Truncated States Obtained by Iteration

Pooling quantum states obtained by indirect measurements

Vector Extrapolation Applied to Truncated Singular Value Decomposition and Truncated Iteration

This paper is concerned with the computation of accurate approximate solutions of linear systems of equations and linear least-squares problems with a very ill-conditioned matrix and error-contaminated data. The solution of this kind of problems requires regularization. Common regularization methods include the truncated singular value decomposition and truncated iteration with a Krylov subspac...

A Truncated RQ - Iteration forLarge Scale Eigenvalue CalculationsD

We introduce a new Krylov subspace iteration for large scale eigen-value problems that is able to accelerate the convergence through an inexact (iterative) solution to a shift-invert equation. The method also takes full advantage of an exact solution when it is possible to apply a sparse direct method to solve the shift-invert equations. We call this new iteration the Truncated RQ iteration (TR...

Quantum nonlocality obtained from local states by entanglement purification.

We have applied an entanglement purification protocol to produce a single entangled pair of photons capable of violating a Clauser-Horne-Shimony-Holt Bell inequality from two pairs that individually could not. The initial poorly entangled photons were created by a controllable decoherence that introduced complex errors. All of the states were reconstructed using quantum state tomography which a...

INVERSE ITERATION FOR p-GROUND STATES

We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for p ∈ (1,∞) and a given domain Ω ⊂ Rn, we analyze a scheme that allows us to approximate the smallest value the ratio ∫ Ω |Dψ| pdx/ ∫ Ω |ψ| pdx can assume for functions ψ that vanish on ∂Ω. The scheme in question also provides a natural way to approximate minimizing ψ. Our an...