67 research outputs found
Universal bound on the cardinality of local hidden variables in networks
We present an algebraic description of the sets of local correlations in
arbitrary networks, when the parties have finite inputs and outputs. We
consider networks generalizing the usual Bell scenarios by the presence of
multiple uncorrelated sources. We prove a finite upper bound on the cardinality
of the value sets of the local hidden variables. Consequently, we find that the
sets of local correlations are connected, closed and semialgebraic, and bounded
by tight polynomial Bell-like inequalities.Comment: 5 pages + 6 pages appendix, 2 figures, comments welcom
Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
We present a technique for reducing the computational requirements by several
orders of magnitude in the evaluation of semidefinite relaxations for bounding
the set of quantum correlations arising from finite-dimensional Hilbert spaces.
The technique, which we make publicly available through a user-friendly
software package, relies on the exploitation of symmetries present in the
optimisation problem to reduce the number of variables and the block sizes in
semidefinite relaxations. It is widely applicable in problems encountered in
quantum information theory and enables computations that were previously too
demanding. We demonstrate its advantages and general applicability in several
physical problems. In particular, we use it to robustly certify the
non-projectiveness of high-dimensional measurements in a black-box scenario
based on self-tests of -dimensional symmetric informationally complete
POVMs.Comment: A. T. and D. R. contributed equally for this projec
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
Possibilistic approach to network nonlocality
The investigation of Bell nonlocality traditionally relies on joint
probabilities of observing certain measurement outcomes. In this work we
explore a possibilistic approach, where only patterns of possible outcomes
matter, and apply it to Bell nonlocality in networks with independent sources.
We present various algorithms for determining whether a given outcome pattern
can be achieved via classical resources or via non-signaling resources. Next we
illustrate these methods considering the triangle and square networks (with
binary outputs and no inputs), identifying patterns that are incompatible with
the network structure, as well as patterns that imply nonlocality. In
particular, we obtain an example of quantum nonlocality in the square network
with binary outcomes. Moreover, we show how to construct certificates for
detecting the nonlocality of a certain pattern, in the form of nonlinear
Bell-type inequalities involving joint probabilities. Finally, we show that
these inequalities remain valid in the case where the sources in the network
become partially correlated.Comment: 17 pages, lots of figures, comments welcom
The type-independent resource theory of local operations and shared randomness
In space-like separated experiments and other scenarios where multiple
parties share a classical common cause but no cause-effect relations, quantum
theory allows a variety of nonsignaling resources which are useful for
distributed quantum information processing. These include quantum states,
nonlocal boxes, steering assemblages, teleportages, channel steering
assemblages, and so on. Such resources are often studied using nonlocal games,
semiquantum games, entanglement-witnesses, teleportation experiments, and
similar tasks. We introduce a unifying framework which subsumes the full range
of nonsignaling resources, as well as the games and experiments which probe
them, into a common resource theory: that of local operations and shared
randomness (LOSR). Crucially, we allow these LOSR operations to locally change
the type of a resource, so that players can convert resources of any type into
resources of any other type, and in particular into strategies for the specific
type of game they are playing. We then prove several theorems relating
resources and games of different types. These theorems generalize a number of
seminal results from the literature, and can be applied to lessen the
assumptions needed to characterize the nonclassicality of resources. As just
one example, we prove that semiquantum games are able to perfectly characterize
the LOSR nonclassicality of every resource of any type (not just quantum
states, as was previously shown). As a consequence, we show that any resource
can be characterized in a measurement-device-independent manner.Comment: 14 pages, 7 figures. Comments welcome
Nonlinear Bell inequalities tailored for quantum networks
In a quantum network, distant observers sharing physical resources emitted by
independent sources can establish strong correlations, which defy any classical
explanation in terms of local variables. We discuss the characterization of
nonlocal correlations in such a situation, when compared to those that can be
generated in networks distributing independent local variables. We present an
iterative procedure for constructing Bell inequalities tailored for networks:
starting from a given network, and a corresponding Bell inequality, our
technique provides new Bell inequalities for a more complex network, involving
one additional source and one additional observer. The relevance of our method
is illustrated on a variety of networks, for which we demonstrate significant
quantum violations.Comment: 8 pages, 2 figures. Comments welcom
Device-independent point estimation from finite data and its application to device-independent property estimation
The device-independent approach to physics is one where conclusions are drawn
directly from the observed correlations between measurement outcomes. In
quantum information, this approach allows one to make strong statements about
the properties of the underlying systems or devices solely via the observation
of Bell-inequality-violating correlations. However, since one can only perform
a {\em finite number} of experimental trials, statistical fluctuations
necessarily accompany any estimation of these correlations. Consequently, an
important gap remains between the many theoretical tools developed for the
asymptotic scenario and the experimentally obtained raw data. In particular, a
physical and concurrently practical way to estimate the underlying quantum
distribution has so far remained elusive. Here, we show that the natural
analogs of the maximum-likelihood estimation technique and the
least-square-error estimation technique in the device-independent context
result in point estimates of the true distribution that are physical, unique,
computationally tractable and consistent. They thus serve as sound algorithmic
tools allowing one to bridge the aforementioned gap. As an application, we
demonstrate how such estimates of the underlying quantum distribution can be
used to provide, in certain cases, trustworthy estimates of the amount of
entanglement present in the measured system. In stark contrast to existing
approaches to device-independent parameter estimations, our estimation does not
require the prior knowledge of {\em any} Bell inequality tailored for the
specific property and the specific distribution of interest.Comment: Essentially published version, but with the typo in Eq. (E5)
correcte
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