19 research outputs found
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
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
Quantum networks reveal quantum nonlocality
The results of local measurements on some composite quantum systems cannot be
reproduced classically. This impossibility, known as quantum nonlocality,
represents a milestone in the foundations of quantum theory. Quantum
nonlocality is also a valuable resource for information processing tasks, e.g.
quantum communication, quantum key distribution, quantum state estimation, or
randomness extraction. Still, deciding if a quantum state is nonlocal remains a
challenging problem. Here we introduce a novel approach to this question: we
study the nonlocal properties of quantum states when distributed and measured
in networks. Using our framework, we show how any one-way entanglement
distillable state leads to nonlocal correlations. Then, we prove that
nonlocality is a non-additive resource, which can be activated. There exist
states, local at the single-copy level, that become nonlocal when taking
several copies of it. Our results imply that the nonlocality of quantum states
strongly depends on the measurement context.Comment: 4 + 3 pages, 4 figure
Random Numbers Certified by Bell's Theorem
Randomness is a fundamental feature in nature and a valuable resource for
applications ranging from cryptography and gambling to numerical simulation of
physical and biological systems. Random numbers, however, are difficult to
characterize mathematically, and their generation must rely on an unpredictable
physical process. Inaccuracies in the theoretical modelling of such processes
or failures of the devices, possibly due to adversarial attacks, limit the
reliability of random number generators in ways that are difficult to control
and detect. Here, inspired by earlier work on nonlocality based and device
independent quantum information processing, we show that the nonlocal
correlations of entangled quantum particles can be used to certify the presence
of genuine randomness. It is thereby possible to design of a new type of
cryptographically secure random number generator which does not require any
assumption on the internal working of the devices. This strong form of
randomness generation is impossible classically and possible in quantum systems
only if certified by a Bell inequality violation. We carry out a
proof-of-concept demonstration of this proposal in a system of two entangled
atoms separated by approximately 1 meter. The observed Bell inequality
violation, featuring near-perfect detection efficiency, guarantees that 42 new
random numbers are generated with 99% confidence. Our results lay the
groundwork for future device-independent quantum information experiments and
for addressing fundamental issues raised by the intrinsic randomness of quantum
theory.Comment: 10 pages, 3 figures, 16 page appendix. Version as close as possible
to the published version following the terms of the journa
Quantum Tasks in Minkowski Space
The fundamental properties of quantum information and its applications to
computing and cryptography have been greatly illuminated by considering
information-theoretic tasks that are provably possible or impossible within
non-relativistic quantum mechanics. I describe here a general framework for
defining tasks within (special) relativistic quantum theory and illustrate it
with examples from relativistic quantum cryptography and relativistic
distributed quantum computation. The framework gives a unified description of
all tasks previously considered and also defines a large class of new questions
about the properties of quantum information in relation to Minkowski causality.
It offers a way of exploring interesting new fundamental tasks and
applications, and also highlights the scope for a more systematic understanding
of the fundamental information-theoretic properties of relativistic quantum
theory
A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
We are interested in the problem of characterizing the correlations that
arise when performing local measurements on separate quantum systems. In a
previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite
hierarchy of conditions necessarily satisfied by any set of quantum
correlations. Each of these conditions could be tested using semidefinite
programming. We present here new results concerning this hierarchy. We prove in
particular that it is complete, in the sense that any set of correlations
satisfying every condition in the hierarchy has a quantum representation in
terms of commuting measurements. Although our tests are conceived to rule out
non-quantum correlations, and can in principle certify that a set of
correlations is quantum only in the asymptotic limit where all tests are
satisfied, we show that in some cases it is possible to conclude that a given
set of correlations is quantum after performing only a finite number of tests.
We provide a criterion to detect when such a situation arises, and we explain
how to reconstruct the quantum states and measurement operators reproducing the
given correlations. Finally, we present several applications of our approach.
We use it in particular to bound the quantum violation of various Bell
inequalities.Comment: 33 pages, 2 figure
Semi-device-independent QKD Based on BB84 and a CHSH-Type Estimation
Device-independent quantum key distribution (QKD) aims to certify the security of a cryptographic key generated between two parties based only on the violation of a Bell inequality. This strongest possible form of QKD requires the manipulation of entanglement, and is thus impossible to implement in a one-way ("prepare and measure") scheme. Here, we introduce a semi-device-independent QKD scheme in the prepare-and-measure configuration where the only assumption is a bound on the dimension of the Hilbert space, and prove its security against collective attacks. Our scheme can be understood as a modification of the original BB84 protocol where an extra CHSH-type estimation is carried out by Bob on the qubits sent by Alice. © Springer-Verlag Berlin Heidelberg 2013.SCOPUS: cp.kinfo:eu-repo/semantics/publishe