8,031 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
Quantum Hidden Subgroup Algorithms: The Devil Is in the Details
We conjecture that one of the main obstacles to creating new non-abelian
quantum hidden subgroup algorithms is the correct choice of a transversal.Comment: 5 pages, to appear in April 2004 Proceedings of SPIE on Quantum
Information and Computatio
A 3-Stranded Quantum Algorithm for the Jones Polynomial
Let K be a 3-stranded knot (or link), and let L denote the number of
crossings in K. Let and be two positive real
numbers such that is less than or equal to 1.
In this paper, we create two algorithms for computing the value of the Jones
polynomial of K at all points of the unit circle in the complex
plane such that the absolute value of is less than or equal to .
The first algorithm, called the classical 3-stranded braid (3-SB) algorithm,
is a classical deterministic algorithm that has time complexity O(L). The
second, called the quantum 3-SB algorithm, is a quantum algorithm that computes
an estimate of the Jones polynomial of K at within a precision of
with a probability of success bounded below by $1-\epsilon_{2}%.
The execution time complexity of this algorithm is O(nL), where n is the
ceiling function of (ln(4/\epsilon_{2}))/(2(\epsilon_{2})^2). The compilation
time complexity, i.e., an asymptotic measure of the amount of time to assemble
the hardware that executes the algorithm, is O(L).Comment: 19 pages, 10 figures, to appear in Proc. SPIE, 6573-29, (2007
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