Physics Department Ph.D. Dissertation, "The Quantum Physics of the Classically Impossible," by Mordecai Waegell, WPI Physics Department Graduate Student
Science / Technology - Colloquium
Friday, April 19, 2013
3:00 PM-4:30 PM
Since the discovery of quantum mechanics, many physicists and philosophers have found its seeming disagreement with classical theories of physics to be of great concern. In 1935 Einstein, Podolsky, and Rosen wrote a famous paper about this issue, suggesting that quantum mechanics was an incomplete theory that needed to be supplemented by some additional ‘hidden variables’ in order to regain the full predictive power of a proper physical theory. With knowledge of these hidden variables, as well as the usual wavefunction representation of quantum mechanics, one would then be able to predict with certainty the outcome of a given experiment, rather than only the a priori probabilities of different outcomes predicted by quantum mechanics. It was also thought that such a hidden variables theory would resolve certain apparent violations of causality in the quantum theory.
In 1964-67 John S. Bell proved that the well-verified rules of quantum mechanics were incompatible with the rules of all possible local hidden variables theories, where by local we mean that the theory obeys causality. Bell, along with Kochen and Specker, also showed that no hidden variables theory of quantum mechanics could be noncontextual. Noncontextuality is a natural feature of classical physics, and while it is not motivated by a rule like causality, the fact that it is violated in quantum mechanics has interesting consequences. The Bell-Kochen-Specker theorem is interestingly not dependent on multi-particle entanglement, and the proof holds for any d-level quantum system with d≥3.
We have introduced and proved an even more fundamental theorem of quantum contextuality in systems of N different 2-level quantum systems (qubits), which we call the Strong BKS theorem. In classical theories, we expect that each individual system should be both noncontextual and independent, but entanglement shows us that this cannot be the case for N≥2.
Simple proofs of Bell’s Nonlocality Theorem and the Bell-Kochen-Specker Theorem depend on particular geometries of measurements in the Hilbert space of the quantum system(s) in question. We will introduce a number of these structures and examine them in detail. Finally we will discuss how the elemental structures that prove the Strong BKS theorem can be trivially extended to prove the usual BKS theorem and Bell’s nonlocality theorem, and show the overall relationship between these various types of nonclassicality in systems of N qubits. Applications of our results to experimental tests of nonlocality and contextuality will be discussed.
Thesis Advisor: P.K. Aravind
Thesis Committee: David Cyganski, L.R. Ram-Mohan
Sponsored by: WPI Physics Department
Suggested Audiences: College
Last Modified: April 10, 2013 at 2:09 PM