Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

AbstractDefinitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated

Structured pseudospectra and random eigenvalues problems in vibrating systems

This paper introduces the concept of pseudospectra as a generalized tool for uncertainty quantification and propagation in structural dynamics. Different types of pseudospectra of matrices and matrix polynomials are explained. Particular emphasis is given to structured pseudospectra for matrix polynomials, which offer a deterministic way of dealing with uncertainties for structural dynamic systems. The pseudospectra analysis is compared with the results from Monte Carlo simulations of uncertain discrete systems. Two illustrative example problems, one with probabilistic uncertainty with various types of statistical distributions and the other with interval type of uncertainty, are studied in detail. Excellent agreement is found between the pseudospectra results and Monte Carlo simulation results

Teleportation-based realization of an optical quantum two-qubit entangling gate

In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by Gottesman and Chuang [Nature \textbf{402}, 390 (1999)], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multi-particle entangled states, Bell state measurements and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods we demonstrate the smallest non-trivial module in such a scheme---a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates and the other uses four-photon hyper-entanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step towards the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.Comment: 10 pages, 6 figure

Experimental Quantum Teleportation of a Two-Qubit Composite System

Quantum teleportation, a way to transfer the state of a quantum system from one location to another, is central to quantum communication and plays an important role in a number of quantum computation protocols. Previous experimental demonstrations have been implemented with photonic or ionic qubits. Very recently long-distance teleportation and open-destination teleportation have also been realized. Until now, previous experiments have only been able to teleport single qubits. However, since teleportation of single qubits is insufficient for a large-scale realization of quantum communication and computation2-5, teleportation of a composite system containing two or more qubits has been seen as a long-standing goal in quantum information science. Here, we present the experimental realization of quantum teleportation of a two-qubit composite system. In the experiment, we develop and exploit a six-photon interferometer to teleport an arbitrary polarization state of two photons. The observed teleportation fidelities for different initial states are all well beyond the state estimation limit of 0.40 for a two-qubit system. Not only does our six-photon interferometer provide an important step towards teleportation of a complex system, it will also enable future experimental investigations on a number of fundamental quantum communication and computation protocols such as multi-stage realization of quantum-relay, fault-tolerant quantum computation, universal quantum error-correction and one-way quantum computation.Comment: 16pages, 4 figure