Strategic Eurasian Natural Gas Model for Energy Security

The mathematical formulation of a large-scale equilibrium natural gas simulation model is presented. Although large-scale natural gas models have been developed and used for energy security and policy analysis quite extensively (e.g., Holz (2007), Egging et al. (2008), Holz et al. (2009) and Lise et al. (2008)), this model differs from earlier ones in its detailed representation of the structure and operations of the Former Soviet Union (FSU) gas sector. In particular, the model represents: (i) market power of transit countries, (ii) transmission pipelines in Russia, Ukraine, Belarus and Central Asia, (iii) differentiation among gas production regions in Russia, and (iv) gas trade relations between FSU countries (e.g., Gazprom’s re-exporting of Central Asian gas). To demonstrate the model, a social benefit-cost analysis of the Nord Stream gas pipeline project from Russia to Germany via the Baltic Sea is provided. It is found that Nord Stream project is profitable for its investors and the project also improves social welfare in all market power scenarios. Also, if transit countries (Ukraine and Belarus) exert substantial market power then the economic value of Nord Stream to its investors and to society improves substantially. We also found that the value of Nord Stream investment is rather sensitive to the degree of downstream competition in European markets and that lack of downstream competition might result in the negative value of the Nord Stream system to Gazprom

Disguising quantum channels by mixing and channel distance trade-off

We consider the reverse problem to the distinguishability of two quantum channels, which we call the disguising problem. Given two quantum channels, the goal here is to make the two channels identical by mixing with some other channels with minimal mixing probabilities. This quantifies how much one channel can disguise as the other. In addition, the possibility to trade off between the two mixing probabilities allows one channel to be more preserved (less mixed) at the expense of the other. We derive lower- and upper-bounds of the trade-off curve and apply them to a few example channels. Optimal trade-off is obtained in one example. We relate the disguising problem and the distinguishability problem by showing the the former can lower and upper bound the diamond norm. We also show that the disguising problem gives an upper bound on the key generation rate in quantum cryptography.Comment: 27 pages, 8 figures. Added new results for using the disguising problem to lower and upper bound the diamond norm and to upper bound the key generation rate in quantum cryptograph

Time-Energy Costs of Quantum Measurements

Time and energy of quantum processes are a tradeoff against each other. We propose to ascribe to any given quantum process a time-energy cost to quantify how much computation it performs. Here, we analyze the time-energy costs for general quantum measurements, along a similar line as our previous work for quantum channels, and prove exact and lower bound formulae for the costs. We use these formulae to evaluate the efficiencies of actual measurement implementations. We find that one implementation for a Bell measurement is optimal in time-energy. We also analyze the time-energy cost for unambiguous state discrimination and find evidence that only a finite time-energy cost is needed to distinguish any number of states.Comment: 10 pages, 6 figure

Time-Energy Measure for Quantum Processes

Quantum mechanics sets limits on how fast quantum processes can run given some system energy through time-energy uncertainty relations, and they imply that time and energy are tradeoff against each other. Thus, we propose to measure the time-energy as a single unit for quantum channels. We consider a time-energy measure for quantum channels and compute lower and upper bounds of it using the channel Kraus operators. For a special class of channels (which includes the depolarizing channel), we can obtain the exact value of the time-energy measure. One consequence of our result is that erasing quantum information requires $\sqrt{(n+1)/n}$ times more time-energy resource than erasing classical information, where $n$ is the system dimension.Comment: 13 pages, 2 figure