850 research outputs found
Local versus non-local information in quantum information theory: formalism and phenomena
In spite of many results in quantum information theory, the complex nature of
compound systems is far from being clear. In general the information is a
mixture of local, and non-local ("quantum") information. To make this point
more clear, we develop and investigate the quantum information processing
paradigm in which parties sharing a multipartite state distill local
information. The amount of information which is lost because the parties must
use a classical communication channel is the deficit. This scheme can be viewed
as complementary to the notion of distilling entanglement. After reviewing the
paradigm, we show that the upper bound for the deficit is given by the relative
entropy distance to so-called psuedo-classically correlated states; the lower
bound is the relative entropy of entanglement. This implies, in particular,
that any entangled state is informationally nonlocal i.e. has nonzero deficit.
We also apply the paradigm to defining the thermodynamical cost of erasing
entanglement. We show the cost is bounded from below by relative entropy of
entanglement. We demonstrate the existence of several other non-local
phenomena. For example,we prove the existence of a form of non-locality without
entanglement and with distinguishability. We analyze the deficit for several
classes of multipartite pure states and obtain that in contrast to the GHZ
state, the Aharonov state is extremely nonlocal (and in fact can be thought of
as quasi-nonlocalisable). We also show that there do not exist states, for
which the deficit is strictly equal to the whole informational content (bound
local information). We then discuss complementary features of information in
distributed quantum systems. Finally we discuss the physical and theoretical
meaning of the results and pose many open questions.Comment: 35 pages in two column, 4 figure
Quantum entanglement
All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory}. But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy.
This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding. However, it appeared that this new resource is
very complex and difficult to detect. Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure.
This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying. In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations. They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon. A basic role of entanglement
witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended)
presentation, updated references, minor changes, submitted to Rev. Mod. Phys
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
Role of Quantumness of Correlations in Entanglement Resource Theory
Quantum correlations: entanglement and quantumness of correlations are main
resource for quantum information theory. In this chapter it is presented the
scenarios which quantumness of correlations plays an interesting role in
entanglement distillation protocol. By means of Koashi - Winter relation, it is
discussed that quantumness of correlations are related to the irreversibility
of the entanglement distillation protocol. The activation protocol is
introduced, and it is proved that quantumness of correlations can create
distillable entanglement between the system and the measurement apparatus
during a local measurement process.Comment: Full chapter contribution of Advanced Technologies of Quantum Key
Distribution, ISBN 978-953-51-5289-
Limitations on Quantum Key Repeaters
A major application of quantum communication is the distribution of entangled
particles for use in quantum key distribution (QKD). Due to noise in the
communication line, QKD is in practice limited to a distance of a few hundred
kilometres, and can only be extended to longer distances by use of a quantum
repeater, a device which performs entanglement distillation and quantum
teleportation. The existence of noisy entangled states that are undistillable
but nevertheless useful for QKD raises the question of the feasibility of a
quantum key repeater, which would work beyond the limits of entanglement
distillation, hence possibly tolerating higher noise levels than existing
protocols. Here we exhibit fundamental limits on such a device in the form of
bounds on the rate at which it may extract secure key. As a consequence, we
give examples of states suitable for QKD but unsuitable for the most general
quantum key repeater protocol.Comment: 11+38 pages, 4 figures, Statements for exact p-bits weakened as
non-locking bound on measured relative entropy distance contained an erro
Private states, quantum data hiding and the swapping of perfect secrecy
We derive a formal connection between quantum data hiding and quantum
privacy, confirming the intuition behind the construction of bound entangled
states from which secret bits can be extracted. We present three main results.
First, we show how to simplify the class of private states and related states
via reversible local operation and one-way communication. Second, we obtain a
bound on the one-way distillable entanglement of private states in terms of
restricted relative entropy measures, which is tight in many cases and shows
that protocols for one-way distillation of key out of states with low
distillable entanglement lead to the distillation of data hiding states. Third,
we consider the problem of extending the distance of quantum key distribution
with help of intermediate stations. In analogy to the quantum repeater, this
paradigm has been called the quantum key repeater. We show that when extending
private states with one-way communication, the resulting rate is bounded by the
one-way distillable entanglement. In order to swap perfect secrecy it is thus
essentially optimal to use entanglement swapping.Comment: v3 published version, some details of the main proofs have been moved
to the appendix, 21 pages. v2 claims changed from LOCC to one-way LOCC in the
process of correcting a mistake found in v1 (in proof of Lemma 3). v1: 15
pages, 9 figure
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