Gleason's Theorem for a Qubit as Part of a Composite System

• URL: http://arxiv.org/abs/2511.15607v1
• Date: Wed, 19 Nov 2025 16:53:58 GMT
• Title: Gleason's Theorem for a Qubit as Part of a Composite System
• Authors: Vincenzo Fiorentino, Stefan Weigert,
• Abstract summary: We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems.<n>The probabilities assigned to measurement outcomes must not depend on whether a system is considered on its own or as a subsystem of a larger one.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$ from a simple requirement: the probabilities assigned to measurement outcomes must not depend on whether a system is considered on its own or as a subsystem of a larger one. In line with Gleason's original theorem, our approach assigns probabilities only to projection-valued measures, while other known extensions rely on considering more general classes of measurements.

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