743 research outputs found
Teleportation, Braid Group and Temperley--Lieb Algebra
We explore algebraic and topological structures underlying the quantum
teleportation phenomena by applying the braid group and Temperley--Lieb
algebra. We realize the braid teleportation configuration, teleportation
swapping and virtual braid representation in the standard description of the
teleportation. We devise diagrammatic rules for quantum circuits involving
maximally entangled states and apply them to three sorts of descriptions of the
teleportation: the transfer operator, quantum measurements and characteristic
equations, and further propose the Temperley--Lieb algebra under local unitary
transformations to be a mathematical structure underlying the teleportation. We
compare our diagrammatical approach with two known recipes to the quantum
information flow: the teleportation topology and strongly compact closed
category, in order to explain our diagrammatic rules to be a natural
diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version
of the preprint, quant-ph/0601050, which includes details of calculation,
more topics such as topological diagrammatical operations and entanglement
swapping, and calls the Temperley--Lieb category for the collection of all
the Temperley--Lieb algebra with physical operations like local unitary
transformation
Quasi-probability representations of quantum theory with applications to quantum information science
This article comprises a review of both the quasi-probability representations
of infinite-dimensional quantum theory (including the Wigner function) and the
more recently defined quasi-probability representations of finite-dimensional
quantum theory. We focus on both the characteristics and applications of these
representations with an emphasis toward quantum information theory. We discuss
the recently proposed unification of the set of possible quasi-probability
representations via frame theory and then discuss the practical relevance of
negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde
Tight quantum teleportation without a shared reference frame
We present a new scheme for teleporting a quantum state between two parties
whose local reference frames are misaligned by the action of a finite symmetry
group. Unlike other proposals, our scheme requires the same amount of classical
communication and entangled resources as conventional teleportation, does not
reveal any reference frame information, and is robust against changes in
reference frame alignment while the protocol is underway. The mathematical
foundation of our scheme is a unitary error basis which is permuted up to a
phase by the conjugation action of the group. We completely classify such
unitary error bases for qubits, exhibit constructions in higher dimension, and
provide a method for proving nonexistence in some cases.Comment: Clarified exposition and added extra figures. 24 pages, 5 figure
Quantum entanglement theory in the presence of superselection rules
Superselection rules severly constrain the operations which can be
implemented on a distributed quantum system. While the restriction to local
operations and classical communication gives rise to entanglement as a nonlocal
resource, particle number conservation additionally confines the possible
operations and should give rise to a new resource. In [Phys. Rev. Lett. 92,
087904 (2004), quant-ph/0310124] we showed that this resource can be quantified
by a single additional number, the superselection induced variance (SiV)
without changing the concept of entanglement. In this paper, we give the
results on pure states in greater detail; additionally, we provide a discussion
of mixed state nonlocality with superselection rules where we consider both
formation and distillation. Finally, we demonstrate that SiV is indeed a
resource, i.e., that it captures how well a state can be used to overcome the
restrictions imposed by the superselection rule.Comment: 16 pages, 5 figure
Quantum Correlations and Quantum Non-Locality: A Review and a Few New Ideas
In this paper we make an extensive description of quantum non-locality, one
of the most intriguing and fascinating facets of quantum mechanics. After a
general presentation of several studies on this subject, we consider if quantum
non-locality, and the friction it carries with special relativity, can
eventually find a "solution" by considering higher dimensional spaces.Comment: 1
Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies
We present a framework for relativistic quantum metrology that is useful for
both Earth-based and space-based technologies. Quantum metrology has been so
far successfully applied to design precision instruments such as clocks and
sensors which outperform classical devices by exploiting quantum properties.
There are advanced plans to implement these and other quantum technologies in
space, for instance Space-QUEST and Space Optical Clock projects intend to
implement quantum communications and quantum clocks at regimes where relativity
starts to kick in. However, typical setups do not take into account the effects
of relativity on quantum properties. To include and exploit these effects, we
introduce techniques for the application of metrology to quantum field theory.
Quantum field theory properly incorporates quantum theory and relativity, in
particular, at regimes where space-based experiments take place. This framework
allows for high precision estimation of parameters that appear in quantum field
theory including proper times and accelerations. Indeed, the techniques can be
applied to develop a novel generation of relativistic quantum technologies for
gravimeters, clocks and sensors. As an example, we present a high precision
device which in principle improves the state-of-the-art in quantum
accelerometers by exploiting relativistic effects.Comment: 7 pages, 2 figures. I. F. previously published under I.
Fuentes-Schuller and I. Fuentes-Guridi. v2: minor changes, published versio
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