Unitary designs for continuous variable systems

ORAL

Abstract

The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos. In discrete variable (DV) systems (finite-dimensional, e.g. spins), the scrambling ‘strength’ of a unitary is often measured by its closeness to a Haar random unitary. This leads to a hierarchy of increasingly fine-grained measures of scrambling known as ‘unitary k-designs’. Here, we extend the notion of unitary designs to continuous variable (CV) systems (infinite-dimensional, e.g. photons). Although there is no generalization of Haar randomness to CV systems, we show that averages of physical quantities over Haar random unitaries remain well-defined in the CV limit, and use this to define CV unitary designs. Surprisingly, Gaussian unitaries, despite being non-interacting, form a CV 2-design and can therefore `quasi-scramble' information. Extending further, we show that unitary 4-designs maximize the phase space volume of generic time-evolved operators.

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Presenters

  • Thomas Schuster

    Department of Physics, University of California, Berkeley, California 94720, USA, University of California, Berkeley

Authors

  • Thomas Schuster

    Department of Physics, University of California, Berkeley, California 94720, USA, University of California, Berkeley

  • Quntao Zhuang

    Physics, University of California, Berkeley, Department of Physics, University of California, Berkeley, California 94720, USA, University of California, Berkeley

  • Beni Yoshida

    Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada, Perimeter Institute for Theoretical Physics

  • Norman Yao

    University of California, Berkeley, Department of Physics, University of California, Berkeley, California 94720, USA, Physics, University of California, Berkeley, Department of Physics, University of California, Berkeley, University of California, Berkeley and Lawrence Berkeley National Laboratory, Materials Sciences Division