Quantum Chaos, Information Gain and Quantum Tomography.



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PIRSA Number: 
12120036

Abstract

Quantum chaos is the study
of quantum systems whose classical description is chaotic.

How does chaos manifest itself in
the quantum world? In recent years, attempts have been made
to address this question from the perspective of quantum information
theory. It is in this spirit that we study the connection
between quantum chaos and information gain in the
time series of a measurement record used for quantum tomography. The
record is obtained as a sequence of expectation values of a Hermitian operator
evolving under repeated application of the Floquet operator of
the quantum kicked top on a large ensemble of identical systems. We
find an increase in information gain and hence higher fidelities
in the process when the Floquet maps employed increase in chaoticity. We make
predictions for the information gain using random matrix theory
in the fully chaotic regime and show a remarkable agreement between
the two.