility as a resource for programmable quantum instruments
• On the compatibility of quantum instruments
• Incompatibility of unbiased qubit observables and Pauli channels
• Characterizing and quantifying the incompatibility of quantum instruments
• Amount of quantum coherence needed for measurement incompatibility
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Quantum Resource Control for noisy EPR-steering with qubit measurements
• Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
• Measurement sharpness and disturbance tradeoff
• WAY beyond conservation laws
• Noise-disturbance relation and the Galois connection of quantum measurements
• Parts and Composites of Quantum Systems
• Testing incompatibility of quantum devices with few states
• Combinations of Quantum Observables and Instruments
• Notes on Deterministic Programming of Quantum Observables and Channels
• Relation between state-distinction power and disturbance in quantum measurements
• Loss of Information in Quantum Guessing Game
• Comparing quantum incompatibility of device sets from an operational perspective
• Postponing the choice: advantage of deferred measurements in quantum information processing