Symmetry And Group

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By Decker T., Janzing D.

We contemplate group-covariant optimistic operator valued measures (POVMs) on afinite dimensional quantum approach. Following Neumark's theorem a POVM can beimplemented via an orthogonal dimension on a bigger method. as a result, ourgoal is to discover a quantum circuit implementation of a given group-covariant POVMwhich makes use of the symmetry of the POVM. according to illustration idea of thesymmetry workforce we enhance a normal procedure for the implementation of groupcovariantPOVMs which include rank-one operators. the development will depend on amethod to decompose matrices that intertwine representations of a finite group.We provide a number of examples for which the ensuing quantum circuits are effective. Inparticular, we receive effective quantum circuits for a category of POVMs generated byWeyl-Heisenberg teams. those circuits let to enforce an approximative simultaneousmeasurement of the location and crystal momentum of a particle movingon a cyclic chain.

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1993: 450). There is a threshold or point of critical mass beyond which the costs and risks of migration are lowered, making it a more and more attractive proposition. Changes through feedback are typically gradual, but may nonetheless be profound, in which case they might be termed cumulative transitions; here there is no particular point or moment at which transition can be observed to occur. One prominent example of a cumulative transition has occurred in many parts of the affluent world in recent times.

Threats to Malaysia’s one million strong immigrant population have nevertheless continued, with further arrests, 34 NEW DIASPORAS deportations and attempts to crack down on migrant smugglers. Early in 1997 the government declared it was preparing to arrest and deport illegal immigrants who failed to make use of an amnesty that expired at the end of 1996 (AP—Dow Jones News Service, 2 January 1997). The currency crisis that hit Malaysia and other Asian economies in mid–1997 may presage further stringent moves against the country’s migrant population.

There is obviously overlap with some of the elements of the previous, structural domain. Again some of these features are to some extent measurable—the economic arena probably more so than the others. This domain includes particular manifestations of the economic, political and environmental disparities—or collectively, of human security— identified above. In a third domain are found what might be termed precipitating factors, or those actually triggering departure. This may be the arena in which individual and household decisions to move or stay put are made.

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