401 research outputs found
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
Two-setting Bell Inequalities for Graph States
We present Bell inequalities for graph states with high violation of local
realism. In particular, we show that there is a two-setting Bell inequality for
every nontrivial graph state which is violated by the state at least by a
factor of two. These inequalities are facets of the convex polytope containing
the many-body correlations consistent with local hidden variable models. We
first present a method which assigns a Bell inequality for each graph vertex.
Then for some families of graph states composite Bell inequalities can be
constructed with a violation of local realism increasing exponentially with the
number of qubits. We also suggest a systematic way for obtaining Bell
inequalities with a high violation of local realism for arbitrary graphs.Comment: 8 pages including 2 figures, revtex4; minor change
Multipartite entanglement percolation
We present percolation strategies based on multipartite measurements to
propagate entanglement in quantum networks. We consider networks spanned on
regular lattices whose bonds correspond to pure but non-maximally entangled
pairs of qubits, with any quantum operation allowed at the nodes. Despite
significant effort in the past, improvements over naive (classical) percolation
strategies have been found for only few lattices, often with restrictions on
the initial amount of entanglement in the bonds. In contrast, multipartite
entanglement percolation outperform the classical percolation protocols, as
well as all previously known quantum ones, over the entire range of initial
entanglement and for every lattice that we considered.Comment: revtex4, 4 page
Grothendieck's constant and local models for noisy entangled quantum states
We relate the nonlocal properties of noisy entangled states to Grothendieck's
constant, a mathematical constant appearing in Banach space theory. For
two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show
that there is a local model for projective measurements if and only if , where is Grothendieck's constant of order 3. Known bounds
on prove the existence of this model at least for ,
quite close to the current region of Bell violation, . We
generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur
All quantum states useful for teleportation are nonlocal resources
Understanding the relation between the different forms of inseparability in
quantum mechanics is a longstanding problem in the foundations of quantum
theory and has implications for quantum information processing. Here we make
progress in this direction by establishing a direct link between quantum
teleportation and Bell nonlocality. In particular, we show that all entangled
states which are useful for teleportation are nonlocal resources, i.e. lead to
deterministic violation of Bell's inequality. Our result exploits the
phenomenon of super-activation of quantum nonlocality, recently proved by
Palazuelos, and suggests that the latter might in fact be generic.Comment: 4 pages. v2: Title and abstract changed, presentation improved,
references updated, same result
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
Multipartite fully-nonlocal quantum states
We present a general method to characterize the quantum correlations obtained
after local measurements on multipartite systems. Sufficient conditions for a
quantum system to be fully-nonlocal according to a given partition, as well as
being (genuinely) multipartite fully-nonlocal, are derived. These conditions
allow us to identify all completely-connected graph states as multipartite
fully-nonlocal quantum states. Moreover, we show that this feature can also be
observed in mixed states: the tensor product of five copies of the Smolin
state, a biseparable and bound entangled state, is multipartite fully-nonlocal.Comment: 5 pages, 1 figure. Version published in PRA. Note that it does not
contain all the results from the previous version; these will be included in
a later, more general, pape
The landscape of quantum transitions driven by single-qubit unitary transformations with implications for entanglement
This paper considers the control landscape of quantum transitions in
multi-qubit systems driven by unitary transformations with single-qubit
interaction terms. The two-qubit case is fully analyzed to reveal the features
of the landscape including the nature of the absolute maximum and minimum, the
saddle points and the absence of traps. The results permit calculating the
Schmidt state starting from an arbitrary two-qubit state following the local
gradient flow. The analysis of multi-qubit systems is more challenging, but the
generalized Schmidt states may also be located by following the local gradient
flow. Finally, we show the relation between the generalized Schmidt states and
the entanglement measure based on the Bures distance
Unbounded randomness certification using sequences of measurements
Unpredictability, or randomness, of the outcomes of measurements made on an
entangled state can be certified provided that the statistics violate a Bell
inequality. In the standard Bell scenario where each party performs a single
measurement on its share of the system, only a finite amount of randomness, of
at most bits, can be certified from a pair of entangled particles
of dimension . Our work shows that this fundamental limitation can be
overcome using sequences of (nonprojective) measurements on the same system.
More precisely, we prove that one can certify any amount of random bits from a
pair of qubits in a pure state as the resource, even if it is arbitrarily
weakly entangled. In addition, this certification is achieved by near-maximal
violation of a particular Bell inequality for each measurement in the sequence.Comment: 4 + 5 pages (1 + 3 images), published versio
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