1,529 research outputs found
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
Unitary Complexity and the Uhlmann Transformation Problem
State transformation problems such as compressing quantum information or
breaking quantum commitments are fundamental quantum tasks. However, their
computational difficulty cannot easily be characterized using traditional
complexity theory, which focuses on tasks with classical inputs and outputs.
To study the complexity of such state transformation tasks, we introduce a
framework for unitary synthesis problems, including notions of reductions and
unitary complexity classes. We use this framework to study the complexity of
transforming one entangled state into another via local operations. We
formalize this as the Uhlmann Transformation Problem, an algorithmic version of
Uhlmann's theorem. Then, we prove structural results relating the complexity of
the Uhlmann Transformation Problem, polynomial space quantum computation, and
zero knowledge protocols.
The Uhlmann Transformation Problem allows us to characterize the complexity
of a variety of tasks in quantum information processing, including decoding
noisy quantum channels, breaking falsifiable quantum cryptographic assumptions,
implementing optimal prover strategies in quantum interactive proofs, and
decoding the Hawking radiation of black holes. Our framework for unitary
complexity thus provides new avenues for studying the computational complexity
of many natural quantum information processing tasks.Comment: 126 pages, comments welcom
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
A Resource Framework for Quantum Shannon Theory
Quantum Shannon theory is loosely defined as a collection of coding theorems,
such as classical and quantum source compression, noisy channel coding
theorems, entanglement distillation, etc., which characterize asymptotic
properties of quantum and classical channels and states. In this paper we
advocate a unified approach to an important class of problems in quantum
Shannon theory, consisting of those that are bipartite, unidirectional and
memoryless.
We formalize two principles that have long been tacitly understood. First, we
describe how the Church of the larger Hilbert space allows us to move flexibly
between states, channels, ensembles and their purifications. Second, we
introduce finite and asymptotic (quantum) information processing resources as
the basic objects of quantum Shannon theory and recast the protocols used in
direct coding theorems as inequalities between resources. We develop the rules
of a resource calculus which allows us to manipulate and combine resource
inequalities. This framework simplifies many coding theorem proofs and provides
structural insights into the logical dependencies among coding theorems.
We review the above-mentioned basic coding results and show how a subset of
them can be unified into a family of related resource inequalities. Finally, we
use this family to find optimal trade-off curves for all protocols involving
one noisy quantum resource and two noiseless ones.Comment: 60 page
Reference frames, superselection rules, and quantum information
Recently, there has been much interest in a new kind of ``unspeakable''
quantum information that stands to regular quantum information in the same way
that a direction in space or a moment in time stands to a classical bit string:
the former can only be encoded using particular degrees of freedom while the
latter are indifferent to the physical nature of the information carriers. The
problem of correlating distant reference frames, of which aligning Cartesian
axes and synchronizing clocks are important instances, is an example of a task
that requires the exchange of unspeakable information and for which it is
interesting to determine the fundamental quantum limit of efficiency. There
have also been many investigations into the information theory that is
appropriate for parties that lack reference frames or that lack correlation
between their reference frames, restrictions that result in global and local
superselection rules. In the presence of these, quantum unspeakable information
becomes a new kind of resource that can be manipulated, depleted, quantified,
etcetera. Methods have also been developed to contend with these restrictions
using relational encodings, particularly in the context of computation,
cryptography, communication, and the manipulation of entanglement. This article
reviews the role of reference frames and superselection rules in the theory of
quantum information processing.Comment: 55 pages, published versio
- …