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 $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$. 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