Two Poorly Measured Quantum Observables as a Complete Set of Commuting Observables

Authors

Mark Olchanyi, Newton South High School

Abstract

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.

Author Bio

Mark Olchanyi is currently a high school senior, Newton South High School, Newton, MA. From 2005 through 2012, he attended the Russian School of Mathematics, an after-school program devoted to mathematics beyond the standard curriculum. In 2011, Mark was selected by the John Hopkins Center for Talented Youth (CTY) to participate in an Intensive Studies program in Cryptography Seattle University. Mark devotes the remainder of his time to free-style skiing and mountain biking.

Faculty Sponsor

Eugene Moskovets, Steven Glenn Jackson

Recommended Citation

Olchanyi, Mark (2015) "Two Poorly Measured Quantum Observables as a Complete Set of Commuting Observables," Rose-Hulman Undergraduate Mathematics Journal: Vol. 16: Iss. 2, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/9