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arxiv: 2511.13839 · v2 · submitted 2025-11-17 · 🪐 quant-ph

Trading athermality for nonstabiliserness

A. de Oliveira Junior , Rafael A. Macedo , Jakub Czartowski , Jonatan Bohr Brask , Rafael Chaves This is my paper

Pith reviewed 2026-05-17 21:19 UTC · model grok-4.3

classification 🪐 quant-ph
keywords nonstabilisernessthermal operationsstabilizer statesquantum thermodynamicsresource theoryqubit statesnonequilibrium free energy
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The pith

A necessary and sufficient condition determines when thermal contact with a heat bath can generate nonstabiliserness from stabilizer states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates whether nonstabiliserness, a property required for quantum computational advantage, can arise when an initial stabilizer state is placed in contact with a heat bath. Under minimal thermodynamic assumptions, it derives a necessary and sufficient condition for when such thermal processes succeed in creating nonstabiliserness. For qubits the work supplies an analytic characterization of every reachable nonstabiliser state together with explicit upper bounds on the nonstabiliserness that can be obtained. Optimal Hamiltonians and the critical temperatures at which nonstabiliserness first appears are identified. For systems of any dimension a general trade-off is shown between the nonstabiliserness that thermal operations can produce and the initial nonequilibrium free energy of the system.

Core claim

Under minimal thermodynamic assumptions, a necessary and sufficient condition is derived for when thermal processes can generate nonstabiliserness from stabilizer states. This yields an analytic characterisation of all nonstabiliser qubit states reachable through such thermal processes, together with explicit bounds on their nonstabiliserness. Optimal regimes for generating this resource are identified, including the Hamiltonians that maximise nonstabiliserness and the critical temperatures at which it emerges. Beyond the qubit case, a general trade-off is established between the nonstabiliserness attainable under thermal operations and the initial nonequilibrium free energy of the system.

What carries the argument

The necessary and sufficient condition, derived from minimal thermodynamic assumptions, that governs when thermal operations on stabilizer states produce nonstabiliserness.

Load-bearing premise

The interaction between the system and the heat bath is fully captured by the minimal thermodynamic operations used to derive the necessary and sufficient condition.

What would settle it

An experiment that produces a nonstabiliser qubit state from a stabilizer state via thermal contact while violating the derived necessary and sufficient condition, or that fails to produce nonstabiliserness when the condition is satisfied.

Figures

Figures reproduced from arXiv: 2511.13839 by A. de Oliveira Junior, Jakub Czartowski, Jonatan Bohr Brask, Rafael A. Macedo, Rafael Chaves.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates whether nonstabiliserness can be generated from an initially stabiliser state by contact with a heat bath. Under minimal thermodynamic assumptions it derives a necessary and sufficient condition for this to occur, yielding an analytic characterisation of all reachable nonstabiliser qubit states together with explicit bounds on their nonstabiliserness. It further identifies optimal Hamiltonians and critical temperatures, and establishes a general trade-off between attainable nonstabiliserness under thermal operations and the system's initial nonequilibrium free energy.

Significance. If the central derivation is correct, the work supplies a quantitative bridge between athermality (a thermodynamic resource) and nonstabiliserness (a resource for quantum advantage). The explicit qubit characterisation, bounds, and free-energy trade-off are concrete enough to be tested experimentally and to guide further resource-theoretic investigations.

major comments (2)
  1. [Abstract and the paragraph introducing the minimal assumptions] The necessary-and-sufficient condition is stated to hold under 'minimal thermodynamic assumptions,' yet the manuscript does not provide an explicit list or justification of those assumptions (e.g., whether the allowed operations are strictly energy-preserving unitaries on system plus Gibbs bath, or whether catalysis and initial correlations are excluded). This is load-bearing for the central claim because relaxing any of these restrictions could enlarge the set of reachable states, rendering the stated condition sufficient but not necessary.
  2. [The qubit-characterisation section] The analytic characterisation of reachable qubit states and the explicit bounds on nonstabiliserness are derived from the necessary-and-sufficient condition; therefore any ambiguity in the scope of the thermal operations directly affects the tightness of those bounds and the identification of optimal Hamiltonians and critical temperatures.
minor comments (2)
  1. Define the nonstabiliserness measure (or measures) employed and state whether the bounds are independent of the choice of measure.
  2. Number all displayed equations and ensure every equation referenced in the text carries an explicit label.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive overall assessment. We agree that greater explicitness regarding the minimal thermodynamic assumptions is needed to support the central claims. We have revised the manuscript to address this and respond point by point below.

read point-by-point responses

  1. Referee: [Abstract and the paragraph introducing the minimal assumptions] The necessary-and-sufficient condition is stated to hold under 'minimal thermodynamic assumptions,' yet the manuscript does not provide an explicit list or justification of those assumptions (e.g., whether the allowed operations are strictly energy-preserving unitaries on system plus Gibbs bath, or whether catalysis and initial correlations are excluded). This is load-bearing for the central claim because relaxing any of these restrictions could enlarge the set of reachable states, rendering the stated condition sufficient but not necessary.

    Authors: We agree that an explicit enumeration and justification of the assumptions strengthens the manuscript. In the revised version we have inserted a dedicated paragraph (immediately after the abstract and again in Section II) that lists the minimal thermodynamic assumptions as follows: (i) interactions occur exclusively via energy-preserving unitaries on the joint system-plus-bath Hilbert space (standard thermal operations with no external work source); (ii) the bath is prepared in a Gibbs state at fixed inverse temperature β; (iii) the system and bath are initially uncorrelated; and (iv) catalysis is disallowed. These are the weakest operations that remain thermodynamically consistent without introducing additional resources. We have added brief justifications with references to the resource-theory literature. With this clarification the necessary-and-sufficient condition is both necessary and sufficient precisely under the stated operations. While we acknowledge that allowing catalysis or initial correlations could enlarge the reachable set, our claims are scoped to the minimal case, which is now stated unambiguously. revision: yes

  2. Referee: [The qubit-characterisation section] The analytic characterisation of reachable qubit states and the explicit bounds on nonstabiliserness are derived from the necessary-and-sufficient condition; therefore any ambiguity in the scope of the thermal operations directly affects the tightness of those bounds and the identification of optimal Hamiltonians and critical temperatures.

    Authors: We concur that the qubit characterisation, bounds, optimal Hamiltonians and critical temperatures inherit their validity from the precise scope of the allowed operations. Following the addition of the explicit assumption list described above, we have inserted a clarifying sentence in Section III stating that the analytic characterisation and all derived bounds apply strictly under the listed minimal thermal operations. We have also added a short remark noting that the identified optimal Hamiltonians and critical temperatures are optimal within this class. These changes remove any residual ambiguity while preserving the original derivations. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained under standard thermodynamic principles with no reduction to self-citation or fitted inputs

full rationale

The paper derives a necessary and sufficient condition for generating nonstabiliserness from stabilizer states via thermal processes under minimal thermodynamic assumptions, yielding qubit characterizations, bounds, and a free-energy trade-off. No equations or steps in the abstract or described claims reduce by construction to prior self-citations, fitted parameters renamed as predictions, or ansatzes smuggled via author overlap. The central results are presented as following from energy-preserving unitaries on system plus bath in Gibbs state, without evidence that the condition is defined in terms of the target nonstabiliserness or that uniqueness is imported from unverified self-work. This is the common case of an independent derivation grounded in external thermodynamic definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work relies on standard concepts from quantum thermodynamics and resource theory but introduces no new free parameters, invented entities, or ad-hoc axioms beyond the stated minimal thermodynamic assumptions.

axioms (1)
  • domain assumption Minimal thermodynamic assumptions
    Invoked in the abstract to derive the necessary and sufficient condition for nonstabiliserness generation under thermal processes.

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Forward citations

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  2. Every Little Thing Heat Does Is Magic

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    Stabiliser theory in a nutshell The starting point is the n-qubit Pauli group Pn = f 1, ig f /x31, X, Y, Zg n, whose elements are tensor products of single-qubit Pauli operators. A stabiliser state on n-qubits is a pure state that is the joint +1 eigenstate of an abelian subgroup S P n of size jS j = 2n. For a single qubit, pure stabiliser states are prec...

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