Saved in:
Bibliographic Details
Main Authors: Fiorentino, Vincenzo, Weigert, Stefan
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.15607
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866914164486701056
author Fiorentino, Vincenzo
Weigert, Stefan
author_facet Fiorentino, Vincenzo
Weigert, Stefan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_15607
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gleason's Theorem for a Qubit as Part of a Composite System
Fiorentino, Vincenzo
Weigert, Stefan
Quantum Physics
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.
title Gleason's Theorem for a Qubit as Part of a Composite System
topic Quantum Physics
url https://arxiv.org/abs/2511.15607