A Gleason-type theorem for qubits based on mixtures of projective measurements

Abstract

We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

arXiv comment19 pages, 3 figures

References in corpus (4)

• A derivation of quantum theory from physical requirements
• Quantum states and generalized observables: a simple proof of Gleason's theorem
• Simulating positive-operator-valued measures with projective measurements
• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements

Cited by in corpus (7)

• General Probabilistic Theories with a Gleason-type Theorem
• Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem
• Gleason-type Theorems from Cauchy's Functional Equation
• Extending Kolmogorov's axioms for a generalized probability theory on collections of contexts
• Quantum violation of the Suppes-Zanotti inequalities and "contextuality"
• Gleason's Theorem for a Qubit as Part of a Composite System
• Intermediate determinism in general probabilistic theories