164 research outputs found
Entanglement Criteria - Quantum and Topological
This paper gives a criterion for detecting the entanglement of a quantum
state, and uses it to study the relationship between topological and quantum
entanglement. It is fundamental to view topological entanglements such as
braids as entanglement operators and to associate to them unitary operators
that are capable of creating quantum entanglement. The entanglement criterion
is used to explore this connection. The paper discusses non-locality in the
light of this criterion.Comment: 8 pages, LaTeX, to appear in proceedings of Spie Conference, Orlando,
Fla, April 200
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
On a suggestion relating topological and quantum mechanical entanglements
We analyze a recent suggestion \cite{kauffman1,kauffman2} on a possible
relation between topological and quantum mechanical entanglements. We show that
a one to one correspondence does not exist, neither between topologically
linked diagrams and entangled states, nor between braid operators and quantum
entanglers. We also add a new dimension to the question of entangling
properties of unitary operators in general.Comment: RevTex, 7 eps figures, to be published in Phys. Lett. A (2004
Quantum Algebras Associated With Bell States
The antisymmetric solution of the braided Yang--Baxter equation called the
Bell matrix becomes interesting in quantum information theory because it can
generate all Bell states from product states. In this paper, we study the
quantum algebra through the FRT construction of the Bell matrix. In its four
dimensional representations via the coproduct of its two dimensional
representations, we find algebraic structures including a composition series
and a direct sum of its two dimensional representations to characterize this
quantum algebra. We also present the quantum algebra using the FRT construction
of Yang--Baxterization of the Bell matrix.Comment: v1: 15 pages, 2 figures, latex; v2: 18 pages, 2 figures, latex,
references and notes adde
Experimental realization of the Yang-Baxter Equation via NMR interferometry
The Yang-Baxter equation is an important tool in theoretical physics, with
many applications in different domains that span from condensed matter to
string theory. Recently, the interest on the equation has increased due to its
connection to quantum information processing. It has been shown that the
Yang-Baxter equation is closely related to quantum entanglement and quantum
computation. Therefore, owing to the broad relevance of this equation, besides
theoretical studies, it also became significant to pursue its experimental
implementation. Here, we show an experimental realization of the Yang-Baxter
equation and verify its validity through a Nuclear Magnetic Resonance (NMR)
interferometric setup. Our experiment was performed on a liquid state
Iodotrifluoroethylene sample which contains molecules with three qubits. We use
Controlled-transfer gates that allow us to build a pseudo-pure state from which
we are able to apply a quantum information protocol that implements the
Yang-Baxter equation.Comment: 10 pages and 6 figure
Towards topological quantum computer
One of the principal obstacles on the way to quantum computers is the lack of
distinguished basis in the space of unitary evolutions and thus the lack of the
commonly accepted set of basic operations (universal gates). A natural choice,
however, is at hand: it is provided by the quantum R-matrices, the entangling
deformations of non-entangling (classical) permutations, distinguished from the
points of view of group theory, integrable systems and modern theory of
non-perturbative calculations in quantum field and string theory. Observables
in this case are (square modules of) the knot polynomials, and their pronounced
integrality properties could provide a key to error correction. We suggest to
use R-matrices acting in the space of irreducible representations, which are
unitary for the real-valued couplings in Chern-Simons theory, to build a
topological version of quantum computing.Comment: 14 page
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