6,673 research outputs found
Optimal measurements for nonlocal correlations
A problem in quantum information theory is to find the experimental setup
that maximizes the nonlocality of correlations with respect to some suitable
measure such as the violation of Bell inequalities. The latter has however some
drawbacks. First and foremost it is unfeasible to determine the whole set of
Bell inequalities already for a few measurements and thus unfeasible to find
the experimental setup maximizing their violation. Second, the Bell violation
suffers from an ambiguity stemming from the choice of the normalization of the
Bell coefficients. An alternative measure of nonlocality with a direct
information-theoretic interpretation is the minimal amount of classical
communication required for simulating nonlocal correlations. In the case of
many instances simulated in parallel, the minimal communication cost per
instance is called nonlocal capacity, and its computation can be reduced to a
convex-optimization problem. This quantity can be computed for a higher number
of measurements and turns out to be useful for finding the optimal experimental
setup. Focusing on the bipartite case, in this paper, we present a simple
method for maximizing the nonlocal capacity over a given configuration space
and, in particular, over a set of possible measurements, yielding the
corresponding optimal setup. Furthermore, we show that there is a functional
relationship between Bell violation and nonlocal capacity. The method is
illustrated with numerical tests and compared with the maximization of the
violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit
as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed
by qutrits turns out to be even stronger if the nonlocal capacity is employed
as a measure of nonlocality.Comment: Some typos and errors have been corrected, especially in the section
concerning the relation between Bell violation and communication complexit
Optimal Bell tests do not require maximally entangled states
Any Bell test consists of a sequence of measurements on a quantum state in
space-like separated regions. Thus, a state is better than others for a Bell
test when, for the optimal measurements and the same number of trials, the
probability of existence of a local model for the observed outcomes is smaller.
The maximization over states and measurements defines the optimal nonlocality
proof. Numerical results show that the required optimal state does not have to
be maximally entangled.Comment: 1 figure, REVTEX
Einstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum
nonlocality which sits between entanglement and Bell nonlocality. A set of
correlations is Bell nonlocal if it does not admit a local hidden variable
(LHV) model, while it is EPR nonlocal if it does not admit a local hidden
variable-local hidden state (LHV-LHS) model. It is interesting to know what
states can generate EPR-nonlocal correlations in the simplest nontrivial
scenario, that is, two projective measurements for each party sharing a
two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal
full correlations (excluding marginal statistics) in this scenario if and only
if it can generate Bell-nonlocal correlations. If full statistics (including
marginal statistics) is taken into account, surprisingly, the same scenario can
manifest the simplest one-way steering and the strongest hierarchy between
steering and Bell nonlocality. To illustrate these intriguing phenomena in
simple setups, several concrete examples are discussed in detail, which
facilitates experimental demonstration. In the course of study, we introduce
the concept of restricted LHS models and thereby derive a necessary and
sufficient semidefinite-programming criterion to determine the steerability of
any bipartite state under given measurements. Analytical criteria are further
derived in several scenarios of strong theoretical and experimental interest.Comment: New results added, 13 pages, 3 figures; published in Phys. Rev.
Limits on non-local correlations from the structure of the local state space
The outcomes of measurements on entangled quantum systems can be nonlocally
correlated. However, while it is easy to write down toy theories allowing
arbitrary nonlocal correlations, those allowed in quantum mechanics are
limited. Quantum correlations cannot, for example, violate a principle known as
macroscopic locality, which implies that they cannot violate Tsirelson's bound.
This work shows that there is a connection between the strength of nonlocal
correlations in a physical theory, and the structure of the state spaces of
individual systems. This is illustrated by a family of models in which local
state spaces are regular polygons, where a natural analogue of a maximally
entangled state of two systems exists. We characterize the nonlocal
correlations obtainable from such states. The family allows us to study the
transition between classical, quantum, and super-quantum correlations, by
varying only the local state space. We show that the strength of nonlocal
correlations - in particular whether the maximally entangled state violates
Tsirelson's bound or not - depends crucially on a simple geometric property of
the local state space, known as strong self-duality. This result is seen to be
a special case of a general theorem, which states that a broad class of
entangled states in probabilistic theories - including, by extension, all
bipartite classical and quantum states - cannot violate macroscopic locality.
Finally, our results show that there exist models which are locally almost
indistinguishable from quantum mechanics, but can nevertheless generate
maximally nonlocal correlations.Comment: 26 pages, 4 figures. v2: Document structure changed. Main theorem has
been extended. It applies to all quantum states now. v3: new abstrac
Quantum Nonlocal Boxes Exhibit Stronger Distillability
The hypothetical nonlocal box (\textsf{NLB}) proposed by Popescu and Rohrlich
allows two spatially separated parties, Alice and Bob, to exhibit stronger than
quantum correlations. If the generated correlations are weak, they can
sometimes be distilled into a stronger correlation by repeated applications of
the \textsf{NLB}. Motivated by the limited distillability of \textsf{NLB}s, we
initiate here a study of the distillation of correlations for nonlocal boxes
that output quantum states rather than classical bits (\textsf{qNLB}s). We
propose a new protocol for distillation and show that it asymptotically
distills a class of correlated quantum nonlocal boxes to the value , whereas in contrast, the optimal non-adaptive
parity protocol for classical nonlocal boxes asymptotically distills only to
the value 3.0. We show that our protocol is an optimal non-adaptive protocol
for 1, 2 and 3 \textsf{qNLB} copies by constructing a matching dual solution
for the associated primal semidefinite program (SDP). We conclude that
\textsf{qNLB}s are a stronger resource for nonlocality than \textsf{NLB}s. The
main premise that develops from this conclusion is that the \textsf{NLB} model
is not the strongest resource to investigate the fundamental principles that
limit quantum nonlocality. As such, our work provides strong motivation to
reconsider the status quo of the principles that are known to limit nonlocal
correlations under the framework of \textsf{qNLB}s rather than \textsf{NLB}s.Comment: 25 pages, 7 figure
Bell nonlocality
Bell's 1964 theorem, which states that the predictions of quantum theory
cannot be accounted for by any local theory, represents one of the most
profound developments in the foundations of physics. In the last two decades,
Bell's theorem has been a central theme of research from a variety of
perspectives, mainly motivated by quantum information science, where the
nonlocality of quantum theory underpins many of the advantages afforded by a
quantum processing of information. The focus of this review is to a large
extent oriented by these later developments. We review the main concepts and
tools which have been developed to describe and study the nonlocality of
quantum theory, and which have raised this topic to the status of a full
sub-field of quantum information science.Comment: 65 pages, 7 figures. Final versio
From Bell's Theorem to Secure Quantum Key Distribution
Any Quantum Key Distribution (QKD) protocol consists first of sequences of
measurements that produce some correlation between classical data. We show that
these correlation data must violate some Bell inequality in order to contain
distillable secrecy, if not they could be produced by quantum measurements
performed on a separable state of larger dimension. We introduce a new QKD
protocol and prove its security against any individual attack by an adversary
only limited by the no-signaling condition.Comment: 5 pages, 2 figures, REVTEX
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