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