Enhanced entanglement from quantum ergodicity

TL;DR

This paper demonstrates that ergodic quantum dynamics can be harnessed to generate higher entanglement in quantum states than traditional scrambling methods, with implications for quantum information processing.

Contribution

It establishes a direct link between spectral statistics of quantum systems and entanglement generation, introducing ergodic dynamics as a resource for quantum state preparation.

Findings

Ergodic dynamics can produce more entanglement than maximally scrambling systems.

An exact relation between spectral statistics and entanglement evolution is derived.

Potential applications in quantum teleportation and information transfer are identified.

Abstract

The quantum chaos conjecture associates the spectral statistics of a quantum system with abstract notions of quantum ergodicity. Such associations are taken to be of fundamental and sometimes defining importance for quantum chaos, but their practical relevance has been challenged by theoretical and experimental developments. Here, in counterpoint, we show that ergodic dynamics can be directly utilized for the preparation of quantum states with parametrically higher entanglement than generated by maximally scrambling dynamics such as in random unitary circuits. Our setting involves quantum systems coupled via a "non-demolition" interaction of conserved charges. We derive an exact relation between the evolving entanglement of an initial product state and a measure of spectral statistics of the interacting charges in this state. This connection is explained via a notion of Krylov vector ergodicity, tied to the ability of quantum dynamics to generate orthonormal states over time. We consider exploiting this phenomenon for the preparation of approximate Einstein-Podolsky-Rosen (EPR) states between complex systems, a crucial resource for tasks such as quantum teleportation. We quantitatively show that the transfer of operators between entangled systems, which underlies the utility of the EPR state, can be performed with parametrically larger capacity for entanglement generated via ergodic dynamics than with maximal scrambling. Our analysis suggests a direct application of "ergodic" spectral statistics as a potential resource for quantum information tasks.