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Quantum chaos; random matrix theory; quantum tomography.

We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in informationgain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory inthe fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different classes of maps and show that these bounds are realized by fully chaotic quantum systems.

VAIBHAV MADHOK¹ CARLOS A RIOFRÍO² IVAN H DEUTSCH³

1. Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver, V6T 1Z4, Canada
2. Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
3. Department of Physics and Astronomy, Room 24, University of New Mexico, 800 Yale Blvd., Albuquerque, NM 87131-1156, Mexico

Published

16 November 2016

Manuscript received

19 May 2015

Manuscript revised

25 November 2015

Accepted

16 December 2015

Early published

28 September 2016