Hi all,
today we'll meet at 4pm in E41.1 to hear from Cyril Stark, back to visit
from MIT. Here is a preview of his talk:
Title: "About the role of compression in quantum tomography"
Abstract: Assume we are considering an experiment which allows us to
prepare unknown states and to perform unknown measurements. An effective
model for this experiment is both a description of each state in terms of a
density matrix and a description of each measurement in terms of a POVM.
Different models can be assigned to the same measurement data. To pick a
specific model from the set of candidate models, we try to find a model
which is compatible with the measured data, i.e., the measured frequencies
for different measurement outcomes are well approximated by the
probabilities predicted by Born's rule.
In this talk I will discuss robustness of the Hilbert space dimension
of quantum models. More precisely, by the definition of an explicit
compression scheme, I will show that quantum models can be compressed into
lower-dimensional quantum models if the measured data is noisy (e.g., due
to finite-size effects). Of course, the compressed model fits the measured
data not as well as the original model. When we compress into a model whose
dimension is only poly-logarithmic in the dimension of the original model,
then the error grows linearly in the trace norm of the POVM elements of the
original model. Here, the error is quantified in terms of the max norm
distance between measured frequencies and predictions in terms of Born's
rule. It follows, for example, that d-dimensional models involving only
projective and non-degenerate measurements admit compression into models of
dimension O(poly(log(d))). This is joint work with Aram Harrow.
Best,
-joe