Scientific Series

There are many results showing that the probability of entanglement is high for large dimensions. Recently, Arveson showed that the probability of entanglement is zero when the rank of a bipartite state is no larger than half the dimension of the smaller space. We show that that the probability of entanglement is zero when the rank of a bipartite state is no larger than half the maximum of the rank of its two reduced density matrices. Our approach is quite different from that of Arveson and uses a different measure. But both approaches show that the separable states lie in a lower dimensional manifold given a reasonable parameterization of the separable states. This is joint work with Elisabeth Werner, using on characterizations of the extreme points of qubit channels given by Ruskai, Szarek and Werner and the extreme points of entanglement breaking channels given by M. Horodecki, Shor and Ruskai.

During the last two decades Alain Connes developed Noncommutative Geometry, which allows to unify two of the basic theories of modern physics: General Relativity and the Standard Model of Particle Physics. In the noncommutative framework the Higgs boson, which had previously to be put in by hand, and many of the ad hoc features of the standard model, appear in a natural way. The aim of my talk is to motivate this unification from basic physical principles and to give a flavour of its derivation. I will give an overview of the basic tools such as almost-commutative spectral triples and the spectral action principle. The latter allows to derive the Einstein-Hilbert Lagrangian and the Standard Model Lagrangian together with a set of relations among the Standard Model parameters.

I will report on efforts to implement a new method for simulating concatenated quantum error correction, where many levels of concatenation are simulated together explicitly. That is, the approach involves a Monte Carlo simulation of a noisy circuit involving many thousands of qubits, rather than tens of qubits previously. The new approach allows the threshold and resource usage of concatenated quantum error correction to be determined more accurately than before. Also, the approach makes it possible to better study the effects of circuit optimizations and message-passing algorithms [Poulin, PRA, 2006] on the performance of fault-tolerant concatenated quantum error correction. Such studies are necessary in order make a proper comparison with competing families of error-correction protocols, such as those involving surface codes. In the talk, a range of new numerical results will be presented.

We will discuss the missing pieces in the understanding of the effective field theory description of string creation, the T-dual of the Hanany-Witten effect, both in the open and closed string picture. We explain the origin of the \'bare\' Chern-Simons term, so far added in by hand. There however remain unsettled issues concerning the need to modify the DBI action and the interpretation of this term in M-theory.

The so-called cosmological backreaction arises when one directly averages the Einstein equations to recover cosmology. While usually applied to avoid employing dark energy models, strictly speaking any cosmological model should be built from such an averaging procedure rather than an assumed background. We apply the Buchert formalism to Einstein-de Sitter, Lambda CDM and quintessence cosmologies, and as a first approach to the full problem, evaluate numerically the discrepancies arising from linear perturbation theory between the averaged behaviour and the assumed behaviour. (References: J. Behrend, IB and G. Robbers, JCAP01(2008)013, aXiv:0710.4964; IB, G. Robbers and J. Behrend, in preperation)

I will report on some work in progress with Dan Freed and Greg Moore. In an orientifold background, D-brane charge takes values in a certain twisted version of KR Theory. Moreover, there is a nontrivial background charge (\'tadpole\'). Up \'til now, this background charge has only been calculated rationally -- i.e., ignoring torsion. We derive a formula for it, over the integers. Only after \'inverting 2\', does the charge localize to the fixed point sets of the orientifold action, and we can give a compact formula for it. This reproduces the previously known rational results, but contains new information.

Theoretical and experimental results on the Quantum Injected Optical Parametric Amplification (QI-OPA) of optical qubits in the high gain regime (g > 6) are reported. The entanglement of the related Schroedinger Cat-State (SCS) is demonstrated as well as the establishment of Phase-Covariant quantum cloning for a Macrostate consisting of about 106 particles. In addition, the violation of the CHSH inequality is has been realized experimentally. According to the original 1935 definition of the SCS, the overall apparatus establishes for the first time the nonlocal correlations between a microcopic spin (qubit) and a high J angular momentum i.e. a macroscopic multiparticle system close to the classical limit. Applications to Quantum Information will be discussed.