5 research outputs found
Device-Independent Quantum Key Distribution
Cryptographic key exchange protocols traditionally rely on computational
conjectures such as the hardness of prime factorisation to provide security
against eavesdropping attacks. Remarkably, quantum key distribution protocols
like the one proposed by Bennett and Brassard provide information-theoretic
security against such attacks, a much stronger form of security unreachable by
classical means. However, quantum protocols realised so far are subject to a
new class of attacks exploiting implementation defects in the physical devices
involved, as demonstrated in numerous ingenious experiments. Following the
pioneering work of Ekert proposing the use of entanglement to bound an
adversary's information from Bell's theorem, we present here the experimental
realisation of a complete quantum key distribution protocol immune to these
vulnerabilities. We achieve this by combining theoretical developments on
finite-statistics analysis, error correction, and privacy amplification, with
an event-ready scheme enabling the rapid generation of high-fidelity
entanglement between two trapped-ion qubits connected by an optical fibre link.
The secrecy of our key is guaranteed device-independently: it is based on the
validity of quantum theory, and certified by measurement statistics observed
during the experiment. Our result shows that provably secure cryptography with
real-world devices is possible, and paves the way for further quantum
information applications based on the device-independence principle.Comment: 5+1 pages in main text and methods with 4 figures and 1 table; 37
pages of supplementary materia
Universality for Multi-terminal Problems via Spatial Coupling
Consider the problem of designing capacity-achieving codes for multi-terminal communication scenarios. For point-to-point communication problems, one can optimize a single code to approach capacity, but for multi-terminal problems this translates to optimizing a single code to perform well over the entire region of channel parameters. A coding scheme is called universal if it allows reliable communication over the entire achievable region promised by information theory.
It was recently shown that terminated low-density parity-check convolutional codes (also known as spatially-coupled low-density parity-check ensembles) have belief-propagation thresholds that approach their maximum a-posteriori thresholds. This phenomenon, called "threshold saturation via spatial-coupling," was proven for binary erasure channels and then for binary memoryless symmetric channels. This approach provides us with a new paradigm for constructing capacity approaching codes. It was also conjectured that the principle of spatial coupling is very general and that the phenomenon of threshold saturation applies to a very broad class of graphical models.
In this work, we consider a noisy Slepian-Wolf problem (with erasure and binary symmetric channel correlation models) and the binary-input Gaussian multiple access channel, which deal with correlation between sources and interference at the receiver respectively. We derive an area theorem for the joint decoder and empirically show that threshold saturation occurs for these multi-user scenarios. We also show that the outer bound derived using the area theorem is tight for the erasure Slepian-Wolf problem and that this bound is universal for regular LDPC codes with large left degrees. As a result, we demonstrate near-universal performance for these problems using spatially-coupled coding systems