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No ψ-epistemic model can fully explain the indistinguishability of quantum states.
This work considers models that are defined for a single quantum system of dimension d, such that the independence condition does not arise, and derives an upper bound on the extent to which the probability distributions can overlap.
Theory-independent limits on correlations from generalized Bayesian networks
This work generalizes the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures, and finds that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes.
Generalized probabilistic theories without the no-restriction hypothesis
The framework of generalized probabilistic theories (GPTs) is a popular approach for studying the physical foundations of quantum theory. The standard framework assumes the no-restriction hypothesis,…
Contextuality, Cohomology and Paradox
- S. Abramsky, Rui Soares Barbosa, K. Kishida, Raymond Lal, Shane Mansfield
- 10 February 2015
A remarkable connection between contexuality and logical paradoxes is exposed and it is shown that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.
Causal Categories: Relativistically Interacting Processes
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure…
On modifications of Reichenbachʼs principle of common cause in light of Bellʼs theorem
Bellʼs 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbachʼs principle of common cause. Despite being a hallmark of scientific…
Possibilities Determine the Combinatorial Structure of Probability Polytopes
Categorical Generalization and Physical Structuralism
- Raymond Lal, Nicholas J. Teh
- PhilosophyThe British Journal for the Philosophy of Science
- 11 April 2014
Category theory has become central to certain aspects of theoretical physics. Bain () has recently argued that this has significance for ontic structural realism. We argue against this claim.…
Causal structure in categorical quantum mechanics
- Raymond Lal
Categorical quantum mechanics is a way of formalising the structural features of quantum theory using category theory. It uses compound systems as the primitive notion, which is formalised by using…
Time asymmetry of probabilities versus relativistic causal structure: an arrow of time.
A nonsignaling device is described which becomes a perfect signaling device under time reversal, where time reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device, leading to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions.