Scott Aaronson
Massachusetts Institute of Technology, USA
Date
27 May 2009
Host
Renato Renner
Title
How Much Information is in a Quantum State?
Abstract
People often talk about the quantum state of n entangled particles as if it contained an amount of information exponential in n. Sometimes, they draw the conclusion from this that quantum mechanics must be an "extravagant" theory valid only for simple systems or small numbers of particles, or that largescale quantum computing must be impossible in principle. In this talk, I'll survey how in the senses relevant for computation, prediction, and learning, quantum states actually don't behave as if they contain exponential amounts of information. Specifically, I'll discuss the limitations of "quantum advice states," the approximate "learnability" of quantum states from random measurement results, and a recently-discovered simulation of arbitrary quantum state preparation tasks by the preparation of ground states of local Hamiltonians. Some of the talk represents joint work with Andrew Drucker and Eyal Dechter.