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

Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles

We provide a comprehensive view on the role of Abelian symmetry and stochasticity in the universality class of directed sandpile models, in context of the underlying spatial correlations of metastable patterns and scars. It is argued that the relevance of Abelian symmetry may depend on whether the dynamic rule is stochastic or deterministic, by means of the interaction of metastable patterns and avalanche flow. Based on the new scaling relations, we conjecture critical exponents for avalanche, which is confirmed reasonably well in large-scale numerical simulations.Comment: 4 pages, 3 figures; published versio

A net export-led downturn?

Exports ; Germany ; Japan

Non-Markovian disentanglement dynamics of two-qubit system

We investigated the disentanglement dynamics of two-qubit system in Non-Markovian approach. We showed that only the couple strength with the environment near to or less than fine-structure constant 1/137, entanglement appear exponential decay for a certain class of two-qubit entangled state. While the coupling between qubit and the environment is much larger, system always appears the sudden-death of entanglement even in the vacuum environment.Comment: 17 pages, 3 figure

Using Avida to test the effects of natural selection on phylogenetic reconstruction methods

Phylogenetic trees group organisms by their ancestral relationships. There are a number of distinct algorithms used to reconstruct these trees from molecular sequence data, but different methods sometimes give conflicting results. Since there are few precisely known phylogenies, simulations are typically used to test the quality of reconstruction algorithms. These simulations randomly evolve strings of symbols to produce a tree, and then the algorithms are run with the tree leaves as inputs. Here we use Avida to test two widely used reconstruction methods, which gives us the chance to observe the effect of natural selection on tree reconstruction. We find that if the organisms undergo natural selection between branch points, the methods will be successful even on very large time scales. However, these algorithms often falter when selection is absent