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arxiv: 2605.03600 · v1 · submitted 2026-05-05 · 🪐 quant-ph · cond-mat.str-el

Recognition: unknown

Interplay of Nonstabilizerness and Ergotropy in Quantum Batteries

Tanoy Kanti Konar , Jakub Zakrzewski
Authors on Pith no claims yet

Pith reviewed 2026-05-07 04:06 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el
keywords quantum batteriesnonstabilizernessergotropyU(1) symmetrymagic statesquantum chargingClifford evolutionspin chains
0
0 comments X

The pith

U(1)-symmetric interactions create a one-to-one match between ergotropy in a quantum battery and the total nonstabilizerness of the charger-battery system.

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

The paper studies how nonstabilizerness, or magic, influences work storage in quantum batteries modeled as spin chains. One half of the chain acts as charger and the other as battery, and different interaction types are compared. When the interaction Hamiltonian preserves U(1) symmetry, the extractable work from the battery equals the total magic across both parts. This exact correspondence vanishes for interactions that break the symmetry. When the battery starts in a magic state and is charged using Clifford operations, the peak average power varies non-monotonically with initial magic and can reach its maximum even at zero initial magic.

Core claim

In an N-spin chain with a fixed left-right bipartition, U(1)-symmetric charger-battery interactions produce an exact equality between the ergotropy stored in the battery and the total nonstabilizerness of the full composite state. Interactions lacking U(1) symmetry destroy this equality. In the complementary protocol where the battery begins in a nonstabilizer state and evolves under Clifford gates, the maximum average charging power depends non-monotonically on the initial nonstabilizerness and attains its highest value for certain states with zero magic.

What carries the argument

U(1)-symmetry-preserving interaction Hamiltonians between the charger and battery halves, which enforce a conserved charge that directly equates battery ergotropy to the composite system's total magic.

Load-bearing premise

The physical system must consist of a fixed bipartition into charger and battery halves whose interactions fall cleanly into symmetry-preserving or symmetry-breaking classes.

What would settle it

A numerical or physical realization with U(1)-preserving interactions in which the computed ergotropy fails to equal the independently calculated total nonstabilizerness would disprove the claimed correspondence.

Figures

Figures reproduced from arXiv: 2605.03600 by Jakub Zakrzewski, Tanoy Kanti Konar.

Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 2
Figure 2. Figure 2: Ergotropy growth of the battery. The ergotropy of the bat￾tery depends upon the spectrum of both the battery and the Hamiltonian. Now one can check that the battery is diago￾nal in the energy basis and importantly, 1 − p > p which indicates the population of the ground state is higher than the excited state. Hence the battery remains passive at short time, hence, the ergotropy of the battery is zero at sho… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 view at source ↗
Figure 4
Figure 4. Figure 4: (a)) [76]. Importantly, this saturation value differs from the Haar-random limit because the U(1)-symmetric cSYK dy￾namics explores only a symmetry-constrained subspace of the total Hilbert space. Similarly, the ergotropy also grows as a power law, ∼ t β with β ≈ 2, and saturates to a finite steady-state value E sat (see right axis of view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 view at source ↗
read the original abstract

Nonstabilizerness plays an essential role in an efficient simulation of quantum systems on quantum computers. In this work, we investigate its role in the context of quantum batteries (QBs). To this end, we consider a system of N spin-1/2 particles, where the left half serves as the charger and the right half acts as the battery. By studying different classes of interactions between the charger and the battery, we quantify the amount of nonstabilizerness required to store work in the QB. Our results reveal that a one-to-one correspondence between the ergotropy stored in the battery and the total nonstabilizerness of the composite system emerges whenever the interaction Hamiltonian preserves a U(1) symmetry. In contrast, this correspondence is generally lost for more generic interactions that do not respect this symmetry. Finally, we examine the complementary scenario in which the battery is initialized in a nonstabilizer state and subsequently charged through Clifford evolution. In this case, we find that the maximum average charging power exhibits a non-monotonic dependence on the initial nonstabilizerness. Remarkably, the highest average power can be achieved even when the initial state carries no magic (nonstabilizerness), demonstrating that the initial magic is not a necessary resource for generating an optimal charging power in this protocol.

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 studies an N-spin-1/2 chain with a fixed left-half charger and right-half battery bipartition. It classifies interaction Hamiltonians and reports that a one-to-one correspondence between battery ergotropy and total composite nonstabilizerness appears precisely when the interaction preserves U(1) symmetry, while the correspondence is lost for generic interactions lacking this symmetry. In the complementary protocol where the battery begins in a nonstabilizer state and is charged by Clifford evolution, the maximum average charging power is found to depend non-monotonically on the initial nonstabilizerness, with the global maximum achievable even for stabilizer initial states.

Significance. If the reported bijection can be shown to hold for arbitrary U(1)-invariant interactions and bipartitions, the result would furnish a concrete link between two operationally distinct quantum resources (ergotropy and nonstabilizerness), with potential implications for resource-efficient quantum battery design. The finding that optimal charging power does not require initial magic is a useful counter-example to the intuition that magic is always a necessary resource for quantum advantage in thermodynamic protocols. The work is technically sound within the models examined and supplies concrete numerical evidence for the interplay, but its broader claims rest on the scope of the symmetry classification.

major comments (2)
  1. [Abstract / main results] Abstract and main results section: the statement that the one-to-one correspondence 'emerges whenever the interaction Hamiltonian preserves a U(1) symmetry' is not accompanied by a general analytic derivation. The evidence is confined to specific families of U(1)-preserving interactions on the fixed half-half bipartition; it remains unclear whether the bijection survives for other U(1)-invariant Hamiltonians (e.g., longer-range or differently structured) or for unequal bipartitions such as 1-vs-(N-1). A counter-example or a proof that the symmetry alone is sufficient would be required to support the 'whenever' claim.
  2. [Clifford charging section] Clifford-charging protocol: the claim that the highest average charging power can be achieved with zero initial nonstabilizerness is interesting, but the manuscript does not specify the precise figure of merit (instantaneous power, time-averaged power, or integrated work), the ensemble over which the average is taken, or the optimization procedure used to identify the maximum. Without these details it is difficult to assess whether the non-monotonic dependence is robust or an artifact of the chosen initial-state parametrization.
minor comments (2)
  1. [Abstract] The abstract mentions 'different classes of interactions' but does not list the explicit Hamiltonians or the symmetry classification criteria; a short table or appendix summarizing the interaction families would improve readability.
  2. [Methods / definitions] Notation for the nonstabilizerness measure (e.g., whether it is the stabilizer Rényi entropy, mana, or another monotone) should be defined at first use and kept consistent throughout.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback, which has prompted us to clarify the scope of our claims and improve the presentation of our results. We address each major comment below and have revised the manuscript to enhance precision and completeness.

read point-by-point responses

  1. Referee: [Abstract / main results] Abstract and main results section: the statement that the one-to-one correspondence 'emerges whenever the interaction Hamiltonian preserves a U(1) symmetry' is not accompanied by a general analytic derivation. The evidence is confined to specific families of U(1)-preserving interactions on the fixed half-half bipartition; it remains unclear whether the bijection survives for other U(1)-invariant Hamiltonians (e.g., longer-range or differently structured) or for unequal bipartitions such as 1-vs-(N-1). A counter-example or a proof that the symmetry alone is sufficient would be required to support the 'whenever' claim.

    Authors: We appreciate this observation. Our results, including the numerical evidence and analytic arguments, are derived for specific families of U(1)-preserving Hamiltonians (nearest-neighbor and certain long-range variants) on the balanced N/2 vs. N/2 bipartition. The U(1) symmetry enforces conservation of total magnetization, which in turn links the battery ergotropy directly to the total nonstabilizerness through the structure of the eigenstates and the resource theory of magic. In the revised manuscript we have updated the abstract and introduction to read 'for the U(1)-symmetric interactions examined in this work' rather than the broader 'whenever' phrasing. We have also added a new discussion paragraph explaining why the symmetry is expected to be the essential ingredient and why we anticipate the correspondence to hold more generally, while explicitly noting that a rigorous proof for arbitrary U(1)-invariant Hamiltonians and unbalanced bipartitions lies beyond the present scope. No counter-examples were found within the models we tested. revision: partial

  2. Referee: [Clifford charging section] Clifford-charging protocol: the claim that the highest average charging power can be achieved with zero initial nonstabilizerness is interesting, but the manuscript does not specify the precise figure of merit (instantaneous power, time-averaged power, or integrated work), the ensemble over which the average is taken, or the optimization procedure used to identify the maximum. Without these details it is difficult to assess whether the non-monotonic dependence is robust or an artifact of the chosen initial-state parametrization.

    Authors: We regret the omission of these technical details. The figure of merit is the time-averaged charging power, defined as the total ergotropy extracted from the battery divided by the total charging time, and then averaged over an ensemble of Clifford circuits. The ensemble consists of random Clifford unitaries drawn uniformly from the Clifford group (implemented via random Clifford gates up to a fixed depth sufficient for convergence). The optimization is performed by parametrizing the initial battery state as a convex combination of a stabilizer state and a non-stabilizer state controlled by a single magic parameter, then numerically maximizing the averaged power over both this parameter and the circuit realizations. In the revised manuscript we have inserted a new subsection that explicitly defines the power measure, describes the ensemble and sampling procedure, details the numerical optimization algorithm, and includes additional figures demonstrating that the non-monotonic dependence and the zero-magic optimum persist across different system sizes and circuit depths, confirming robustness beyond the original parametrization. revision: yes

Circularity Check

0 steps flagged

No significant circularity: correspondence is an observed outcome of explicit computations across interaction classes

full rationale

The paper defines ergotropy (maximum extractable work) and nonstabilizerness (magic) as independent quantities and evaluates both for concrete families of charger-battery interactions in a fixed left-right bipartition of the N-spin chain. The reported one-to-one link appears only for the U(1)-preserving classes and is absent for generic interactions; this is presented as a comparative numerical/analytic result rather than a definitional identity or a fitted parameter relabeled as a prediction. No load-bearing self-citation, ansatz smuggling, or uniqueness theorem imported from prior author work is required for the central claim. The derivation chain therefore remains self-contained within the model calculations and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract supplies no explicit free parameters, invented entities, or non-standard axioms; the model relies on standard quantum spin Hamiltonians and the definition of nonstabilizerness and ergotropy from prior literature.

axioms (1)
  • domain assumption The composite system is modeled as N spin-1/2 particles bipartitioned into charger and battery halves with well-defined interaction Hamiltonians that either preserve or break U(1) symmetry.
    This modeling choice is stated directly in the abstract as the setup used to quantify the interplay.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Clifford Ergotropy

    quant-ph 2026-05 unverdicted novelty 7.0

    Clifford ergotropy is upper-bounded by a magic measure, exhibits a control transition in two qubits, and implies a second law under Clifford operations for typical many-body states.

Reference graph

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