Selecting Algorithms for Black Box Matrices: Checking for Matrix Properties That Can Simplify Computations

Processes to automate the selection of appropriate algorithms for various matrix computations are described. In particular, processes to check for, and certify, various matrix properties of black box matrices are presented. These include sparsity patterns and structural properties that allow "superfast" algorithms to be used in place of black-box algorithms. Matrix properties that hold generically, and allow the use of matrix preconditioning to be reduced or eliminated, can also be checked for and certified - notably including in the small-field case, where this presently has the greatest impact on the efficiency of the computation.Comment: Department of Computer Science Technical Report 2016-1085-0

Qubit Entanglement Driven by Remote Optical Fields

We examine the entanglement between two qubits, supposed to be remotely located and driven by independent quantized optical fields. No interaction is allowed between the qubits, but their degree of entanglement changes as a function of time. We report a collapse and revival of entanglement that is similar to the collapse and revival of single-atom properties in cavity QED.Comment: v3, major changes, published in Optics Letter

Phonon decoherence of quantum entanglement: Robust and fragile states

We study the robustness and fragility of entanglement of open quantum systems in some exactly solvable models in which the decoherence is caused by a pure dephasing process. In particular, for the toy models presented in this paper, we identify two different time scales, one is responsible for local dephasing, while the other is for entanglement decay. For a class of fragile entangled states defined in this paper, we find that the entanglement of two qubits, as measured by concurrence, decays faster asymptotically than the quantum dephasing of an individual qubit.Comment: 11 pages, revtex, no figure