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arxiv: 2606.19180 · v2 · pith:6CSAQO35new · submitted 2026-06-17 · 🪐 quant-ph

Quantum magic is necessary but not sufficient for wormhole-inspired teleportation

Sudhanva Joshi , Sunil Kumar Mishra This is my paper

Pith reviewed 2026-06-26 20:47 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum magicnon-stabilizernessSYK modelwormhole teleportationstabilizer Renyi entropyquantum scramblingholographic teleportation
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The pith

Quantum magic must be redistributed in a structured way by the coupling to enable wormhole-inspired teleportation rather than simply accumulating to high levels.

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

The paper tracks the stabilizer Rényi entropy, a measure of quantum magic or non-stabilizerness, through the scrambling, message insertion, coupling, and extraction stages of the wormhole-inspired teleportation protocol in the SYK model. Fidelity improves together with magic in the low-temperature gravitational regime, but the double-trace coupling first suppresses then directs the magic toward the teleportation signal. A chaotic random two-local model that reaches near-maximal magic and a magic-free Clifford scrambler that mixes operators efficiently both fail to teleport, showing that the amount of magic is insufficient without the right structure. Magic transiently dips at the fidelity peak, and the patterns are robust across system sizes with approximate collapse under Haar normalization.

Core claim

In the SYK model, successful wormhole-inspired teleportation requires the structured redistribution of non-stabilizerness resources by the left-right coupling, as evidenced by the failure of both high-magic chaotic models and magic-free scramblers to achieve high fidelity, with the magic measure showing a dip at the teleportation event.

What carries the argument

The double-trace coupling in the SYK model, which suppresses then channels non-stabilizer resources toward the teleportation signal, tracked via stabilizer Rényi entropy across protocol stages.

Load-bearing premise

The double-trace coupling in the SYK model with the chosen parameters accurately implements the wormhole-inspired teleportation protocol whose fidelity is being measured.

What would settle it

Observing high teleportation fidelity in a chaotic random two-local model that generates near-maximal magic would falsify the claim that structured redistribution is required beyond the total amount of magic.

Figures

Figures reproduced from arXiv: 2606.19180 by Sudhanva Joshi, Sunil Kumar Mishra.

Figure 1
Figure 1. Figure 1: Protocol-resolved magic dynamics in the SYK WITP at [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Parametric fidelity–magic trajectories during right [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of magic dynamics across three models at [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Baseline-subtracted magic during wormhole traversal. (a) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Finite-size scaling of the magic channeling diagnostic across three system sizes. (a) [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Haar-normalized magic dynamics. (a) Normalized SRE [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Magic distribution at the teleportation peak for the three models at [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Teleportation fidelity F at the fidelity peak ver￾sus stabilizer Rényi entropy M2 for the three Hamiltonian scramblers (SYK, blue circle; TFIM, red triangle; R2L, or￾ange square) and a random Clifford encoder (black star), at β = 2.0 J −1 , Nmaj = 10. The Clifford encoder replaces the SYK scrambling unitaries (Eqs. (6), (8)) by a random Clifford circuit on the full L ⊗ R register, which mixes operators ef￾… view at source ↗
read the original abstract

We investigate the dynamics of Quantum magic, formally known as non-stabilizerness, quantified by the stabilizer R\'enyi entropy (SRE), across the stages of the wormhole-inspired teleportation protocol (WITP) in the Sachdev-Ye-Kitaev (SYK) model. By tracking the SRE of the full pure state across scrambling, message insertion, left-right coupling, and right-side extraction, we uncover a regime-dependent relationship between magic accumulation and teleportation fidelity. In the gravitational (low temperature) regime, fidelity rises concurrently with magic from early times, whereas in the peaked-size (high temperature) regime, the magic saturates near the Haar-typical value before teleportation onset. A baseline-subtracted diagnostic comparing coupled and uncoupled protocols reveals that the double-trace coupling first suppresses and then channels non-stabilizer resources toward the teleportation signal, with the channel amplitude decreasing monotonically with inverse temperature. Comparison with a chaotic random two-local model that generates near-maximal magic yet fails to teleport, and with a magic-free Clifford scrambler that fails equally despite mixing operators efficiently, demonstrates that structured magic redistribution, rather than the amount of non-stabilizerness, underlies successful wormhole traversal. Moreover, the magic transiently dips at the fidelity peak, marking the teleportation event in the time domain. Our results are robust across the three system sizes studied ($N_{\mathrm{maj}}=8,10,12$), and the fidelity-magic trajectories exhibit an approximate collapse when the SRE is normalized by the Haar-typical prediction.

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 / 1 minor

Summary. The paper claims that in the SYK model, tracking stabilizer Rényi entropy (SRE) through the stages of the wormhole-inspired teleportation protocol (WITP) reveals a regime-dependent link between magic and fidelity; a baseline-subtracted diagnostic shows the double-trace coupling channels magic resources, and comparisons with a near-maximally magic random two-local model and a magic-free Clifford scrambler demonstrate that structured magic redistribution (rather than SRE magnitude) is required for successful teleportation. The results are stated to be robust for N_maj=8,10,12 with an approximate collapse after Haar normalization, and a transient SRE dip marks the fidelity peak.

Significance. If the central comparison holds, the work would usefully separate the role of magic structure from its total amount in a holographic teleportation setting, with the reported robustness across three system sizes and the normalized collapse constituting concrete strengths. The numerical nature of the study makes reproducibility of the SRE and fidelity trajectories particularly relevant to the claim.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'structured magic redistribution, rather than the amount of non-stabilizerness, underlies successful wormhole traversal' rests on the two control models failing to teleport under the same left-right double-trace coupling. Because both controls replace the SYK all-to-all Hamiltonian with different dynamics, it is not shown that the coupling term produces an equivalent effective channel or operator mixing; without this equivalence the attribution of failure specifically to the absence of structured magic redistribution is not load-bearing.
  2. [Abstract] Abstract (numerical results paragraph): the reported SRE trajectories, fidelity rise, transient dip, and approximate collapse after normalization for N_maj=8,10,12 are presented without error bars, sampling details, or justification of the temperature regimes; these omissions directly affect the statistical support for the regime-dependent relationship and the robustness statement.
minor comments (1)
  1. The baseline-subtracted diagnostic is invoked in the abstract but its precise definition and normalization procedure are not stated in the provided text, which would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments point by point below. Both points identify areas where the manuscript can be strengthened with additional discussion and data presentation; we commit to revisions accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'structured magic redistribution, rather than the amount of non-stabilizerness, underlies successful wormhole traversal' rests on the two control models failing to teleport under the same left-right double-trace coupling. Because both controls replace the SYK all-to-all Hamiltonian with different dynamics, it is not shown that the coupling term produces an equivalent effective channel or operator mixing; without this equivalence the attribution of failure specifically to the absence of structured magic redistribution is not load-bearing.

    Authors: The referee correctly identifies that the control models employ different scrambling dynamics, which could in principle alter how the fixed left-right double-trace coupling mixes operators. Our intent was to hold the coupling fixed while varying only the scrambling Hamiltonian to isolate the necessity of SYK-specific structured magic redistribution. We agree that explicit verification of channel equivalence would make the attribution more robust. In the revised manuscript we will add a dedicated paragraph analyzing the effective operator content and mixing induced by the coupling in each model, drawing on the existing numerical data for the controls. revision: partial

  2. Referee: [Abstract] Abstract (numerical results paragraph): the reported SRE trajectories, fidelity rise, transient dip, and approximate collapse after normalization for N_maj=8,10,12 are presented without error bars, sampling details, or justification of the temperature regimes; these omissions directly affect the statistical support for the regime-dependent relationship and the robustness statement.

    Authors: We acknowledge that the abstract and main-text presentation of the numerical results omits error bars, explicit sampling counts, and temperature-regime justification, even though these details appear in the methods and supplementary sections. This presentation choice weakens the immediate readability of the robustness claims. In the revision we will (i) add error bars to all SRE and fidelity plots, (ii) state the number of disorder realizations used for each system size, and (iii) expand the methods paragraph to justify the chosen inverse-temperature windows that define the gravitational and peaked-size regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper conducts numerical simulations tracking stabilizer Rényi entropy across WITP stages in the SYK model, with direct comparisons to two external control models (chaotic random two-local and Clifford scrambler). The central claim that structured magic redistribution (not SRE magnitude) underlies teleportation is supported by these empirical observations and the baseline-subtracted diagnostic, none of which reduce by the paper's own equations to a fitted parameter or self-referential definition. Haar-typical normalization is an external benchmark. No load-bearing step matches any of the enumerated circularity patterns; the work is self-contained against external controls.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on numerical evolution of the SRE in the SYK model under the WITP protocol; no free parameters, axioms, or invented entities are explicitly listed, but the protocol itself and the choice of SRE as the diagnostic are implicit modeling assumptions whose details are unavailable.

pith-pipeline@v0.9.1-grok · 5810 in / 1314 out tokens · 25512 ms · 2026-06-26T20:47:12.254658+00:00 · methodology

discussion (0)

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Reference graph

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