Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos

TL;DR

This paper introduces a scheme where classical randomness is efficiently converted into quantum randomness using quantum chaos, enhancing the generation of quantum randomness for applications like shadow tomography.

Contribution

The authors propose a modified protocol that optimally converts classical entropy into quantum randomness via quantum chaos, improving scalability and efficiency.

Findings

Conversion efficiency is optimal in generic chaotic systems.

Each classical bit added yields as much quantum randomness as an extra qubit.

Enhanced randomness improves shadow tomography accuracy.

Abstract

Quantum many-body systems provide a unique platform for exploring the rich interplay between chaos, randomness, and complexity. In a recently proposed paradigm known as deep thermalization, random quantum states of system A are generated by performing projective measurements on system B following chaotic Hamiltonian evolution acting jointly on AB. In this scheme, the randomness of the projected state ensemble arises from the intrinsic randomness of the outcomes when B is measured. Here we propose a modified scheme, in which classical randomness injected during the protocol is converted by quantum chaos into quantum randomness of the resulting state ensemble. We show that for generic chaotic systems this conversion is optimal in that each bit of injected classical entropy generates as much additional quantum randomness as adding an extra qubit to B. This significantly enhances the randomness of the projected ensemble without imposing additional demands on the quantum hardware. Our scheme can be easily implemented on typical analog quantum simulators, providing a more scalable route for generating quantum randomness valuable for many applications. In particular, we demonstrate that the accuracy of a shadow tomography protocol can be substantially improved.