58 research outputs found
Correlations, Bell Inequality Violation & Quantum Entanglement
It is one of the most remarkable features of quantum physics that
measurements on spatially separated systems cannot always be described by a
locally causal theory. In such a theory, the outcomes of local measurements are
determined in advance solely by some unknown (or hidden) variables and the
choice of local measurements. Correlations that are allowed within the
framework of a locally causal theory are termed classical. Typically, the fact
that quantum mechanics does not always result in classical correlations is
revealed by the violation of Bell inequalities, which are constraints that have
to be satisfied by any classical correlations. It has been known for a long
time that entanglement is necessary to demonstrate nonclassical correlations,
and hence a Bell inequality violation. However, since some entangled quantum
states are known to admit explicit locally causal models, the exact role of
entanglement in Bell inequality violation has remained obscure. This thesis
provides both a comprehensive review on these issues as well as a report on new
discoveries made to clarify the relationship between entanglement and Bell
inequality violation.Comment: PhD Thesis (176 pages). This thesis contains (1) a pedagogical review
of the field (2) results previously reported in quant-ph/0604045,
quant-ph/0608128, quant-ph/0703268, arXiv:0710.5350 (3) some relevant details
omitted from these publications (4) a formal proof of equivalence between the
class of CGLMP inequalities and the I_{22dd} inequalitie
All bipartite entangled states display some hidden nonlocality
We show that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality
can be demonstrated in a certain kind of Bell experiment for all bipartite
entangled states. Our protocol allows local filtering measurements and involves
shared ancilla states that do not themselves violate CHSH. Our result follows
from two main steps. We first provide a simple characterization of the states
that violate the CHSH-inequality after local filtering operations in terms of
witness-like operators. Second, we prove that for each entangled state
, there exists another state not violating CHSH, such that
violates CHSH. Hence, in this scenario, cannot be
substituted by classical correlations without changing the statistics of the
experiment; we say that is not simulable by classical correlations and
our result is that entanglement is equivalent to non-simulability.Comment: 5 pages, 1 figur
Bounding the plausibility of physical theories in a device-independent setting via hypothesis testing
The device-independent approach to physics is one where conclusions about
physical systems (and hence of Nature) are drawn directly and solely from the
observed correlations between measurement outcomes. This operational approach
to physics arose as a byproduct of Bell's seminal work to distinguish, via a
Bell test, quantum correlations from the set of correlations allowed by
local-hidden-variable theories. In practice, since one can only perform a
finite number of experimental trials, deciding whether an empirical observation
is compatible with some class of physical theories will have to be carried out
via the task of hypothesis testing. In this paper, we show that the
prediction-based-ratio method---initially developed for performing a hypothesis
test of local-hidden-variable theories---can equally well be applied to test
many other classes of physical theories, such as those constrained only by the
nonsignaling principle, and those that are constrained to produce any of the
outer approximation to the quantum set of correlations due to
Navascu\'es-Pironio-Ac\'{\i}n. We numerically simulate Bell tests using
hypothetical nonlocal sources of correlations to illustrate the applicability
of the method in both the independent and identically distributed (i.i.d.)
scenario and the non-i.i.d. scenario. As a further application, we demonstrate
how this method allows us to unveil an apparent violation of the nonsignaling
conditions in certain experimental data collected in a Bell test. This, in
turn, highlights the importance of the randomization of measurement settings,
as well as a consistency check of the nonsignaling conditions in a Bell test.Comment: 10 pages, 1 figure, 3 tables (essentially the published version with
simplified discussion and clearer presentation of results
Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities
Quantum theory has the intriguing feature that is inconsistent with
noncontextual hidden variable models, for which the outcome of a measurement
does not depend on which other compatible measurements are being performed
concurrently. While various proofs of such contextual behavior of quantum
systems have been established, relatively little is known concerning the
possibility to demonstrate this intriguing feature for indistinguishable
particles. Here, we show in a simple and systematic manner that with projective
measurements alone, it is possible to demonstrate quantum contextuality for
such systems of arbitrary Hilbert space dimensions, including those
corresponding to a qubit. Our demonstration is applicable to a single fermion
as well as multiple fermions, and thus also a composite boson formed from an
even number of fermions. In addition, our approach gives a clear demonstration
of the intimate connection between complementarity and contextuality, two
seemingly unrelated aspects of quantum theory.Comment: 9 pages, no figure; Major changes; More changes. Accepted in
Scientific Report
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