1,732 research outputs found
Polynomial Bell inequalities
It is a recent realization that many of the concepts and tools of causal
discovery in machine learning are highly relevant to problems in quantum
information, in particular quantum nonlocality. The crucial ingredient in the
connection between both fields is the tool of Bayesian networks, a graphical
model used to reason about probabilistic causation. Indeed, Bell's theorem
concerns a particular kind of a Bayesian network and Bell inequalities are a
special case of linear constraints following from such models. It is thus
natural to look for generalized Bell scenarios involving more complex Bayesian
networks. The problem, however, relies on the fact that such generalized
scenarios are characterized by polynomial Bell inequalities and no current
method is available to derive them beyond very simple cases. In this work, we
make a significant step in that direction, providing a general and practical
method for the derivation of polynomial Bell inequalities in a wide class of
scenarios, applying it to a few cases of interest. We also show how our
construction naturally gives rise to a notion of non-signalling in generalized
networks.Comment: 9 pages (including appendix
Probing the Non-Classicality of Temporal Correlations
Correlations between spacelike separated measurements on entangled quantum
systems are stronger than any classical correlations and are at the heart of
numerous quantum technologies. In practice, however, spacelike separation is
often not guaranteed and we typically face situations where measurements have
an underlying time order. Here we aim to provide a fair comparison of classical
and quantum models of temporal correlations on a single particle, as well as
timelike-separated correlations on multiple particles. We use a causal modeling
approach to show, in theory and experiment, that quantum correlations
outperform their classical counterpart when allowed equal, but limited
communication resources. This provides a clearer picture of the role of quantum
correlations in timelike separated scenarios, which play an important role in
foundational and practical aspects of quantum information processing.Comment: 8 pages, 6 figures, 2 pages appendix, Accepted versio
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
Causal hierarchy of multipartite Bell nonlocality
As with entanglement, different forms of Bell nonlocality arise in the
multipartite scenario. These can be defined in terms of relaxations of the
causal assumptions in local hidden-variable theories. However, a
characterisation of all the forms of multipartite nonlocality has until now
been out of reach, mainly due to the complexity of generic multipartite causal
models. Here, we employ the formalism of Bayesian networks to reveal
connections among different causal structures that make a both practical and
physically meaningful classification possible. Our framework holds for
arbitrarily many parties. We apply it to study the tripartite scenario in
detail, where we fully characterize all the nonlocality classes. Remarkably, we
identify new highly nonlocal causal structures that cannot reproduce all
quantum correlations. This shows, to our knowledge, the strongest form of
quantum multipartite nonlocality known to date. Finally, as a by-product
result, we derive a non-trivial Bell-type inequality with no quantum violation.
Our findings constitute a significant step forward in the understanding of
multipartite Bell nonlocality and open several venues for future research.Comment: 6 pages + appendix, 3 figures, 3 tables. Minor errors corrected,
discovery of strongest form of quantum multipartite non-locality known so far
added. v3: text improved. v4: Accepted by Quantu
Device-Independent Tests of Entropy
We show that the entropy of a message can be tested in a device-independent
way. Specifically, we consider a prepare-and-measure scenario with classical or
quantum communication, and develop two different methods for placing lower
bounds on the communication entropy, given observable data. The first method is
based on the framework of causal inference networks. The second technique,
based on convex optimization, shows that quantum communication provides an
advantage over classical, in the sense of requiring a lower entropy to
reproduce given data. These ideas may serve as a basis for novel applications
in device-independent quantum information processing
Testing nonlocality of a single photon without a shared reference frame
The question of testing the nonlocality of a single photon has raised much
debate over the last years. The controversy is intimately related to the issue
of providing a common reference frame for the observers to perform their local
measurements. Here we address this point by presenting a simple scheme for
demonstrating the nonlocality of a single photon which does not require a
shared reference frame. Specifically, Bell inequality violation can be obtained
with certainty with unaligned devices, even if the relative frame fluctuates
between each experimental run of the Bell test. Our scheme appears feasible
with current technology, and may simplify the realization of quantum
communication protocols based on single-photon entanglement.Comment: 5 pages, 3 figure
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