Decoherence of an nn-qubit quantum memory

We analyze decoherence of a quantum register in the absence of non-local operations i.e. of $n$ non-interacting qubits coupled to an environment. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: first decoherence must be small and second the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to a random matrix model, and illustrate its reach considering a GHZ state coupled to a spin bath.Comment: 4 pages, 2 figure

Airline revenue management : sell-up and forecasting algorithms

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2000.Also available online at the MIT Theses Online homepage .Includes bibliographical references.Recent technological improvements have allowed airlines to implement sophisticated Revenue Management systems in order to maximize revenues. Computational capabilities make it possible to perform network-based analysis of supply and demand and therefore to increase the gains achieved with the help of "0- D control" Revenue Management algorithms. However, the more commonly used and cheaper flight leg-based algorithms have not yet been used to the best of their potential and can still benefit from better modeling of passenger behavior. Our first purpose in this thesis is therefore to evaluate the benefits of incorporating sell-up models into current leg-based airline Revenue Management algorithms. Another question we would like to try and address is whether it would be possible to improve the leg-based models to reach revenue gains comparable to those of O-D control algorithms. To try and achieve this goal, we improve the modeling in our leg-based Revenue Management algorithms by accounting for the possibility of sellup, that is the probability that a passenger will accept a more expensive ticket than originally desired if seats are not available at the lower fare. In addition, previous research has shown that there are revenue gains to be achieved through better forecasting, therefore, we also evaluate the use of better forecasting methods and quantify their revenue impact. In particular, we focus our efforts on understanding the impact of the unconstraining models on revenue gains by using various detruncation methods and comparing their effect.by Thomas O. Gorin.S.M

Assessing Predation in Airline Markets with Low-Fare Competition

Assessment of unfair competitive practices in airline markets has traditionally been based on the analysis of changes in average fares, revenue and traffic following low-fare entry. This paper demonstrates the severe limitations of using such measures. In particular, our case studies show that despite very different perceptions by some analysts of apparent incumbent carrier response to entry, average fares, revenues and traffic measures showed very similar patterns of change in the cases studied. We then use a competitive airline market simulation to illustrate the importance of often ignored factors – revenue management and the flows of connecting network passengers on the flight legs affected by low-fare entry – in explaining the effects of entry on these aggregate measures of airline performance. These simulations results further reinforce the danger in using such measures as indicators of predatory behavior in airline markets

Assessing low-fare entry in airline markets : impacts of revenue management and network flows

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 263-269).(cont.) the essential factors affecting traditional measures of airline performance following low-fare entry. Our simulation results show that these measures are greatly affected by the entrant's capacity relative to the incumbent, by the incumbent carrier's competitive pricing response, and by the competitive revenue management situation. For example, average fares on the incumbent carrier can either increase or decrease following entry by a new competitor, depending on whether one or both airlines perform revenue management. In an extension of the simulations to a larger network environment, it is also shown that network flows of passengers affect the performance of all competitors, as measured by aggregate measures of performance. Furthermore, use of advanced network revenue management allows the incumbent carriers to rely on connecting passengers to mitigate the effect of entry on network revenues, but leads to amplified effects at the local market level. Consequently, this research establishes that traditional aggregate measures of airline performance on their own do not constitute a reliable indication of the response of incumbent carriers, and provide even less information on their strategic intent, which is critical in identifying predation. This research also demonstrates the relationships between aggregate measures of performance and previously overlooked factors including relative entrant capacity, competitive pricing and revenue management, and flows of network passengers.The recent growth of low-fare, low-cost carriers has changed the competitive airline environment. In the US alone, low-fare carrier market shares have increased from just over 5% in 1990 to almost 25% in 2003. Traditional network carriers have consequently had to adjust to the changing competitive environment, which has led to cost reductions, fare structure simplifications and service adjustments. In addition, competitive responses of incumbent network carriers to low-fare entry have prompted concern regarding the potential for predatory practices in the airline industry. Assessment of unfair competitive practices in airline markets has typically been based on the analysis of changes in aggregate measures, such as average fares, traffic and revenues. In this research, the effect of low-fare entry on incumbent network carriers is examined, with special focus on the impacts of entry on traditional measures of airline performance. An analysis of various markets with low-fare competition highlights the typical effects of low-fare entry on these traditional aggregate measures. In a thorough analysis of two specific cases, we show that these measures, although affected similarly by entry, were very poor predictors of the new entrant's success in these markets, and inadequate indicators of incumbent response. AirTran successfully entered the Atlanta-Orlando market, while Spirit failed to maintain its operations in the Detroit-Boston market. We highlight the differences between these two markets and explain why the performance of these two carriers was so different. In a second part, a simulator of competitive airline networks--the Passenger Origin Destination Simulator--is used to model various scenarios of entry in a single market environment so as to determineby Thomas O. Gorin.Ph.D