177 research outputs found
No-go theorems for \psi-epistemic models based on a continuity assumption
The quantum state \psi is a mathematical object used to determine the
probabilities of different outcomes when measuring a physical system. Its
fundamental nature has been the subject of discussions since the inception of
quantum theory: is it ontic, that is, does it correspond to a real property of
the physical system? Or is it epistemic, that is, does it merely represent our
knowledge about the system? Assuming a natural continuity assumption and a weak
separability assumption, we show here that epistemic interpretations of the
quantum state are in contradiction with quantum theory. Our argument is
different from the recent proof of Pusey, Barrett, and Rudolph and it already
yields a non-trivial constraint on \psi-epistemic models using a single copy of
the system in question.Comment: Version 1 contains both theory and an illustrative experiment.
Version 2 contains only the theory (the experiment with expanded discussion
will be posted separatly at a later date). The main novelty of Version 2 is a
detailed comparison in appendix 2 with L. Hardy arXiv:1205.14396. Version 2
is 6 pages of text and 1 figure; v3: minor change
Using complete measurement statistics for optimal device-independent randomness evaluation
The majority of recent works investigating the link between non-locality and
randomness, e.g. in the context of device-independent cryptography, do so with
respect to some specific Bell inequality, usually the CHSH inequality. However,
the joint probabilities characterizing the measurement outcomes of a Bell test
are richer than just the degree of violation of a single Bell inequality. In
this work we show how to take this extra information into account in a
systematic manner in order to optimally evaluate the randomness that can be
certified from non-local correlations. We further show that taking into account
the complete set of outcome probabilities is equivalent to optimizing over all
possible Bell inequalities, thereby allowing us to determine the optimal Bell
inequality for certifying the maximal amount of randomness from a given set of
non-local correlations.Comment: 12 pages, 4 figures. v2, v3, v4: minor corrections. See also the
related independent work arXiv:1309.389
Characterizing the nonlocal correlations of particles that never interacted
Quantum systems that have never interacted can become nonlocally correlated
through a process called entanglement swapping. To characterize nonlocality in
this context, we introduce local models where quantum systems that are
initially uncorrelated are described by uncorrelated local variables. While a
pair of maximally entangled qubits prepared in the usual way (i.e., emitted
from a common source) requires a visibility close to 70% to violate a Bell
inequality, we show that an entangled pair generated through entanglement
swapping will already violate a Bell inequality for visibilities as low as 50%
under our assumption.Comment: 5 pages, 2 figure
Looking for symmetric Bell inequalities
Finding all Bell inequalities for a given number of parties, measurement
settings, and measurement outcomes is in general a computationally hard task.
We show that all Bell inequalities which are symmetric under the exchange of
parties can be found by examining a symmetrized polytope which is simpler than
the full Bell polytope. As an illustration of our method, we generate 238885
new Bell inequalities and 1085 new Svetlichny inequalities. We find, in
particular, facet inequalities for Bell experiments involving two parties and
two measurement settings that are not of the
Collins-Gisin-Linden-Massar-Popescu type.Comment: Joined the associated website as an ancillary file, 17 pages, 1
figure, 1 tabl
A paradox in bosonic energy computations via semidefinite programming relaxations
We show that the recent hierarchy of semidefinite programming relaxations
based on non-commutative polynomial optimization and reduced density matrix
variational methods exhibits an interesting paradox when applied to the bosonic
case: even though it can be rigorously proven that the hierarchy collapses
after the first step, numerical implementations of higher order steps generate
a sequence of improving lower bounds that converges to the optimal solution. We
analyze this effect and compare it with similar behavior observed in
implementations of semidefinite programming relaxations for commutative
polynomial minimization. We conclude that the method converges due to the
rounding errors occurring during the execution of the numerical program, and
show that convergence is lost as soon as computer precision is incremented. We
support this conclusion by proving that for any element p of a Weyl algebra
which is non-negative in the Schrodinger representation there exists another
element p' arbitrarily close to p that admits a sum of squares decomposition.Comment: 22 pages, 4 figure
Bilocal versus non-bilocal correlations in entanglement swapping experiments
Entanglement swapping is a process by which two initially independent quantum
systems can become entangled and generate nonlocal correlations. To
characterize such correlations, we compare them to those predicted by bilocal
models, where systems that are initially independent are described by
uncorrelated states. We extend in this paper the analysis of bilocal
correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular,
we derive new Bell-type inequalities based on the bilocality assumption in
different scenarios, we study their possible quantum violations, and analyze
their resistance to experimental imperfections. The bilocality assumption,
being stronger than Bell's standard local causality assumption, lowers the
requirements for the demonstration of quantumness in entanglement swapping
experiments
Lifting Bell inequalities
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings, or measurement outcomes. In this article, such "liftings" of Bell inequalities are studied. It is shown that if the original inequality defines a facet of the polytope of local joint outcome probabilities then the lifted one also defines a facet of the more complex polytope
Efficient quantum key distribution secure against no-signalling eavesdroppers
By carrying out measurements on entangled states, two parties can generate a
secret key which is secure not only against an eavesdropper bound by the laws
of quantum mechanics, but also against a hypothetical "post-quantum"
eavesdroppers limited by the no-signalling principle only. We introduce a
family of quantum key distribution protocols of this type, which are more
efficient than previous ones, both in terms of key rate and noise resistance.
Interestingly, the best protocols involve large number of measurements. We show
that in the absence of noise, these protocols can yield one secret bit per
entanglement bit, implying that the key rates in the no-signalling post-quantum
scenario are comparable to the key rates in usual quantum key distribution.Comment: 11 pages, 2 color figures. v2: minor modifications, added references,
added note on the relation to quant-ph/060604
Guess your neighbour's input: a multipartite non-local game with no quantum advantage
We present a multipartite nonlocal game in which each player must guess the
input received by his neighbour. We show that quantum correlations do not
perform better than classical ones at this game, for any prior distribution of
the inputs. There exist, however, input distributions for which general
no-signalling correlations can outperform classical and quantum correlations.
Some of the Bell inequalities associated to our construction correspond to
facets of the local polytope. Thus our multipartite game identifies parts of
the boundary between quantum and post-quantum correlations of maximal
dimension. These results suggest that quantum correlations might obey a
generalization of the usual no-signalling conditions in a multipartite setting.Comment: 4+3 pages; 1 figur
Robust Randomness Amplifiers: Upper and Lower Bounds
A recent sequence of works, initially motivated by the study of the nonlocal
properties of entanglement, demonstrate that a source of
information-theoretically certified randomness can be constructed based only on
two simple assumptions: the prior existence of a short random seed and the
ability to ensure that two black-box devices do not communicate (i.e. are
non-signaling). We call protocols achieving such certified amplification of a
short random seed randomness amplifiers.
We introduce a simple framework in which we initiate the systematic study of
the possibilities and limitations of randomness amplifiers. Our main results
include a new, improved analysis of a robust randomness amplifier with
exponential expansion, as well as the first upper bounds on the maximum
expansion achievable by a broad class of randomness amplifiers. In particular,
we show that non-adaptive randomness amplifiers that are robust to noise cannot
achieve more than doubly exponential expansion. Finally, we show that a wide
class of protocols based on the use of the CHSH game can only lead to (singly)
exponential expansion if adversarial devices are allowed the full power of
non-signaling strategies. Our upper bound results apply to all known
non-adaptive randomness amplifier constructions to date.Comment: 28 pages. Comments welcom
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