569 research outputs found
The resource theory of steering
We present an operational framework for Einstein-Podolsky-Rosen steering as a
physical resource. To begin with, we characterize the set of steering
non-increasing operations (SNIOs) --i.e., those that do not create steering--
on arbitrary-dimensional bipartite systems composed of a quantum subsystem and
a black-box device. Next, we introduce the notion of convex steering monotones
as the fundamental axiomatic quantifiers of steering. As a convenient example
thereof, we present the relative entropy of steering. In addition, we prove
that two previously proposed quantifiers, the steerable weight and the
robustness of steering, are also convex steering monotones. To end up with, for
minimal-dimensional systems, we establish, on the one hand, necessary and
sufficient conditions for pure-state steering conversions under stochastic
SNIOs and prove, on the other hand, the non-existence of steering bits, i.e.,
measure-independent maximally steerable states from which all states can be
obtained by means of the free operations. Our findings reveal unexpected
aspects of steering and lay foundations for further resource-theory approaches,
with potential implications in Bell non-locality.Comment: Presentation and structure improve
Robust amplification of Santha-Vazirani sources with three devices
We demonstrate that amplification of arbitrarily weak randomness is possible
using quantum resources. We present a randomness amplification protocol that
involves Bell experiments. We find a Bell inequality which can amplify
arbitrarily weak randomness and give a detailed analysis of the protocol
involving it. Our analysis includes finding a sufficient violation of Bell
inequality as a function of the initial quality of randomness. It has a very
important property that for any quality the required violation is strictly
lower than possible to obtain using quantum resources. Among other things, it
means that the protocol takes a finite amount of time to amplify arbitrarily
weak randomness.Comment: published versio
Statistical ensembles without typicality
Maximum-entropy ensembles are key primitives in statistical mechanics from
which thermodynamic properties can be derived. Over the decades, several
approaches have been put forward in order to justify from minimal assumptions
the use of these ensembles in statistical descriptions. However, there is still
no full consensus on the precise reasoning justifying the use of such
ensembles. In this work, we provide a new approach to derive maximum-entropy
ensembles taking a strictly operational perspective. We investigate the set of
possible transitions that a system can undergo together with an environment,
when one only has partial information about both the system and its
environment. The set of all these allowed transitions encodes thermodynamic
laws and limitations on thermodynamic tasks as particular cases. Our main
result is that the set of allowed transitions coincides with the one possible
if both system and environment were assigned the maximum entropy state
compatible with the partial information. This justifies the overwhelming
success of such ensembles and provides a derivation without relying on
considerations of typicality or information-theoretic measures.Comment: 9+9 pages, 3 figure
Bounding Hilbert Space dimension from Temporal Correlations
Projecte realitzat en col.laboració amb l'IFCOIn this work, we tackle the problem of assessing the Hilbert space
dimension from the set of correlations obtained when measuring in a nonlocal black box
scheme. The concept of a dimension witness and its recent applications are explored.
We also extend these new ideas to the case of a single local box with measurements at
different times, and provide some examples of dimension criteria for this case
An operational framework for nonlocality
Due to the importance of entanglement for quantum information purposes, a
framework has been developed for its characterization and quantification as a
resource based on the following operational principle: entanglement among
parties cannot be created by local operations and classical communication, even
when parties collaborate. More recently, nonlocality has been identified
as another resource, alternative to entanglement and necessary for
device-independent quantum information protocols. We introduce an operational
framework for nonlocality based on a similar principle: nonlocality among
parties cannot be created by local operations and allowed classical
communication even when parties collaborate. We then show that the
standard definition of multipartite nonlocality, due to Svetlichny, is
inconsistent with this operational approach: according to it, genuine
tripartite nonlocality could be created by two collaborating parties. We
finally discuss alternative definitions for which consistency is recovered
Detection loophole attacks on semi-device-independent quantum and classical protocols
Semi-device-independent quantum protocols realize information tasks - e.g.
secure key distribution, random access coding, and randomness generation - in a
scenario where no assumption on the internal working of the devices used in the
protocol is made, except their dimension. These protocols offer two main
advantages: first, their implementation is often less demanding than
fully-device-independent protocols. Second, they are more secure than their
device-dependent counterparts. Their classical analogous is represented by
random access codes, which provide a general framework for describing one-sided
classical communication tasks. We discuss conditions under which detection
inefficiencies can be exploited by a malicious provider to fake the performance
of semi-device-independent quantum and classical protocols - and how to prevent
it.Comment: 13 pages, 1 figure, published versio
Nonlocality free wirings and the distinguishability between Bell boxes
Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishability between Bell correlations optimized over all fixed measurement choices. This has implications in nonlocality quantification, and leads us to a natural universal definition of Bell nonlocality measures. To end up with, we also consider the statistical strength of nonlocality proofs. We point out some issues of its standard definition in the resource-theoretic operational framework, and suggest simple fixes for them. Our findings reveal nontrivial features of the geometry of the set of wirings and may have implications in the operational distinguishability of nonlocal behaviors
Device-independent tests of classical and quantum dimensions
We address the problem of testing the dimensionality of classical and quantum
systems in a `black-box' scenario. We develop a general formalism for tackling
this problem. This allows us to derive lower bounds on the classical dimension
necessary to reproduce given measurement data. Furthermore, we generalise the
concept of quantum dimension witnesses to arbitrary quantum systems, allowing
one to place a lower bound on the Hilbert space dimension necessary to
reproduce certain data. Illustrating these ideas, we provide simple examples of
classical and quantum dimension witnesses.Comment: To appear in PR
Nonlocality in sequential correlation scenarios
As first shown by Popescu [S. Popescu, Phys. Rev. Lett. 74, 2619 (1995)],
some quantum states only reveal their nonlocality when subjected to a sequence
of measurements while giving rise to local correlations in standard Bell tests.
Motivated by this manifestation of "hidden nonlocality" we set out to develop a
general framework for the study of nonlocality when sequences of measurements
are performed. Similar to [R. Gallego et al., Phys. Rev. Lett. 109, 070401
(2013)] our approach is operational, i.e. the task is to identify the set of
allowed operations in sequential correlation scenarios and define nonlocality
as the resource that cannot be created by these operations. This leads to a
characterisation of sequential nonlocality that contains as particular cases
standard nonlocality and hidden nonlocality.Comment: 13 pages, 3 figure
Robustness of Device Independent Dimension Witnesses
Device independent dimension witnesses provide a lower bound on the
dimensionality of classical and quantum systems in a "black box" scenario where
only correlations between preparations, measurements and outcomes are
considered. We address the problem of the robustness of dimension witnesses,
namely that to witness the dimension of a system or to discriminate between its
quantum or classical nature, even in the presence of loss. We consider the case
when shared randomness is allowed between preparations and measurements and we
provide a threshold in the detection efficiency such that dimension witnessing
can still be performed.Comment: 8 pages, 5 figures, published versio
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