Trading athermality for nonstabiliserness

TL;DR

This paper explores how nonstabiliserness, a quantum property linked to quantum advantage, can be generated through thermal processes starting from stabiliser states, providing conditions, bounds, and trade-offs.

Contribution

It offers a necessary and sufficient condition for generating nonstabiliserness via thermal contact, along with explicit bounds and optimal regimes for qubits and general trade-offs.

Findings

Derived an analytic characterization of reachable nonstabiliser qubit states.

Identified Hamiltonians that maximize nonstabiliserness and critical temperatures for its emergence.

Established a general trade-off between nonstabiliserness and initial free energy under thermal operations.

Abstract

Quantum advantage arises from quantum states that cannot be efficiently simulated on a classical computer. Such states are characterised by a property known as nonstabiliserness. In this work, we investigate whether nonstabiliserness can be generated by placing an initially stabiliser state in contact with a heat bath. Under minimal thermodynamic assumptions, we derive a necessary and sufficient condition for when this is possible. This yields an analytic characterisation of all nonstabiliser qubit states reachable through such thermal processes, together with explicit bounds on their nonstabiliserness. This, in turn, allows us to identify optimal regimes for generating this resource, including the Hamiltonians that maximise nonstabiliserness and the critical temperatures at which it emerges. Beyond the qubit case, we establish a general trade-off between the nonstabiliserness attainable under thermal operations and the initial nonequilibrium free energy of the system.