Simultaneous Measurement of Two Quantum Observables: Compatibility, Broadcasting, and In-between

Abstract

One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary ingredient in several quantum phenomena, such as measurement uncertainty relations, violation of Bell inequalities and steering. Two quantum observables that admit a simultaneous measurement are, in this respect, classical. A finer classification of classicality can be made by formulating four symmetric relations on the set of observables that are stronger than compatibility; they are broadcastability, one-side broadcastability, mutual nondisturbance and nondisturbance. It is proven that the five relations form a hierarchy, and their differences in terms of the required devices needed in a simultaneous measurement is explained. All the four relations stronger than compatibility are completely characterized in the case of qubit observables.

References in corpus (4)

• Joint measurability of generalized measurements implies classicality
• Non-disturbing quantum measurements
• Lüders Theorem for Unsharp Quantum Measurements
• Coexistence of qubit effects

Cited by in corpus (17)

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• Macroscopic Quantum Measurements of noncommuting observables
• Naimark dilations of qubit POVMs and joint measurements
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Quantum incompatibility from the viewpoint of entanglement theory
• Dispensing of quantum information beyond no-broadcasting theorem -- is it possible to broadcast anything genuinely quantum?
• On optimal cloning and incompatibility
• Relating CP divisibility of dynamical maps with compatibility of channels
• Symmetries and Wigner representations of operational theories
• Quantifying incompatibility of quantum measurements through non-commutativity
• Distance-based measures and Epsilon-measures for measurement-based quantum resources
• Information leak and incompatibility of physical context: A modified approach