27 research outputs found
Emergence of Quantum Correlations from Non-Locality Swapping
By studying generalized non-signalling theories, the hope is to find out what
makes quantum mechanics so special. In the present paper, we revisit the
paradigmatic model of non-signalling boxes and introduce the concept of a
genuine box. This will allow us to present the first generalized non-signalling
model featuring quantum-like dynamics. In particular, we present the coupler, a
device enabling non-locality swapping, the analogue of quantum entanglement
swapping, as well as teleportation. Remarkably, part of the boundary between
quantum and post-quantum correlations emerges in our study.Comment: 5 pages. 6 figures. Minor Revisions. To appear in PR
An entropic approach to local realism and noncontextuality
For any Bell locality scenario (or Kochen-Specker noncontextuality scenario),
the joint Shannon entropies of local (or noncontextual) models define a convex
cone for which the non-trivial facets are tight entropic Bell (or
contextuality) inequalities. In this paper we explore this entropic approach
and derive tight entropic inequalities for various scenarios. One advantage of
entropic inequalities is that they easily adapt to situations like bilocality
scenarios, which have additional independence requirements that are non-linear
on the level of probabilities, but linear on the level of entropies. Another
advantage is that, despite the nonlinearity, taking detection inefficiencies
into account turns out to be very simple. When joint measurements are conducted
by a single detector only, the detector efficiency for witnessing quantum
contextuality can be arbitrarily low.Comment: 12 pages, 8 figures, minor mistakes correcte
Limitations of entropic inequalities for detecting nonclassicality in the postselected Bell causal structure
Classical and quantum physics impose different constraints on the joint
probability distributions of observed variables in a causal structure. These
differences mean that certain correlations can be certified as non-classical,
which has both foundational and practical importance. Rather than working with
the probability distribution itself, it can instead be convenient to work with
the entropies of the observed variables. In the Bell causal structure with two
inputs and outputs per party, a technique that uses entropic inequalities is
known that can always identify non-classical correlations. Here we consider the
analogue of this technique in the generalization of this scenario to more
outcomes. We identify a family of non-classical correlations in the Bell
scenario with two inputs and three outputs per party whose non-classicality
cannot be detected through the direct analogue of the previous technique. We
also show that use of Tsallis entropy instead of Shannon entropy does not help
in this case. Furthermore, we give evidence that natural extensions of the
technique also do not help. More precisely, our evidence suggests that even if
we allow the observed correlations to be post-processed according to a natural
class of non-classicality non-generating operations, entropic inequalities for
either the Shannon or Tsallis entropies cannot detect the non-classicality, and
hence that entropic inequalities are generally not sufficient to detect
non-classicality in the Bell causal structure. In addition, for the bipartite
Bell scenario with two inputs and three outputs we find the vertex description
of the polytope of non-signalling distributions that satisfy all of the
CHSH-type inequalities, which is one of the main regions of investigation in
this work.Comment: 14+7 pages, 3 figures, v2: new results added and parts of the text
restructured, v3: version accepted for publication (title differs from
published version due to editorial convention
Feasibility of loophole-free nonlocality tests with a single photon
Recently much interest has been directed towards designing setups that
achieve realistic loss thresholds for decisive tests of local realism, in
particular in the optical regime. We analyse the feasibility of such Bell tests
based on a W-state shared between multiple parties, which can be realised for
example by a single photon shared between spatial modes. We develop a general
error model to obtain thresholds on the efficiencies required to violate local
realism, and also consider two concrete optical measurement schemes.Comment: 8 pages, 5 figure
Macrorealism from entropic Leggett-Garg inequalities
We formulate entropic Leggett-Garg inequalities, which place constraints on
the statistical outcomes of temporal correlations of observables. The
information theoretic inequalities are satisfied if macrorealism holds. We show
that the quantum statistics underlying correlations between time-separated spin
component of a quantum rotor mimics that of spin correlations in two spatially
separated spin- particles sharing a state of zero total spin. This brings
forth the violation of the entropic Leggett-Garg inequality by a rotating
quantum spin- system in similar manner as does the entropic Bell inequality
(Phys. Rev. Lett. 61, 662 (1988)) by a pair of spin- particles forming a
composite spin singlet state.Comment: 5 pages, RevTeX, 2 eps figures, Accepted for publication in Phys.
Rev.
Entanglement and non-locality are different resources
Bell's theorem states that, to simulate the correlations created by
measurement on pure entangled quantum states, shared randomness is not enough:
some "non-local" resources are required. It has been demonstrated recently that
all projective measurements on the maximally entangled state of two qubits can
be simulated with a single use of a "non-local machine". We prove that a
strictly larger amount of this non-local resource is required for the
simulation of pure non-maximally entangled states of two qubits
with
.Comment: 8 pages, 3 figure
Secrecy extraction from no-signalling correlations
Quantum cryptography shows that one can guarantee the secrecy of correlation
on the sole basis of the laws of physics, that is without limiting the
computational power of the eavesdropper. The usual security proofs suppose that
the authorized partners, Alice and Bob, have a perfect knowledge and control of
their quantum systems and devices; for instance, they must be sure that the
logical bits have been encoded in true qubits, and not in higher-dimensional
systems. In this paper, we present an approach that circumvents this strong
assumption. We define protocols, both for the case of bits and for generic
-dimensional outcomes, in which the security is guaranteed by the very
structure of the Alice-Bob correlations, under the no-signalling condition. The
idea is that, if the correlations cannot be produced by shared randomness, then
Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes,
on the one hand that the eavesdropper Eve performs only individual attacks
(this is a limitation to be removed in further work), on the other hand that
Eve can distribute any correlation compatible with the no-signalling condition
(in this sense her power is greater than what quantum physics allows). Under
these assumptions, we prove that the protocols defined here allow extracting
secrecy from noisy correlations, when these correlations violate a Bell-type
inequality by a sufficiently large amount. The region, in which secrecy
extraction is possible, extends within the region of correlations achievable by
measurements on entangled quantum states.Comment: 23 pages, 4 figure
Comments on "There is no axiomatic system for the quantum theory"
In a recent paper, Nagata [1] claims to derive inconsistencies from quantum
mechanics. In this paper, we show that the inconsistencies do not come from
quantum mechanics, but from extra assumptions about the reality of observables
Logical independence and quantum randomness
We propose a link between logical independence and quantum physics. We
demonstrate that quantum systems in the eigenstates of Pauli group operators
are capable of encoding mathematical axioms and show that Pauli group quantum
measurements are capable of revealing whether or not a given proposition is
logically dependent on the axiomatic system. Whenever a mathematical
proposition is logically independent of the axioms encoded in the measured
state, the measurement associated with the proposition gives random outcomes.
This allows for an experimental test of logical independence. Conversely, it
also allows for an explanation of the probabilities of random outcomes observed
in Pauli group measurements from logical independence without invoking quantum
theory. The axiomatic systems we study can be completed and are therefore not
subject to Goedel's incompleteness theorem.Comment: 9 pages, 4 figures, published version plus additional experimental
appendi
Quantum Communication between N partners and Bell's inequalities
We consider a family of quantum communication protocols involving
partners. We demonstrate the existence of a link between the security of these
protocols against individual attacks by the eavesdropper, and the violation of
some Bell's inequalities, generalizing the link that was noticed some years ago
for two-partners quantum cryptography. The arguments are independent of the
local hidden variable debate.Comment: 4 pages, 2 figure