Wigner negativity, random matrices and gravity

Abstract: Given a choice of an ordered, orthonormal basis for a finite D-dimensional Hilbert space, one can define a discrete version of the Wigner function — a quasi-probability distribution which represents any state in the Hilbert space on a discrete phase space. The Wigner function can, in general, take on negative values, and the amount of negativity in the Wigner function gives a measure of the complexity of simulating the quantum state on a classical computer. In this talk, we study the growth of Wigner negativity for a generic initial state under time evolution with chaotic Hamiltonians. We first give a perturbative argument to show that the Krylov basis minimizes the early time growth of Wigner negativity in the large D limit. Using tools from random matrix theory, we then show that for a generic choice of basis, the Wigner negativity becomes exponentially large in an O(1) amount of time evolution. On the other hand, in the Krylov basis, the negativity grows gradually (i.e., as a power law) for an exponential amount of time, before saturating close to its maximum value. We take this as evidence that the Krylov basis is ideally suited for a dual, semi-classical description of chaotic quantum dynamics at large D. We discuss connections with the emergence of the dual gravitational description in AdS/CFT.

general relativity and quantum cosmologyHEP - phenomenologyHEP - theorymathematical physicsquantum physics

Audience: researchers in the topic

High Energy Theory NYU Abu Dhabi