Source-linked AI summary
No-go theorem for the composition of quantum systems
Maximilian Schlosshauer, Arthur Fine
TL;DR
The paper asks whether deterministic hidden-variables theories can reproduce quantum predictions while composing subsystem states classically for nonentangled tensor-product systems. It reformulates the PBR strategy in terms of tracking and proves a no-go theorem for theories satisfying assumption A and PIc,tr, including qubit models consistent on their own domain. The result challenges classical realist intuitions about composing “real states,” while noting that the composition assumptions themselves may be questionable.
Problem
The paper examines whether deterministic hidden-variables theories can consistently compose subsystem states for nonentangled tensor-product systems while reproducing quantum predictions.
Source: pp. 1, 3Method
The paper replaces PBR’s association-based composition premise with tracking-based PIc,tr and combines it with assumption A, a two-dimensional lemma, and the PBR measurement argument.
Source: p. 3Results
No ontological deterministic hidden-variables theory satisfying assumption A and PIc,tr can reproduce quantum mechanics, including qubit models that are quantum-consistent on their domains.
Source: p. 3Takeaways & Limitations
The result challenges classical realist intuitions that the complete states of independently prepared subsystems suffice to determine outcomes on their tensor product, even without entanglement.
Source: pp. 3–4The no-go result depends on PIc,tr, whose physical rationale the paper questions; the same reservations apply to PIc in the PBR theorem.
Source: pp. 3–4
Abstract
from arXiv · showhide
Building on the Pusey-Barrett-Rudolph theorem, we derive a no-go theorem for a vast class of deterministic hidden-variables theories, including those consistent on their targeted domain. The strength of this result throws doubt on seemingly natural assumptions (like the "preparation independence" of the Pusey-Barrett-Rudolph theorem) about how "real states" of subsystems compose for joint systems in nonentangled states. This points to constraints in modeling tensor-product states, similar to constraints demonstrated for more complex states by the Bell and Bell-Kochen-Specker theorems.