Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic

We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over the integers modulo d. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.Comment: 10 pages, RevTe

Stabilizer state breeding

We present a breeding protocol that distills pure copies of any stabilizer state from noisy copies and a pool of predistilled pure copies of the same state, by means of local Clifford operations, Pauli measurements and classical communication.Comment: RevTeX4, 9 pages, 1 figur

“A wind of change” in recreational fisheries? Recreational fishermen and wind farms: current use and perception

Offshore wind farms create opportunities for recreational fishermen in Belgium, since the presence of hard substrates and the closure for trawling create a favorable habitat for fish. After the construction in 2008, a concentration of anglers was observed in the vicinity of the first wind farm during monitoring. In the following years, however, the interest of anglers for the wind farms seemed to disappear. To elucidate the evolution in the relation between recreational angling intensity and wind farms, this study aimed to assess how Belgian recreational fishermen perceive wind farms, how often they visit them and why, and which fish species they (expect to) catch. Data were derived from the annual DCF survey for recreational fishermen. Less than 2% of the sea anglers reported to go fishing in the larger wind farm area, even when 30 to 40 percent of the respondents either expected more fish, bigger fish or other fish species. The main reasons to stay away from wind farms is because entering the wind farms themselves is not allowed, because the distance to the wind farms is relatively large, because charter vessels do not offer fish trips to wind farms, and because wind farms are protection zones and nursery areas for fish. 40% of the respondents would consider fishing inside wind farms if it were allowed, mainly because they expect more or other fish. This is a clear indication that the enforcement of wind farm closure for fisheries and shipping is vital when aiming at the creation and/or restoration of nursing grounds in the area. However, the large distance to the wind farms will probably continue to limit fishing pressure, even if wind farms would (partly) be opened for recreational fisheries

Improvement of stabilizer based entanglement distillation protocols by encoding operators

This paper presents a method for enumerating all encoding operators in the Clifford group for a given stabilizer. Furthermore, we classify encoding operators into the equivalence classes such that EDPs (Entanglement Distillation Protocol) constructed from encoding operators in the same equivalence class have the same performance. By this classification, for a given parameter, the number of candidates for good EDPs is significantly reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]] stabilizer codes. This EDP has a better performance than previously known EDPs over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding operators in the Clifford group, and fix the wrong classification of encoding operators in version