Incompatible measurements in quantum information science

Abstract

Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.

review article, 28 pages, 9 figures. v3: small changes, final version

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Cited by in corpus (58)

• Semidefinite programming relaxations for quantum correlations
• Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems
• Measurement incompatibility and quantum advantage in communication
• Exact Steering Bound for Two-Qubit Werner States
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
• Engineering unsteerable quantum states with active feedback
• Compatibility of Generalized Noisy Qubit Measurements
• Certifying the Topology of Quantum Networks: Theory and Experiment
• Unlimited One-Way Steering
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Entropic uncertainty relations for multiple measurements assigned with biased weights
• Unveiling quantum steering by quantum-classical uncertainty complementarity
• Distance-based resource quantification for sets of quantum measurements
• Equivalence between simulability of high-dimensional measurements and high-dimensional steering
• Interplays between classical and quantum entanglement-assisted communication scenarios
• Incompatibility of quantum instruments
• No-broadcasting characterizes operational contextuality
• Distributed quantum incompatibility
• The Hadamard gate cannot be replaced by a resource state in universal quantum computation
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Naimark dilations of qubit POVMs and joint measurements
• Joint-measurability and quantum communication with untrusted devices
• One-shot manipulation of coherence in dynamic quantum resource theory
• Control of open quantum systems: Manipulation of a qubit coupled to a thermal bath by an external driving field
• Necessary and Sufficient Condition for Randomness Certification from Incompatibility
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Spin-Energy Entanglement of a Time-Focused Neutron
• Contextual quantum metrology
• Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
• Multi-object operational tasks for measurement incompatibility
• Retrievability of information in quantum and realistic hidden variable theories
• Measurement incompatibility at all remote parties do not always permit Bell nonlocality
• Resource theory of interactive quantum instruments
• Complete characterisation of state conversions by work extraction
• Quantum-to-Classical Transition via Single-Shot Generalized Measurements
• Semi-classical geometric tensor in multiparameter quantum information
• Operationally classical simulation of quantum states
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• Compressing continuous variable quantum measurements
• Compatibility of projective measurements subject to white noise and loss
• Tripartite entanglement and tripartite steering in three-qubit pure states induced by vacuum--one-photon superpositions
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
• On the simulation of quantum multimeters
• Semi-device-independent certification of number of measurements
• Barycentric decomposition for quantum instruments
• General quantum resources providing advantages in work-extraction tasks
• On compatibility of binary qubit measurements
• Generating Asymmetric Einstein-Podolsky-Rosen Steering between Two movable Mirrors Exploiting Correlated-Emission Laser
• Observing tight triple uncertainty relations in two-qubit systems
• Theory-Independent Context Incompatibility: Quantification and Experimental Demonstration
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Comparing quantum incompatibility of device sets from an operational perspective
• Structure of quantum measurements implementable with one round of classical communication
• Operational Coherent Measurements with Steering and Randomness
• Non-commutative Index of Measurement-only Entanglement Phase Transition
• Detecting quantumness with generalized Loschmidt echoes
• Robust device-independent characterization of sharpness and incompatibility of unsharp instruments
• Quantum Random Access Codes Implementation for Resource Allocation and Coexistence with Classical Telecommunication