Notes on Joint Measurability of Quantum Observables

Abstract

For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed.

published version, some minor corrections

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• Heisenberg's Uncertainty Principle
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Cited by in corpus (74)

• Quantum Resource Theories
• 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
• Incompatible measurements in quantum information science
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• A no-go theorem for the persistent reality of Wigner's friend's perception
• Non-disturbing quantum measurements
• Incompatibility robustness of quantum measurements: a unified framework
• Quantum measurement incompatibility does not imply Bell nonlocality
• Measurement incompatibility does not give rise to Bell violation in general
• Operational framework for quantum measurement simulability
• Quantum realization of arbitrary joint measurability structures
• Identifying Nonconvexity in the Sets of Limited-Dimension Quantum Correlations
• Most incompatible measurements for robust steering tests
• Adaptive strategy for joint measurements
• Quantum random access codes and incompatibility of measurements
• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Necessary and sufficient condition for contextuality from incompatibility
• Simulability of observables in general probabilistic theories
• Incompatible quantum measurements admitting a local hidden variable model
• Minimal state-dependent proof of measurement contextuality for a qubit
• Distributed sampling, quantum communication witnesses, and measurement incompatibility
• Contextuality without incompatibility
• Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication
• Jordan products of quantum channels and their compatibility
• Device-independent tests of structures of measurement incompatibility
• Unsharpness of generalized measurement and its effects in entropic uncertainty relations
• Universality of Sequential Quantum Measurements
• When do pieces determine the whole? Extremal marginals of a completely positive map
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Almost Quantum Correlations are Inconsistent with Specker's Principle
• Quantum theory realises all joint measurability graphs
• A simple sufficient condition for the coexistence of quantum effects
• Joint Measurability and Temporal Steering
• Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality
• Estimating Quantum Hamiltonians via Joint Measurements of Noisy Non-Commuting Observables
• Detecting genuine multipartite entanglement in steering scenarios
• Random positive operator valued measures
• Quantum Incompatibility of a Physical Context
• Compatibility of covariant quantum channels with emphasis on Weyl symmetry
• Incompatibility as a resource for programmable quantum instruments
• Local measurement uncertainties impose a limit on non-local quantum correlations
• Joint measurability, steering and entropic uncertainty
• Operational foundations of complementarity and uncertainty relations
• Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements
• Compatibility properties of extreme quantum observables
• Improvement in quantum communication using quantum switch
• Compatibility for Probabilistic Theories
• Heisenberg's error-disturbance relations: a joint measurement-based experimental test
• Order preserving maps on quantum measurements
• Joint measurability structures realizable with qubit measurements: incompatibility via marginal surgery
• Geometry of joint reality: device-independent steering and operational completeness
• Incompatibility of quantum instruments
• Distributed quantum incompatibility
• The compatibility dimension of quantum measurements
• Several foundational and information theoretic implications of Bell's theorem
• Verification of joint measurability using phase-space quasiprobability distributions
• A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
• Quantum incompatibility from the viewpoint of entanglement theory
• Joint-measurability and quantum communication with untrusted devices
• N term pairwise correlation inequalities, steering and joint measurability
• Post-processing minimal joint observables
• Electromagnetism in terms of quantum measurements
• Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
• Symmetries and Wigner representations of operational theories
• Measurement incompatibility at all remote parties do not always permit Bell nonlocality
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• Margenau-Hill operator valued measures and joint measurability
• Differential Geometry of Contextuality
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
• Semi-device-independent certification of number of measurements
• Theory-Independent Context Incompatibility: Quantification and Experimental Demonstration