3 research outputs found
Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results
A formulation of the generalized minimal output entropy conjecture for
Gaussian channels is presented. It asserts that, for states with fixed input
entropy, the minimal value of the output entropy of the channel (i.e. the
minimal output entropy increment for fixed input entropy) is achieved by
Gaussian states. In the case of centered channels (i.e. channels which do not
add squeezing to the input state) this implies that the minimum is obtained by
thermal (Gibbs) inputs. The conjecture is proved to be valid in some special
cases.Comment: 7 pages, updated version minor typos correcte
Rank-based model selection for multiple ions quantum tomography
The statistical analysis of measurement data has become a key component of
many quantum engineering experiments. As standard full state tomography becomes
unfeasible for large dimensional quantum systems, one needs to exploit prior
information and the "sparsity" properties of the experimental state in order to
reduce the dimensionality of the estimation problem. In this paper we propose
model selection as a general principle for finding the simplest, or most
parsimonious explanation of the data, by fitting different models and choosing
the estimator with the best trade-off between likelihood fit and model
complexity. We apply two well established model selection methods -- the Akaike
information criterion (AIC) and the Bayesian information criterion (BIC) -- to
models consising of states of fixed rank and datasets such as are currently
produced in multiple ions experiments. We test the performance of AIC and BIC
on randomly chosen low rank states of 4 ions, and study the dependence of the
selected rank with the number of measurement repetitions for one ion states. We
then apply the methods to real data from a 4 ions experiment aimed at creating
a Smolin state of rank 4. The two methods indicate that the optimal model for
describing the data lies between ranks 6 and 9, and the Pearson test
is applied to validate this conclusion. Additionally we find that the mean
square error of the maximum likelihood estimator for pure states is close to
that of the optimal over all possible measurements.Comment: 24 pages, 6 figures, 3 table