39,711 research outputs found
Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation
Quantum correlations have fundamental and technological interest, and hence
many measures have been introduced to quantify them. Some hierarchical
orderings of these measures have been established, e.g., discord is bigger than
entanglement, and we present a class of bipartite states, called premeasurement
states, for which several of these hierarchies collapse to a single value.
Because premeasurement states are the kind of states produced when a system
interacts with a measurement device, the hierarchy collapse implies that the
uncertainty of an observable is quantitatively connected to the quantum
correlations (entanglement, discord, etc.) produced when that observable is
measured. This fascinating connection between uncertainty and quantum
correlations leads to a reinterpretation of entropic formulations of the
uncertainty principle, so-called entropic uncertainty relations, including ones
that allow for quantum memory. These relations can be thought of as
lower-bounds on the entanglement created when incompatible observables are
measured. Hence, we find that entanglement creation exhibits complementarity, a
concept that should encourage exploration into "entanglement complementarity
relations".Comment: 19 pages, 2 figures. Added Figure 1 and various remarks to improve
clarity of presentatio
A Tight High-Order Entropic Quantum Uncertainty Relation With Applications
We derive a new entropic quantum uncertainty relation involving min-entropy.
The relation is tight and can be applied in various quantum-cryptographic
settings.
Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit
Commitment are presented and the uncertainty relation is used to prove the
security of these protocols in the bounded quantum-storage model according to
new strong security definitions.
As another application, we consider the realistic setting of Quantum Key
Distribution (QKD) against quantum-memory-bounded eavesdroppers. The
uncertainty relation allows to prove the security of QKD protocols in this
setting while tolerating considerably higher error rates compared to the
standard model with unbounded adversaries. For instance, for the six-state
protocol with one-way communication, a bit-flip error rate of up to 17% can be
tolerated (compared to 13% in the standard model).
Our uncertainty relation also yields a lower bound on the min-entropy key
uncertainty against known-plaintext attacks when quantum ciphers are composed.
Previously, the key uncertainty of these ciphers was only known with respect to
Shannon entropy.Comment: 21 pages; editorial changes, additional applicatio
State-Dependent Approach to Entropic Measurement-Disturbance Relations
Heisenberg's intuition was that there should be a tradeoff between measuring
a particle's position with greater precision and disturbing its momentum.
Recent formulations of this idea have focused on the question of how well two
complementary observables can be jointly measured. Here, we provide an
alternative approach based on how enhancing the predictability of one
observable necessarily disturbs a complementary one. Our
measurement-disturbance relation refers to a clear operational scenario and is
expressed by entropic quantities with clear statistical meaning. We show that
our relation is perfectly tight for all measurement strengths in an existing
experimental setup involving qubit measurements.Comment: 9 pages, 2 figures. v4: published versio
The Role of Relative Entropy in Quantum Information Theory
Quantum mechanics and information theory are among the most important
scientific discoveries of the last century. Although these two areas initially
developed separately it has emerged that they are in fact intimately related.
In this review I will show how quantum information theory extends traditional
information theory by exploring the limits imposed by quantum, rather than
classical mechanics on information storage and transmission. The derivation of
many key results uniquely differentiates this review from the "usual"
presentation in that they are shown to follow logically from one crucial
property of relative entropy. Within the review optimal bounds on the speed-up
that quantum computers can achieve over their classical counter-parts are
outlined using information theoretic arguments. In addition important
implications of quantum information theory to thermodynamics and quantum
measurement are intermittently discussed. A number of simple examples and
derivations including quantum super-dense coding, quantum teleportation,
Deutsch's and Grover's algorithms are also included.Comment: 40 pages, 11 figure
Controlling entropic uncertainty bound through memory effects
One of the defining traits of quantum mechanics is the uncertainty principle
which was originally expressed in terms of the standard deviation of two
observables. Alternatively, it can be formulated using entropic measures, and
can also be generalized by including a memory particle that is entangled with
the particle to be measured. Here we consider a realistic scenario where the
memory particle is an open system interacting with an external environment.
Through the relation of conditional entropy to mutual information, we provide a
link between memory effects and the rate of change of conditional entropy
controlling the lower bound of the entropic uncertainty relation. Our treatment
reveals that the memory effects stemming from the non-Markovian nature of
quantum dynamical maps directly control the lower bound of the entropic
uncertainty relation in a general way, independently of the specific type of
interaction between the memory particle and its environment.Comment: 5 pages, 3 figure
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
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