Dear quanta, We have an exciting roster of speakers and visitors coming up this week. Visitors: Steve Flammia (Sydney): May 20-27 Robin Blume-Kohout (Sandia) : May 22-23 Nicole Yunger Halpern (Caltech): May 22 If you want to meet any of them, either email me, or email them directly. Their office locations are on the blackboard at the entrance of the CTP. Talks, each in 6c-442: Wed, 11am: Kevin Zatloukal (MIT), Subset sum and the hidden subgroup problem for nilpotent groups Thurs, 4pm: Nicole Yunger Halpern, Beyond heat baths: Resource theories for small-scale thermodynamics Fri, 1:30pm: Robin Blume-Kohout, Quantum information is (inconveniently!) a gauge theory There is (inconveniently!) no abstract for the last talk. Abstracts for the first two talks are: 1. Zatloukal - HSP In this talk, we demonstrate that there exists an efficient quantum algorithm for solving the hidden subgroup problem (HSP) in k-nilpotent groups if we are provided with an oracle for solving average-case subset sum. The same fact was already known for the dihedral group. In fact, solving HSP for the dihedral group is thought to be equivalent to solving average-case subset sum. Thus, our result can be interpreted as showing that the HSP for any k-nilpotent group is no harder than the HSP for the dihedral group. Using classical algorithms for solving subset sum (even just the brute-force algorithm), we are able to get a non-trivial speedup for all k-nilpotent groups. In particular, for 2-groups, the subset sum problem is easy, so we get efficient quantum algorithms for k-nilpotent 2-groups. This is an especially interesting case because the dihedral group can be a 2-group as well, albeit one of high nilpotency class. 2. Halpern - thermodynamics How can thermodynamics, which involves vast numbers of particles, describe cutting-edge technology, which involves tiny scales? Heat exchanges have been modeled with the resource-theory framework famous for elucidating entanglement. “Helmholtz” resource theories have shown that the work cost W_cost of creating one copy of a state can differ from the work W_dist distillable from the state. This “one-shot” result contrasts with the thermodynamic limit, in which W_cost = W_dist. I will generalize the resource-theory framework from heat exchanges to more-arbitrary thermodynamic interactions. I will introduce resource theories of non-equilibrium, a family of models that includes the Helmholtz theories. In addition to shedding new light on Helmholtz theories, the non-equilibrium framework expands the resource theories’ potential to describe experiments and quantum phenomena. I will quantify the distinction between W_cost and W_dist in terms of the hypothesis-testing entropy D_H. This research is motivated by the interplay between information and energy on small scales exemplified by single-molecule experiments, nanoscale engines, and molecular motors. This work was conducted partially (arXiv:1309.6586) at the Perimeter Institute for Theoretical physics with Markus Müller and Rob Spekkens, as well as with Gilad Gour and Varun Narasimhachar. Part of this work is being conducted with Joe Renes. _______________________________________________ qip mailing list qip(a)mit.edu http://mailman.mit.edu/mailman/listinfo/qip