Symmetry Reduction of sh-Lie Structures and of Local Functionals

Reduced sh-Lie structures have been studied for the case when a Lie group acts on the fibers of a vector bundle while preserving the base space of the bundle. In this paper we investigate how one obtains a reduced sh-Lie structure using the ideas of symmetry reduction where the action of the Lie group is transversal to the fibers of the bundle. We also show how local functionals are reduced using these ideas.Comment: 18 page

Observing quantum non-locality in the entanglement between modes of massive particles

We consider the question of whether it is possible to use the entanglement between spatially separated modes of massive particles to observe nonlocal quantum correlations. Mode entanglement can be obtained using a single particle, indicating that it requires careful consideration before concluding whether experimental observation, e.g. violation of Bell inequalities, is possible or not. In the simplest setups analogous to optics experiments, that observation is prohibited by fundamental conservation laws. However, we show that using auxiliary particles, mode entanglement can be converted into forms that allow the observation of quantum non-locality. The probability of successful conversion depends on the nature and number of auxiliary particles used. In particular, we find that an auxiliary Bose-Einstein condensate allows the conversion arbitrarily many times with a small error that depends only on the initial state of the condensate.Comment: 8 pages (two-column), 2 figure

The information about the state of a charge qubit gained by a weakly coupled quantum point contact

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. We consider the general case where the qubit Hamiltonian and the qubit's operator probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and the measurement data is mixed with a detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the initial state of the qubit can be extracted. Our approach complements the usual master-equation and quantum-trajectory approaches, which describe the evolution of the qubit's quantum state during the measurement process but do not keep track of the acquired measurement information.Comment: 5 pages, 3 figures; Published in the proceedings of the Nobel Symposium 141: Qubits for Future Quantum Informatio