De Finetti theorems for conditional probability
Monday, August 28th, 2006Date: Friday 1st September
Who: Ben Toner
Seminar type: Research Seminar
Time: 12 Midday
Where: Interaction Room
Abstract:
Measuring a quantum system disturbs it, eliminating our ability to make a second, incompatible, measurement on the same system. We can describe the state of a quantum system via a conditional probability distribution for the measurement outcomes, conditioned on which measurement we choose to perform. The need for the probability distribution to be conditional does not arise classically, where all measurement are compatible.Ben has also supplied the following information.
In this talk, I prove de Finetti representation theorems for conditional probability distributions. I’ll devote most of the talk to describing what a de Fineti theorem is, why such results are important, and how a de Finetti theorem should be formulated for conditional probability distributions. Our results apply to correlations arising in quantum theory and, more generally, to correlations arising in theories with a no-signalling principle. We also obtain a new quantum de Finetti theorem for separable states.
Joint work with Matthias Christandl.