Incompatibility of quantum channels

Abstract

Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and conjugation, and we show that all pairs of sufficiently noisy quantum channels are compatible. The complement relation of incompatibility can be seen as a unifying aspect for many quantum features. We demonstrate that several phenomena, such as impossibility of universal broadcasting and unavoidable measurement disturbance, appear naturally in this framework.

References in corpus (20)

• Noncommuting mixed states cannot be broadcast
• General Entanglement Breaking Channels
• Quantum cloning and the capacity of the Pauli channel
• An Invitation to Quantum Incompatibility
• The structure of degradable quantum channels
• Quantum broadcast channels
• Comparing the degrees of incompatibility inherent in probabilistic physical theories
• Verifying the quantumness of a channel with an untrusted device
• Robustness of incompatibility for quantum devices
• Incompatibility breaking quantum channels
• Steering, incompatibility, and Bell inequality violations in a class of probabilistic theories
• Maximally incompatible quantum observables
• All measurements in a probabilistic theory are compatible if and only if the state space is a simplex
• Measurement incompatibility and Schrödinger-EPR steering in a class of probabilistic theories
• Strongly Incompatible Quantum Devices
• On quantum estimation, quantum cloning and finite quantum de Finetti theorems
• Approximate simulation of quantum channels
• Game-theoretic characterization of antidegradable channels
• Qualitative Noise-Disturbance Relation for Quantum Measurements
• Incompatible measurements on quantum causal networks

Cited by in corpus (39)

• Incompatible measurements in quantum information science
• Probe incompatibility in multiparameter noisy quantum metrology
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• One-Shot Manipulation of Dynamical Quantum Resources
• Operational characterization of incompatibility of quantum channels with quantum state discrimination
• Quantification of quantum dynamics with input-output games
• Witnessing incompatibility of quantum channels
• Quantum marginal problem and incompatibility
• Jordan products of quantum channels and their compatibility
• Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters
• Simulability of high-dimensional quantum measurements
• No-free-information principle in general probabilistic theories
• 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
• Quantum incompatibility of channels with general outcome operator algebras
• Compatibility of covariant quantum channels with emphasis on Weyl symmetry
• On the compatibility of quantum instruments
• Incompatibility as a resource for programmable quantum instruments
• Characterizing and quantifying the incompatibility of quantum instruments
• Incompatibility of unbiased qubit observables and Pauli channels
• Incompatibility of quantum instruments
• Experimental Communication Through Superposition of Quantum Channels
• Interplay of nonlocality and incompatibility breaking qubit channels
• Relating compatibility and divisibility of quantum channels
• Noise-disturbance relation and the Galois connection of quantum measurements
• Testing incompatibility of quantum devices with few states
• Quantum incompatibility from the viewpoint of entanglement theory
• Dispensing of quantum information beyond no-broadcasting theorem -- is it possible to broadcast anything genuinely quantum?
• The incompatibility of quantum channels in general probabilistic theories
• Directed-completeness of quantum statistical experiments in the randomization order
• Entanglement-breaking channels with general outcome operator algebras
• A Fisher information-based incompatibility criterion for quantum channels
• Multi-object operational tasks for measurement incompatibility
• Relating CP divisibility of dynamical maps with compatibility of channels
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
• Comparing quantum incompatibility of device sets from an operational perspective
• Postponing the choice: advantage of deferred measurements in quantum information processing
• Infinite dimensionality of the post-processing order of measurements on a general state space
• A physical noise model for quantum measurements