Hastings, Ambainis, and Harrow wrote a paper. Most of us forgot to read it. http://arxiv.org/abs/0910.0472 There is a new version of the paper on bound entanglement and negative partial transpose. It's still wrong. The result violates a theorem by Watrous. http://arxiv.org/abs/0910.0744 Daniel Nagaj told us about approximating partition functions. Computing the partition function exactly is at least #P-hard. There is a FPRAS (fully polynomial randomized approximation scheme). Daniel is interested in using phase estimation, which is asymptotically faster in terms of both the minimum gap and the required precision. --Andy _______________________________________________ qip mailing list qip(a)mit.edu http://mailman.mit.edu/mailman/listinfo/qip