In this article, we revisit the century-old question of the minimal set of observables needed to identify a quantum state: here, we replace the natural coincidences in their spectra by effective ones, induced by an imperfect measurement. We show that if the detection error is smaller than the mean level spacing, then two observables with Poisson spectra will suffice, no matter how large the system is. The primary target of our findings is the integrable (that is, exactly solvable) quantum systems whose spectra do obey the Poisson statistics. We also consider the implications of our findings for classical pattern recognition techniques.
Project Advisor: Dr. Eugene Moskovets, Senior Research Scientist, SESI/MassTech Inc. Faculty Sponsor: Steven Glenn Jackson, Department of Mathematics, University of Massachusetts Boston
"Two Poorly Measured Quantum Observables as a Complete Set of Commuting Observables,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16
, Article 9.
Available at: http://scholar.rose-hulman.edu/rhumj/vol16/iss2/9