Deep Thermalization and Measurements of Quantum Resources

TL;DR

This paper introduces a unified protocol based on deep thermalization to quantify the resource-generating power of quantum evolutions across various quantum resource theories, linking thermalization phenomena to resource assessment.

Contribution

It presents a novel method using deep thermalization and twirling identities to directly measure quantum resource generation in complex quantum circuits.

Findings

Deep thermalization can be used to infer resource-generating power.

New twirling identities enable direct assessment of quantum resources.

Quantum resources undergo deep thermalization at the subsystem level.

Abstract

Quantum resource theories (QRTs) provide a unified framework for characterizing useful quantum phenomena subject to physical constraints, but are notoriously hard to assess in experimental systems. In this letter, we introduce a unified protocol for quantifying the resource-generating power (RGP) of arbitrary quantum evolutions applicable to multiple QRTs. It is based on deep thermalization (DT), which has recently gained attention for its role in the emergence of quantum state designs from partial projective measurements. Central to our approach is the use of projected ensembles, recently employed to probe DT, together with new twirling identities that allow us to directly infer the RGP of the underlying dynamics. These identities further reveal how resources build up and thermalize in generic quantum circuits. Finally, we show that quantum resources themselves undergo deep thermalization at the subsystem level, offering a complementary and another experimentally accessible route to infer the RGP. Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs.