18,430 research outputs found
Computer program offers new method for constructing periodic orbits in nonlinear dynamical systems
Computer program uses an iterative method to construct precisely periodic orbits which dynamically approximate solutions that converge to precise dynamical solutions in the limit of the sequence. The method used is a modification of the generalized Newton-Raphson algorithm used in analyzing two point boundary problems
Method for constructing periodic orbits in nonlinear dynamic systems
Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems
Deutsch-Jozsa algorithm as a test of quantum computation
A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a
refined algorithm, which reduces the size of the register and simplifies the
function evaluation, is proposed. The refined version allows a simpler analysis
of the use of entanglement between the qubits in the algorithm and provides
criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful
test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev
The Parity Bit in Quantum Cryptography
An -bit string is encoded as a sequence of non-orthogonal quantum states.
The parity bit of that -bit string is described by one of two density
matrices, and , both in a Hilbert space of
dimension . In order to derive the parity bit the receiver must
distinguish between the two density matrices, e.g., in terms of optimal mutual
information. In this paper we find the measurement which provides the optimal
mutual information about the parity bit and calculate that information. We
prove that this information decreases exponentially with the length of the
string in the case where the single bit states are almost fully overlapping. We
believe this result will be useful in proving the ultimate security of quantum
crytography in the presence of noise.Comment: 19 pages, RevTe
The Influence of Superpositional Wave Function Oscillations on Shor's Quantum Algorithm
We investigate the influence of superpositional wave function oscillations on
the performance of Shor's quantum algorithm for factorization of integers. It
is shown that the wave function oscillations can destroy the required quantum
interference. This undesirable effect can be routinely eliminated using a
resonant pulse implementation of quantum computation, but requires special
analysis for non-resonant implementations.Comment: 4 pages, NO figures, revte
How Algorithmic Confounding in Recommendation Systems Increases Homogeneity and Decreases Utility
Recommendation systems are ubiquitous and impact many domains; they have the
potential to influence product consumption, individuals' perceptions of the
world, and life-altering decisions. These systems are often evaluated or
trained with data from users already exposed to algorithmic recommendations;
this creates a pernicious feedback loop. Using simulations, we demonstrate how
using data confounded in this way homogenizes user behavior without increasing
utility
Comparing Ecological Sensitivity with Stream Flow Rates in the Apalachicola-Chattahoochee-Flint River Basin
Environmental Economics and Policy, Resource /Energy Economics and Policy,
Quantum teleportation of EPR pair by three-particle entanglement
Teleportation of an EPR pair using triplet in state of the
Horne-Greenberger-Zeilinger form to two receivers is considered. It needs a
three-particle basis for joint measurement. By contrast the one qubit
teleportation the required basis is not maximally entangled. It consists of the
states corresponding to the maximally entanglement of two particles only. Using
outcomes of measurement both receivers can recover an unknown EPR state however
one of them can not do it separately. Teleportation of the N-particle
entanglement is discussed.Comment: 7 pages, LaTeX, 3 figure
Indeterminate-length quantum coding
The quantum analogues of classical variable-length codes are
indeterminate-length quantum codes, in which codewords may exist in
superpositions of different lengths. This paper explores some of their
properties. The length observable for such codes is governed by a quantum
version of the Kraft-McMillan inequality. Indeterminate-length quantum codes
also provide an alternate approach to quantum data compression.Comment: 32 page
An expectation value expansion of Hermitian operators in a discrete Hilbert space
We discuss a real-valued expansion of any Hermitian operator defined in a
Hilbert space of finite dimension N, where N is a prime number, or an integer
power of a prime. The expansion has a direct interpretation in terms of the
operator expectation values for a set of complementary bases. The expansion can
be said to be the complement of the discrete Wigner function.
We expect the expansion to be of use in quantum information applications
since qubits typically are represented by a discrete, and finite-dimensional
physical system of dimension N=2^p, where p is the number of qubits involved.
As a particular example we use the expansion to prove that an intermediate
measurement basis (a Breidbart basis) cannot be found if the Hilbert space
dimension is 3 or 4.Comment: A mild update. In particular, I. D. Ivanovic's earlier derivation of
the expansion is properly acknowledged. 16 pages, one PS figure, 1 table,
written in RevTe
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