5,922 research outputs found
Gaussian Quantum Information
The science of quantum information has arisen over the last two decades
centered on the manipulation of individual quanta of information, known as
quantum bits or qubits. Quantum computers, quantum cryptography and quantum
teleportation are among the most celebrated ideas that have emerged from this
new field. It was realized later on that using continuous-variable quantum
information carriers, instead of qubits, constitutes an extremely powerful
alternative approach to quantum information processing. This review focuses on
continuous-variable quantum information processes that rely on any combination
of Gaussian states, Gaussian operations, and Gaussian measurements.
Interestingly, such a restriction to the Gaussian realm comes with various
benefits, since on the theoretical side, simple analytical tools are available
and, on the experimental side, optical components effecting Gaussian processes
are readily available in the laboratory. Yet, Gaussian quantum information
processing opens the way to a wide variety of tasks and applications, including
quantum communication, quantum cryptography, quantum computation, quantum
teleportation, and quantum state and channel discrimination. This review
reports on the state of the art in this field, ranging from the basic
theoretical tools and landmark experimental realizations to the most recent
successful developments.Comment: 51 pages, 7 figures, submitted to Reviews of Modern Physic
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
Non-commutative flux representation for loop quantum gravity
The Hilbert space of loop quantum gravity is usually described in terms of
cylindrical functionals of the gauge connection, the electric fluxes acting as
non-commuting derivation operators. It has long been believed that this
non-commutativity prevents a dual flux (or triad) representation of loop
quantum gravity to exist. We show here, instead, that such a representation can
be explicitly defined, by means of a non-commutative Fourier transform defined
on the loop gravity state space. In this dual representation, flux operators
act by *-multiplication and holonomy operators act by translation. We describe
the gauge invariant dual states and discuss their geometrical meaning. Finally,
we apply the construction to the simpler case of a U(1) gauge group and compare
the resulting flux representation with the triad representation used in loop
quantum cosmology.Comment: 12 pages, matches published versio
A very brief introduction to quantum computing and quantum information theory for mathematicians
This is a very brief introduction to quantum computing and quantum
information theory, primarily aimed at geometers. Beyond basic definitions and
examples, I emphasize aspects of interest to geometers, especially connections
with asymptotic representation theory. Proofs of most statements can be found
in standard references
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