Sequences of projective measurements in generalized probabilistic models

Abstract

We define a simple rule that allows to describe sequences of projective measurements for a broad class of generalized probabilistic models. This class embraces quantum mechanics and classical probability theory, but, for example, also the hypothetical Popescu-Rohrlich box. For quantum mechanics, the definition yields the established Lüders's rule, which is the standard rule how to update the quantum state after a measurement. In the general case it can be seen as the least disturbing or most coherent way to perform sequential measurements. As example we show that Spekkens's toy model is an instance of our definition. We also demonstrate the possibility of strong post-quantum correlations as well as the existence of triple-slit correlations for certain non-quantum toy models.

14 pages; accepted version

References in corpus (4)

• State-independent experimental test of quantum contextuality
• Translation of Lueders' "Uber die Zustandsanderung durch den Messprozess"
• Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations
• Generalizations of Boxworld

Cited by in corpus (17)

• Kochen-Specker Contextuality
• General probabilistic theories: An introduction
• Converting contextuality into nonlocality
• Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality
• Tracking the dynamics of an ideal quantum measurement
• Simple explanation of the quantum limits of genuine $n$-body nonlocality
• Quantum correlations from simple assumptions
• Exclusivity principle and the quantum bound of the Bell inequality
• Memory cost of temporal correlations
• General Bayesian theories and the emergence of the exclusivity principle
• Quantum Simulation Logic, Oracles, and the Quantum Advantage
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Probabilistic Theories and Reconstructions of Quantum Theory (Les Houches 2019 lecture notes)
• Quantum correlations with a gap between the sequential and spatial cases
• Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules
• The unspeakable why
• Uncertainty-Complementarity Balance as a General Constraint on Non-locality