No-faster-than-light-signaling implies linear evolutions. A re-derivation

There is a growing interest, both from the theoretical as well as experimental side, to test the validity of the quantum superposition principle, and of theories which explicitly violate it by adding nonlinear terms to the Schr\"odinger equation. We review the original argument elaborated by Gisin (1989 Helv. Phys. Acta 62 363), which shows that the non-superluminal-signaling condition implies that the dynamics of the density matrix must be linear. This places very strong constraints on the permissible modifications of the Schr\"odinger equation, since they have to give rise, at the statistical level, to a linear evolution for the density matrix. The derivation is done in a heuristic way here and is appropriate for the students familiar with the textbook quantum mechanics and the language of density matrices.Comment: 17 pages, 7 figure

Simplified Compute-and-Forward and Its Performance Analysis

The compute-and-forward (CMF) method has shown a great promise as an innovative approach to exploit interference toward achieving higher network throughput. The CMF was primarily introduced by means of information theory tools. While there have been some recent works discussing different aspects of efficient and practical implementation of CMF, there are still some issues that are not covered. In this paper, we first introduce a method to decrease the implementation complexity of the CMF method. We then evaluate the exact outage probability of our proposed simplified CMF scheme, and hereby provide an upper bound on the outage probability of the optimum CMF in all SNR values, and a close approximation of its outage probability in low SNR regimes. We also evaluate the effect of the channel estimation error (CEE) on the performance of both optimum and our proposed simplified CMF by simulations. Our simulation results indicate that the proposed method is more robust against CEE than the optimum CMF method for the examples considered.Comment: Submitted to IET Communications, 29 pages, 7 figures, 1 table, latex, The authors are with the Wireless Research Laboratory (WRL), Department of Electrical Engineering, Sharif University of Technology, Tehran, Ira

Degree of Internationalization and Performance: An Analysis of Canadian Banks

The international business literature measures the link between the degree of internationalization (DOI) of a firm's activities and its performance. The results of this literature are mixed. The authors extend the analysis to Canadian bank-level data, but they also take into account the riskiness of each bank's foreign-asset exposure. The results establish a positive, but weak, relationship between DOI and performance--one that is dependent on each bank's risk profile. The authors discuss the policy implications of their analysis.Financial institutions