Source-linked AI summary
The quantum state should be interpreted statistically
Holger F. Hofmann
TL;DR
The paper argues that Pusey, Barrett and Rudolph’s challenge targets hidden-variable realism rather than statistical interpretations generally. It proposes a measurement-contextual decomposition of quantum states into sub-ensembles and concludes that negative joint probabilities explain the paradox and support the statistical interpretation.
Problem
Pusey, Barrett and Rudolph analyze a hidden-variable model while implicitly assuming that every statistical interpretation requires measurement-independent reality.
Source: p. 1Method
The paper decomposes quantum states into sub-ensembles associated with possible measurement outcomes, allowing negative joint probabilities for outcomes that cannot be jointly observed.
Source: pp. 1–2Results
The statistical interpretation explains the zero output probability through negative joint probabilities while distributing the common sub-ensemble positively across outcomes.
Source: p. 2Takeaways & Limitations
The paradox is presented as support for a statistical interpretation grounded in measurement outcomes rather than unobserved measurement-independent realities.
Source: p. 3The paper warns that dogmatic formalism can discourage intuitive understanding of the relation between mathematical description and experimental evidence.
Source: p. 3
Abstract
from arXiv · showhide
In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden variable realism. Effectively, the authors demand from the start that reality must be decided by mathematics, and not by measurements. If this unjustified assumption is dropped, the quantum formalism has a natural statistical interpretation that fully explains the paradox presented by the authors. It is therefore possible to conclude that the paradox actually supports the statistical interpretation, demonstrating once more that quantum mechanics should not be explained by measurement independent realities that are never observed and therefore lie beyond the reach of empirical tests.