Joint measurability of generalized measurements implies classicality

Abstract

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. We prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.

5 pages, 1 figure

References in corpus (5)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Grothendieck's constant and local models for noisy entangled quantum states
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Non-disturbing quantum measurements
• Commutative POVMs and Fuzzy Observables

Cited by in corpus (14)

• All sets of incompatible measurements give an advantage in quantum state discrimination
• Verifying the quantumness of a channel with an untrusted device
• Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture
• All measurements in a probabilistic theory are compatible if and only if the state space is a simplex
• Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
• Channel Steering
• Unsharpness of generalized measurement and its effects in entropic uncertainty relations
• Conditions for the compatibility of channels in general probabilistic theory and their connection to steering and Bell nonlocality
• Joint Measurability and Temporal Steering
• Joint measurability, steering and entropic uncertainty
• Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
• Emergence of Objectivity for Quantum Many-Body Systems
• Experimentally determining the incompatibility of two qubit measurements
• A Note on Hierarchy of Quantum Measurement Incompatibilities