33 research outputs found
Contextuality without incompatibility
The existence of incompatible measurements is often believed to be a feature
of quantum theory which signals its inconsistency with any classical worldview.
To prove the failure of classicality in the sense of Kochen-Specker
noncontextuality, one does indeed require sets of incompatible measurements.
However, a more broadly applicable and more permissive notion of classicality
is the existence of a generalized-noncontextual ontological model. In
particular, this notion can imply constraints on the representation of outcomes
even within a single nonprojective measurement. We leverage this fact to
demonstrate that measurement incompatibility is neither necessary nor
sufficient for proofs of the failure of generalized noncontextuality.
Furthermore, we show that every proof of the failure of generalized
noncontextuality in a prepare-measure scenario can be converted into a proof of
the failure of generalized noncontextuality in a corresponding scenario with no
incompatible measurements
Contextual advantage for state discrimination
Finding quantitative aspects of quantum phenomena which cannot be explained
by any classical model has foundational importance for understanding the
boundary between classical and quantum theory. It also has practical
significance for identifying information processing tasks for which those
phenomena provide a quantum advantage. Using the framework of generalized
noncontextuality as our notion of classicality, we find one such nonclassical
feature within the phenomenology of quantum minimum error state discrimination.
Namely, we identify quantitative limits on the success probability for minimum
error state discrimination in any experiment described by a noncontextual
ontological model. These constraints constitute noncontextuality inequalities
that are violated by quantum theory, and this violation implies a quantum
advantage for state discrimination relative to noncontextual models.
Furthermore, our noncontextuality inequalities are robust to noise and are
operationally formulated, so that any experimental violation of the
inequalities is a witness of contextuality, independently of the validity of
quantum theory. Along the way, we introduce new methods for analyzing
noncontextuality scenarios, and demonstrate a tight connection between our
minimum error state discrimination scenario and a Bell scenario.Comment: 18 pages, 9 figure
Noise-robust preparation contextuality shared between any number of observers via unsharp measurements
Multiple observers who independently harvest nonclassical correlations from a
single physical system share the system's ability to enable quantum
correlations. We show that any number of independent observers can share the
preparation contextual outcome statistics enabled by state ensembles in quantum
theory. Furthermore, we show that even in the presence of any amount of white
noise, there exists quantum ensembles that enable such shared preparation
contextuality. The findings are experimentally realised by applying sequential
unsharp measurements to an optical qubit ensemble which reveals three shared
demonstrations of preparation contextuality.Comment: H. A. and N. W. contributed equally to this wor
Connecting XOR and XOR* games
In this work we focus on two classes of games: XOR nonlocal games and XOR*
sequential games with monopartite resources. XOR games have been widely studied
in the literature of nonlocal games, and we introduce XOR* games as their
natural counterpart within the class of games where a resource system is
subjected to a sequence of controlled operations and a final measurement.
Examples of XOR* games are quantum random access codes (QRAC)
and the CHSH* game introduced by Henaut et al. in [PRA 98,060302(2018)]. We
prove, using the diagrammatic language of process theories, that under certain
assumptions these two classes of games can be related via an explicit theorem
that connects their optimal strategies, and so their classical (Bell) and
quantum (Tsirelson) bounds. We also show that two of such assumptions -- the
reversibility of transformations and the bi-dimensionality of the resource
system in the XOR* games -- are strictly necessary for the theorem to hold by
providing explicit counterexamples. We conclude with several examples of pairs
of XOR/XOR* games and by discussing in detail the possible resources that power
the quantum computational advantages in XOR* games.Comment: 15 pages double column, 2 figures/diagrams. Typos corrected,
conclusions update