406 research outputs found
A Rigorous Analysis of the Clauser-Horne-Shimony-Holt Inequality Experiment When Trials Need Not Be Independent
The Clauser-Horne-Shimony-Holt (CHSH) inequality is a constraint that local
theories must obey. Quantum Mechanics predicts a violation of this inequality
in certain experimental settings. Treatments of this subject frequently make
simplifying assumptions about the probability spaces available to a local
hidden variable theory, such as assuming the state of the system is a discrete
or absolutely continuous random variable, or assuming that repeated
experimental trials are independent and identically distributed. In this paper,
we do two things: first, show that the CHSH inequality holds even for
completely general state variables in the measure-theoretic setting, and
second, demonstrate how to drop the assumption of independence of subsequent
trials while still being able to perform a hypothesis test that will
distinguish Quantum Mechanics from local theories. The statistical strength of
such a test is computed.Comment: 23 pages, 2 figures. To appear in Foundations of Physic
A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses
According to recent new definitions, a multi-party behavior is genuinely
multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an
underlying network of bipartite-only nonlocal resources, possibly supplemented
with local (classical) resources shared by all parties. The new definitions
differ on whether to allow entangled measurements upon, and/or superquantum
behaviors among, the underlying bipartite resources. Here, we categorize the
full hierarchy of these new candidate definitions of GMNL in three-party
quantum networks, highlighting the intimate link to device-independent
witnesses of network effects. A key finding is the existence of a behavior in
the simplest nontrivial multi-partite measurement scenario (3 parties, 2
measurement settings, and 2 outcomes) that cannot be simulated in a bipartite
network prohibiting entangled measurements and superquantum resources -- thus
witnessing the most general form of GMNL -- but can be simulated with
bipartite-only quantum states with an entangled measurement, indicating an
approach to device independent certification of entangled measurements with
fewer settings than in previous protocols. Surprisingly, we also find that this
(3,2,2) behavior, as well as the others previously studied as
device-independent witnesses of entangled measurements, can all be simulated at
a higher echelon of the GMNL hierarchy that allows superquantum bipartite
resources while still prohibiting entangled measurements. This poses a
challenge to a theory-independent understanding of entangled measurements as an
observable phenomenon distinct from bipartite nonlocality.Comment: Close to the published version, 17 pages, 3 figure
- …