30,153 research outputs found
Robust Bell Inequalities from Communication Complexity
The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities
Entanglement and communication-reducing properties of noisy N-qubit states
We consider properties of states of many qubits, which arise after sending
certain entangled states via various noisy channels (white noise, coloured
noise, local depolarization, dephasing and amplitude damping). Entanglement of
these states is studied and their ability to violate certain classes of Bell
inequalities. States which violate them allow for higher than classical
efficiency of solving related distributed computational tasks with constrained
communication. This is a direct property of such states -- not requiring their
further modification via stochastic local operations and classical
communication such as entanglement purification or distillation procedures. We
identify novel families of multi-particle states which are entangled but
nevertheless allow local realistic description of specific Bell experiments.
For some of them, the "gap" between the critical values for entanglement and
violation of Bell inequality remains finite even in the limit of infinitely
many qubits.Comment: new version, more results adde
Multipartite quantum nonlocality under local decoherence
We study the nonlocal properties of two-qubit maximally-entangled and N-qubit
Greenberger-Horne-Zeilinger states under local decoherence. We show that the
(non)resilience of entanglement under local depolarization or dephasing is not
necessarily equivalent to the (non)resilience of Bell-inequality violations.
Apart from entanglement and Bell-inequality violations, we consider also
nonlocality as quantified by the nonlocal content of correlations, and provide
several examples of anomalous behaviors, both in the bipartite and multipartite
cases. In addition, we study the practical implications of these anomalies on
the usefulness of noisy Greenberger-Horne-Zeilinger states as resources for
nonlocality-based physical protocols given by communication complexity
problems. There, we provide examples of quantum gains improving with the number
of particles that coexist with exponentially-decaying entanglement and
non-local contents.Comment: 6 pages, 4 figure
Classical and quantum partition bound and detector inefficiency
We study randomized and quantum efficiency lower bounds in communication
complexity. These arise from the study of zero-communication protocols in which
players are allowed to abort. Our scenario is inspired by the physics setup of
Bell experiments, where two players share a predefined entangled state but are
not allowed to communicate. Each is given a measurement as input, which they
perform on their share of the system. The outcomes of the measurements should
follow a distribution predicted by quantum mechanics; however, in practice, the
detectors may fail to produce an output in some of the runs. The efficiency of
the experiment is the probability that the experiment succeeds (neither of the
detectors fails).
When the players share a quantum state, this gives rise to a new bound on
quantum communication complexity (eff*) that subsumes the factorization norm.
When players share randomness instead of a quantum state, the efficiency bound
(eff), coincides with the partition bound of Jain and Klauck. This is one of
the strongest lower bounds known for randomized communication complexity, which
subsumes all the known combinatorial and algebraic methods including the
rectangle (corruption) bound, the factorization norm, and discrepancy.
The lower bound is formulated as a convex optimization problem. In practice,
the dual form is more feasible to use, and we show that it amounts to
constructing an explicit Bell inequality (for eff) or Tsirelson inequality (for
eff*). We give an example of a quantum distribution where the violation can be
exponentially bigger than the previously studied class of normalized Bell
inequalities.
For one-way communication, we show that the quantum one-way partition bound
is tight for classical communication with shared entanglement up to arbitrarily
small error.Comment: 21 pages, extended versio
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
A Bell-type test of energy-time entangled qutrits
We have performed a Bell-type test for energy-time entangled qutrits. A
method of inferring the Bell violation in terms of an associated interference
visibility is derived. Using this scheme we obtained a Bell value of , representing a violation of above the limit for local
variables. The scheme has been developed for use at telecom wavelengths and
using proven long distance quantum communication architecture to optimize the
utility of this high dimensional entanglement resource.Comment: replaced lost acknowledement
Bell scenarios with communication
Classical and quantum physics provide fundamentally different predictions
about experiments with separate observers that do not communicate, a phenomenon
known as quantum nonlocality. This insight is a key element of our present
understanding of quantum physics, and also enables a number of information
processing protocols with security beyond what is classically attainable.
Relaxing the pivotal assumption of no communication leads to new insights into
the nature quantum correlations, and may enable new applications where security
can be established under less strict assumptions. Here, we study such
relaxations where different forms of communication are allowed. We consider
communication of inputs, outputs, and of a message between the parties. Using
several measures, we study how much communication is required for classical
models to reproduce quantum or general no-signalling correlations, as well as
how quantum models can be augmented with classical communication to reproduce
no-signalling correlations.Comment: 12 pages, 3 figures. Includes a more detailed explanation of results
appearing in the appendix of arXiv:1411.4648 [quant-ph
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
Experimental device-independent certified randomness generation with an instrumental causal structure
The intrinsic random nature of quantum physics offers novel tools for the
generation of random numbers, a central challenge for a plethora of fields.
Bell non-local correlations obtained by measurements on entangled states allow
for the generation of bit strings whose randomness is guaranteed in a
device-independent manner, i.e. without assumptions on the measurement and
state-generation devices. Here, we generate this strong form of certified
randomness on a new platform: the so-called instrumental scenario, which is
central to the field of causal inference. First, we theoretically show that
certified random bits, private against general quantum adversaries, can be
extracted exploiting device-independent quantum instrumental-inequality
violations. To that end, we adapt techniques previously developed for the Bell
scenario. Then, we experimentally implement the corresponding
randomness-generation protocol using entangled photons and active feed-forward
of information. Moreover, we show that, for low levels of noise, our protocol
offers an advantage over the simplest Bell-nonlocality protocol based on the
Clauser-Horn-Shimony-Holt inequality.Comment: Modified Supplementary Information: removed description of extractor
algorithm introduced by arXiv:1212.0520. Implemented security of the protocol
against general adversarial attack
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