14,845 research outputs found
Tight steering inequalities from generalized entropic uncertainty relations
We establish a general connection between entropic uncertainty relations,
Einstein-Podolsky-Rosen steering, and joint measurability. Specifically, we
construct steering inequalities from any entropic uncertainty relation, given
that the latter satisfies two natural properties. We obtain steering
inequalities based on R\'enyi entropies. These turn out to be tight in many
scenarios, using max- and min-entropy. Considering steering tests with two
noisy measurements, our inequalities exactly recover the noise threshold for
steerability. This is the case for any pair of qubit 2-outcome measurements, as
well as for pairs of mutually unbiased bases in any dimension. This shows that
easy-to-evaluate quantities such as entropy can optimally witness steering,
despite the fact that they are coarse-grained representations of the underlying
statistics
Quantum to Classical Randomness Extractors
The goal of randomness extraction is to distill (almost) perfect randomness
from a weak source of randomness. When the source yields a classical string X,
many extractor constructions are known. Yet, when considering a physical
randomness source, X is itself ultimately the result of a measurement on an
underlying quantum system. When characterizing the power of a source to supply
randomness it is hence a natural question to ask, how much classical randomness
we can extract from a quantum system. To tackle this question we here take on
the study of quantum-to-classical randomness extractors (QC-extractors). We
provide constructions of QC-extractors based on measurements in a full set of
mutually unbiased bases (MUBs), and certain single qubit measurements. As the
first application, we show that any QC-extractor gives rise to entropic
uncertainty relations with respect to quantum side information. Such relations
were previously only known for two measurements. As the second application, we
resolve the central open question in the noisy-storage model [Wehner et al.,
PRL 100, 220502 (2008)] by linking security to the quantum capacity of the
adversary's storage device.Comment: 6+31 pages, 2 tables, 1 figure, v2: improved converse parameters,
typos corrected, new discussion, v3: new reference
Entropic uncertainty relations - A survey
Uncertainty relations play a central role in quantum mechanics. Entropic
uncertainty relations in particular have gained significant importance within
quantum information, providing the foundation for the security of many quantum
cryptographic protocols. Yet, rather little is known about entropic uncertainty
relations with more than two measurement settings. In this note we review known
results and open questions.Comment: 12 pages, revte
- âŠ