Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups

Given an quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be computed. These methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography, the statistical estimation of superoperators and their generators, from a wide variety of experimental data. Theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data.Comment: RevTeX4, 31 pages, no figures; v4 adds new introduction and a numerical example illustrating the application of these results to Quantum Process Tomograph

Seeing Numbers

In 1890 William James listed several “elementary mental categories” that he postulated as having a natural origin. Among them, alongside the ideas of time and space, he also listed the idea of number. A symptomatic feature of Informatics as well as Cognitive Science today is the tendency not to talk so much about ideas as about their representations, either in the computer or in the brain. Taking up somewhat different perspective I will discuss the way natural numbers, viewed as counts of real or imagined objects, may be experienced phenomenally. I put forth even some speculative ideas about mental number processing by numerical savants

A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a 6-D Euclidean Vector Space

Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which to represent the classical groups as subgroups of rotation groups, and similarly their Lie algebras. In this article we show how the geometric algebra of a six-dimensional real Euclidean vector space naturally allows one to construct the special unitary group on a two-qubit (quantum bit) Hilbert space, in a fashion similar to that used in the well-established Bloch sphere model for a single qubit. This is then used to illustrate the Cartan decompositions and subalgebras of the four-dimensional special unitary group, which have recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev. A 67, 042313, 2003] to study the entangling capabilities of two-qubit unitaries.Comment: 14 pages, 2 figures, in press (Proceedings of SPIE Conference on Defense & Security

Expressing the operations of quantum computing in multiparticle geometric algebra

We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism of NMR spectroscopy, and hence its notation leads directly to implementations of these operations via NMR pulse sequences.Comment: RevTeX, 10 pages, no figures; Physics Letters A, in pres

Al-alloy die-castings for automotive industry

Tato rešeršní práce je zaměřena na téma Tlakově lité odlitky z Al slitin pro automobilový průmysl. V teoretické části je toto téma popsáno z hlediska technologie lití pro Al slitiny se zaměřením na vysokotlaké lití, na slitinu hliníku AlSi9Cu3 a na metody zjišťování zbytkové napjatosti. V experimentální části je uvedena ukázka měření zbytkových napětí na vzorcích odlitých ze slitiny AlSi9Cu3.This search is concentrated on Pressure-castings of aluminum alloys for the automotive industry. In the theoretical part of this topic is described in terms of technology for casting aluminum alloys with a focus on high-pressure casting of aluminum alloy AlSi9Cu3 and methods of detecting residual stress. In the experimental section is a sample of residual stress measurements on samples cast alloy AlSi9Cu3.