Uncollapse of a partial-collapsed quantum state has been accomplished in the laboratory. Here is a popular article http://www.scienceagogo.com/news/20080706233709data_trunc_sys.shtml An article on this by Nadav Katz et al has just appeared in Nature News. I believe this is the preprint of the article: http://arxiv.org/abs/0806.3547 Uncollapsing of a quantum state in a superconducting phase qubit Nadav Katz, Matthew Neeley, M. Ansmann, Radoslaw C. Bialczak, M. Hofheinz, Erik Lucero, A. O'Connell, H. Wang, A. N. Cleland, John M. Martinis, Alexander N. Korotkov 4 pages, 4 figures (Submitted on 22 Jun 2008) "We demonstrate in a superconducting qubit the conditional recovery ('uncollapsing') of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a non-unitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, effectively canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6." There were were theory papers 2007 and earlier about the theoretical possibility, like this one by Jordan and Korotkov: http://arxiv.org/abs/0708.0365 Uncollapsing the wavefunction but that was theory so still needed experimental demonstration.