Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contextuality under weak assumptions   The presence of contextuality in quantum theory was first highlighted by
Bell, Kochen and Specker, who discovered that for quantum systems of three or
more dimensions, measurements cannot be viewed as revealing pre-existing
properties of the system. More precisely, no model can assign deterministic
outcomes to the projectors of a quantum measurement in a way that depends only
on the projector and not the context (the full set of projectors) in which it
appeared, despite the fact that the Born rule probabilities associated with
projectors are independent of the context. A more general, operational
definition of contextuality introduced by Spekkens, which we will term
"probabilistic contextuality", drops the assumption of determinism and allows
for operations other than measurements to be considered contextual.
Probabilistic noncontextuality represents the postulate that elements of an
operational theory that cannot be distinguished from each other based on the
statistics of arbitrarily many repeated experiments are ontologically
identical. In this paper, we introduce a framework that enables us to
distinguish between different noncontextuality assumptions in terms of the
relationships between the ontological representations of objects in the theory
given a certain relation between their operational representations. This
framework can be used to motivate and define a "possibilistic" analogue,
encapsulating the idea that elements of an operational theory that cannot be
unambiguously distinguished operationally can also not be unambiguously
distinguished ontologically. We then prove that possibilistic noncontextuality
is equivalent to an alternative notion proposed by Hardy. Finally, we
demonstrate that these weaker noncontextuality assumptions are sufficient to
prove alternative versions of known "no-go" theorems that constrain
$\psi$-epistemic models for quantum mechanics.

23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex