Our next colloquium of the spring semester is Monday, April 4 at 4pm MT in Weber 223.

Nicholas Witte (Victoria University of Wellington) will be speaking about “typical quantum states.” The title and abstract are below.

Title: What is a typical quantum state?

Abstract: There is much interest in the understanding of non-classical correlations of observables in quantum systems, such as entanglement. We consider this question for a finite pair of coupled systems, the simplest setting of this problem. Now the dimension of the Hilbert spaces generically grows exponentially with the number of components and only the smallest cases are completely understood. With this in mind we adopt a statistical approach and pose the question – what is a typical quantum state and how can one best (i.e. uniformly) sample these from the state space? Consideration of this question has lead to a particular joint probability distribution governing the eigenvalues of a certain density matrix, known as the Bures-Hall ensemble. Some of the essential results in this understanding will be derived in a simple pedagogical manner, without assuming a prior background and suitable for students in mathematics, statistics and physics.

This then leads to a further question, namely, how do the largest and smallest eigenvalues of the density matrix behave as the system size (number of components) grows? Through recent work (with Lu Wei, TTU) by the speaker the answer to this question has been found using cutting-edge tools from integrable probability and approximation theory. Time permitting a brief snapshot of some results will be revealed.