75 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
A resource theory of quantum memories and their faithful verification with minimal assumptions
We provide a complete set of game-theoretic conditions equivalent to the
existence of a transformation from one quantum channel into another one, by
means of classically correlated pre/post processing maps only. Such conditions
naturally induce tests to certify that a quantum memory is capable of storing
quantum information, as opposed to memories that can be simulated by
measurement and state preparation (corresponding to entanglement-breaking
channels). These results are formulated as a resource theory of genuine quantum
memories (correlated in time), mirroring the resource theory of entanglement in
quantum states (correlated spatially). As the set of conditions is complete,
the corresponding tests are faithful, in the sense that any non
entanglement-breaking channel can be certified. Moreover, they only require the
assumption of trusted inputs, known to be unavoidable for quantum channel
verification. As such, the tests we propose are intrinsically different from
the usual process tomography, for which the probes of both the input and the
output of the channel must be trusted. An explicit construction is provided and
shown to be experimentally realizable, even in the presence of arbitrarily
strong losses in the memory or detectors.Comment: Addition of a quantitative study of memories as resources, and
reformulated part of the results in that ligh
Quantifying multipartite nonlocality via the size of the resource
The generation of (Bell-)nonlocal correlations, i.e., correlations leading to
the violation of a Bell-like inequality, requires the usage of a nonlocal
resource, such as an entangled state. When given a correlation (a collection of
conditional probability distributions) from an experiment or from a theory, it
is desirable to determine the extent to which the participating parties would
need to collaborate nonlocally for its (re)production. Here, we propose to
achieve this via the minimal group size (MGS) of the resource, i.e., the
smallest number of parties that need to share a given type of nonlocal resource
for the above-mentioned purpose. In addition, we provide a general recipe ---
based on the lifting of Bell-like inequalities --- to construct MGS witnesses
for non-signaling resources starting from any given ones. En route to
illustrating the applicability of this recipe, we also show that when
restricted to the space of full-correlation functions, non-signaling resources
are as powerful as unconstrained signaling resources. Explicit examples of
correlations where their MGS can be determined using this recipe and other
numerical techniques are provided.Comment: 8+3 pages, 2 figures, 2 theorems + 1 corollary; comments very
welcomed
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
Exploring the framework of assemblage moment matrices and its applications in device-independent characterizations
In a recent work [Phys. Rev. Lett. 116, 240401 (2016)], a framework known by
the name of "assemblage moment matrices" (AMMs) has been introduced for the
device-independent quantification of quantum steerability and measurement
incompatibility. In other words, even with no assumption made on the
preparation device nor the measurement devices, one can make use of this
framework to certify, directly from the observed data, the aforementioned
quantum features. Here, we further explore the framework of AMM and provide
improved device-independent bounds on the generalized robustness of
entanglement, the incompatibility robustness and the incompatibility weight. We
compare the tightness of our device-independent bounds against those obtained
from other approaches. Along the way, we also provide an analytic form for the
generalized robustness of entanglement for an arbitrary two-qudit isotropic
state. When considering a Bell-type experiment in a tri- or more-partite
scenario, we further show that the framework of AMM provides a natural way to
characterize a superset to the set of quantum correlations, namely, one which
also allows post-quantum steering.Comment: 17 pages, 6 figures. Comments welcome
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