QI SEMINAR: The Absolute Separability Problem in Quantum Information Theory

SPEAKER:  Nathan Johnston

ABSTRACT:

The central feature of quantum mechanics that makes it useful for information processing and computational tasks is the existence of entanglement---strong correlations between particles that cannot be described classically. However, given a mathematical description of a quantum state, it is hard to determine whether or not it contains any entanglement. This is called the "separability problem", and we discuss how to phrase this problem mathematically and what methods we can use to make partial progress on it. We also discuss the "absolute separability problem", which asks us to determine whether or not a quantum state could be made to have entanglement if we are allowed to alter it in certain (physically reasonable) ways, and we present some recent progress on this problem that was made via a connection with completely positive matrices.