42 research outputs found
Security of Quantum Key Distribution with entangled quNits
We consider a generalisation of Ekert's entanglement-based quantum
cryptographic protocol where qubits are replaced by quits (i.e.,
N-dimensional systems). In order to study its robustness against optimal
incoherent attacks, we derive the information gained by a potential
eavesdropper during a cloning-based individual attack. In doing so, we
generalize Cerf's formalism for cloning machines and establish the form of the
most general cloning machine that respects all the symmetries of the problem.
We obtain an upper bound on the error rate that guarantees the confidentiality
of quNit generalisations of the Ekert's protocol for qubits.Comment: 15 pages, equation 15 and conclusions corrected the 14th of April
2003, new results adde
Inequalities that test locality in quantum mechanics
Quantum theory violates Bell's inequality, but not to the maximum extent that
is logically possible. We derive inequalities (generalizations of Cirel'son's
inequality) that quantify the upper bound of the violation, both for the
standard formalism and the formalism of generalized observables (POVMs). These
inequalities are quantum analogues of Bell inequalities, and they can be used
to test the quantum version of locality. We discuss the nature of this kind of
locality. We also go into the relation of our results to an argument by Popescu
and Rohrlich (Found. Phys. 24, 379 (1994)) that there is no general connection
between the existence of Cirel'son's bound and locality.Comment: 5 pages, 1 figure; the argument has been made clearer in the revised
version; 1 reference adde
Non-local correlations as an information theoretic resource
It is well known that measurements performed on spatially separated entangled
quantum systems can give rise to correlations that are non-local, in the sense
that a Bell inequality is violated. They cannot, however, be used for
super-luminal signalling. It is also known that it is possible to write down
sets of ``super-quantum'' correlations that are more non-local than is allowed
by quantum mechanics, yet are still non-signalling. Viewed as an information
theoretic resource, super-quantum correlations are very powerful at reducing
the amount of communication needed for distributed computational tasks. An
intriguing question is why quantum mechanics does not allow these more powerful
correlations. We aim to shed light on the range of quantum possibilities by
placing them within a wider context. With this in mind, we investigate the set
of correlations that are constrained only by the no-signalling principle. These
correlations form a polytope, which contains the quantum correlations as a
(proper) subset. We determine the vertices of the no-signalling polytope in the
case that two observers each choose from two possible measurements with d
outcomes. We then consider how interconversions between different sorts of
correlations may be achieved. Finally, we consider some multipartite examples.Comment: Revtex. 12 pages, 6 figure
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
Classifying N-qubit Entanglement via Bell's Inequalities
All the states of N qubits can be classified into N-1 entanglement classes
from 2-entangled to N-entangled (fully entangled) states. Each class of
entangled states is characterized by an entanglement index that depends on the
partition of N. The larger the entanglement index of an state, the more
entangled or the less separable is the state in the sense that a larger maximal
violation of Bell's inequality is attainable for this class of state.Comment: 4 pages, 3 figure
Testing the bounds on quantum probabilities
Bounds on quantum probabilities and expectation values are derived for
experimental setups associated with Bell-type inequalities. In analogy to the
classical bounds, the quantum limits are experimentally testable and therefore
serve as criteria for the validity of quantum mechanics.Comment: 9 pages, Revte
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
Sufficient conditions for three-particle entanglement and their tests in recent experiments
We point out a loophole problem in some recent experimental claims to produce
three-particle entanglement. The problem consists in the question whether
mixtures of two-particle entangled states might suffice to explain the
experimental data.
In an attempt to close this loophole, we review two sufficient conditions
that distinguish between N-particle states in which all N particles are
entangled to each other and states in which only M particles are entangled
(with M<N). It is shown that three recent experiments to obtain three-particle
entangled states (Bouwmeester et al., Pan et al., and Rauschenbeutel et al.) do
not meet these conditions. We conclude that the question whether these
experiments provide confirmation of three-particle entanglement remains
unresolved. We also propose modifications of the experiments that would make
such confirmation feasible.Comment: 16 page
Quadratic Bell inequalities as tests for multipartite entanglement
This letter presents quantum mechanical inequalities which distinguish, for
systems of spin-\half particles (), between fully entangled states
and states in which at most particles are entangled. These inequalities
are stronger than those obtained by Gisin and Bechmann-Pasquinucci [Phys.\
Lett. A {\bf 246}, 1 (1998)] and by Seevinck and Svetlichny [quant-ph/0201046].Comment: 4 pages, including 1 figure. Typo's removed and one proof simplified
in revised versio
A toy model for quantum mechanics
The toy model used by Spekkens [R. Spekkens, Phys. Rev. A 75, 032110 (2007)]
to argue in favor of an epistemic view of quantum mechanics is extended by
generalizing his definition of pure states (i.e. states of maximal knowledge)
and by associating measurements with all pure states. The new toy model does
not allow signaling but, in contrast to the Spekkens model, does violate
Bell-CHSH inequalities. Negative probabilities are found to arise naturally
within the model, and can be used to explain the Bell-CHSH inequality
violations.Comment: in which the author breaks his vow to never use the words "ontic" and
"epistemic" in publi