17 research outputs found
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
The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories
To make precise the sense in which the operational predictions of quantum
theory conflict with a classical worldview, it is necessary to articulate a
notion of classicality within an operational framework. A widely applicable
notion of classicality of this sort is whether or not the predictions of a
given operational theory can be explained by a generalized-noncontextual
ontological model. We here explore what notion of classicality this implies for
the generalized probabilistic theory (GPT) that arises from a given operational
theory, focusing on prepare-measure scenarios. We first show that, when mapping
an operational theory to a GPT by quotienting relative to operational
equivalences, the constraint of explainability by a generalized-noncontextual
ontological model is mapped to the constraint of explainability by an
ontological model. We then show that, under the additional assumption that the
ontic state space is of finite cardinality, this constraint on the GPT can be
expressed as a geometric condition which we term simplex-embeddability. Whereas
the traditional notion of classicality for a GPT is that its state space be a
simplex and its effect space be the dual of this simplex, simplex-embeddability
merely requires that its state space be embeddable in a simplex and its effect
space in the dual of that simplex. We argue that simplex-embeddability
constitutes an intuitive and freestanding notion of classicality for GPTs. Our
result also has applications to witnessing nonclassicality in prepare-measure
experiments.Comment: 5 pages + 5 page appendi
Quantum Advantage in Information Retrieval
Random access codes have provided many examples of quantum advantage in
communication, but concern only one kind of information retrieval task. We
introduce a related task - the Torpedo Game - and show that it admits greater
quantum advantage than the comparable random access code. Perfect quantum
strategies involving prepare-and-measure protocols with experimentally
accessible three-level systems emerge via analysis in terms of the discrete
Wigner function. The example is leveraged to an operational advantage in a
pacifist version of the strategy game Battleship. We pinpoint a characteristic
of quantum systems that enables quantum advantage in any bounded-memory
information retrieval task. While preparation contextuality has previously been
linked to advantages in random access coding we focus here on a different
characteristic called sequential contextuality. It is shown not only to be
necessary and sufficient for quantum advantage, but also to quantify the degree
of advantage. Our perfect qutrit strategy for the Torpedo Game entails the
strongest type of inconsistency with non-contextual hidden variables, revealing
logical paradoxes with respect to those assumptions.Comment: 15 pages, 11 figures; new presentation, additional figures and
reference