Clifford and Haar scramblers yield equal mean fidelity but unequal fluctuations in black hole-inspired teleportation

arXiv:2606.19180 · quant-ph · Submitted 2026-06-17 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Clifford and Haar scramblers yield equal mean fidelity but unequal fluctuations in black hole-inspired teleportation".

Mira: The gist The comparison between Clifford and Haar scramblers yields equal mean fidelity but unequal fluctuations in black hole-inspired teleportation Model and Protocol The study investigates the dynamics of Quantum…

Kai: First, who's behind it and why it matters.

Title and authors: Mira: Let's talk about who wrote this. The authors are Sudhanva Joshi and Sunil Kumar Mishra from the Indian Institute of Technology Banaras Hindu University. They’re clearly deep into the Sachdev-Ye-Kitaev model, which is a huge area for studying quantum gravity ideas.

Kai: Yeah, their background is right there in the physics department, which makes sense given they're working with these kinds of complex many-body systems. The paper also references some foundational work like Maldacena and Stanford on chaos and AdS space four, which tells us this isn't just a random scramble; it’s connected to these holographic ideas <ref:2606.19180#pg3>.

Lev: From an error correction standpoint, seeing work rooted in the SYK model is valuable because it connects scrambling dynamics to concepts that might actually be relevant for building robust quantum systems later on.

Kai: So, what's the main point of this paper regarding the title? It’s about showing that we need more than just magic to get successful wormhole teleportation; we need the right kind of structure in how that magic is distributed.

Mira: That’s because they aren't just looking at how much magic accumulates overall; they are tracking it through every single step of this teleportation circuit, from the initial preparation all the way to extracting the message on the other side.

Lev: And what I find compelling is that they are using a baseline-subtracted diagnostic—that specific formula delta M2(tR) = M(g=g*) two(tR) - M(g=zero) two(tR) —to really isolate the actual coupling-induced redistribution of resources, separating it from just generic magic growth <ref:2606.19180#pg3>.

Kai: That isolation is key because it lets them see the effect of that double-trace coupling, which is what actually makes the teleportation work in this model. It shows how that coupling channels those non-stabilizer resources into the signal.

Mira: And they find something specific about how this channeling works depending on temperature; it’s not uniform across all conditions.

Lev: Yeah, it suggests that the physics of non-stabilizerness isn't just a static property; it’s a dynamic resource that gets managed during the actual process of teleportation.

Kai: It points toward the idea that raw non-stabilizerness alone isn't enough to traverse these wormholes; you need this specific channeling mechanism at work.

The paper's summary: Kai: So, let’s get into what the paper actually says in terms of results. They’re using a second-order stabilizer Rényi entropy, or SRE, to measure this magic across the different stages of the wormhole inspired teleportation protocol in the SYK model.

Mira: The main finding is that they found a qualitative difference in how non-stabilizerness relates to teleportation fidelity depending on whether we are in the gravitational regime or the peaked-size regime.

Lev: In the gravitational, low temperature regime, they found that fidelity starts rising at the same time as magic from the very beginning of the process, which they link to something called sizewinding.

Kai: That means in that low temperature scenario, you get a structured channel for information transfer right out of the gate because of how magic builds up early on.

Mira: But then in the high temperature, peaked-size regime, they found that magic builds up to near the Haar-typical value before teleportation actually starts happening.

Lev: That means in that high temperature scenario, you wait for a lot of the non-stabilizer resources to accumulate before you see any actual successful teleportation signal.

Kai: What’s really striking is how they use that baseline-subtracted diagnostic we talked about earlier, delta Mpeak2, which measures the coupling-induced magic right at the moment of optimal teleportation.

Mira: And they found that this diagnostic is positive across all the temperatures studied, meaning the coupling actually helps channel those resources into a signal whenever it matters most.

Lev: It reinforces that this isn't just about generating magic; it’s about how the system manages and redirects those resources during the operational teleportation circuit itself.

Kai: So, to put it simply, the paper shows that raw non-stabilizerness isn't enough for wormhole traversal; you need this specific dynamic channeling driven by the coupling.

The paper's improvements: Mira: Now let’s look at what the authors suggest for future work or how they improve their understanding. They point out that comparing this SYK protocol to other models, like a Clifford scrambler or a chaotic all-to-all random two-local model, gives them crucial insight.

Lev: They use that comparison to show that structured magic redistribution is what actually underlies successful wormhole traversal, not just the total amount of non-stabilizerness itself.

Kai: And they introduce a key diagnostic contrast involving the normalized SRE, M2/MHaar2 across different system sizes. This suggests there's a degree of universality in how fractional magic saturation relates to teleportation performance.

Mira: That idea that the fidelity-magic trajectories show an approximate collapse when normalized by Haar values hints at a universal relationship that holds across different system sizes, which is very powerful for theoretical physics.

Lev: They also use the time-domain signature of the SRE dipping transiently right at the fidelity peak in the peaked-size regime as a way to mark that teleportation event in time.

Kai: That dip is a strong signal; it means you can actually track when the teleportation happens dynamically, rather than just looking at an average result.

Mira: And they also note that because this protocol operates outside the usual one/N expansion limits of SYK, traditional holographic diagnostics might lose their resolution here <ref:2606.19180#pg3>.

Lev: So, a limitation they flag is that while these protocol-level diagnostics are useful, the paper doesn't provide a closed-form prediction for how the coupling evolves on its own during right-side evolution.

Conclusion: Kai: So, to wrap this up on "Clifford and Haar scramblers yield equal mean fidelity but unequal fluctuations in black hole-inspired teleportation," the paper really hammers home that raw non-stabilizerness isn't sufficient for wormhole traversal.

Mira: They show that the key difference lies in how magic is channeled during the operational protocol, and they provide a clear way to diagnose this channeling using that baseline-subtracted diagnostic, delta M2(tR).

Lev: And they’ve given us a picture of a two-phase temporal structure for this coupling effect: an initial suppression followed by a positive peak near the fidelity maximum whose amplitude shrinks as the inverse temperature goes up.

Kai: That’s really telling. It links the coupling-induced channeling directly to how well the teleportation performs across all those temperature regimes, from gravitational to peaked-size.

Mira: This work suggests that understanding this dynamic channeling is what separates successful wormhole traversal from just having a lot of non-stabilizer resources available in the system.

Lev: For me, it shows that we can use these protocol-level SRE analyses to probe physics that isn't accessible through static or free-evolution diagnostics.

Kai: It’s a great paper because it gives us concrete, measurable quantities—like that time-domain signature at the fidelity peak—to track the process in real simulations.

Mira: And for future work, they are looking to extend this analysis with Monte Carlo SRE sampling to see if that approximate collapse across system sizes tightens into a true scaling function.

Lev: It’s an important step toward connecting these theoretical results to what we might actually be able to measure on quantum simulation platforms soon.

Department of Physics, Indian Institute of Technology (Banaras Hindu University)

quant-ph

Submitted: 2026-06-17

Updated: 2026-10-08

Comments: 8 pages. To be communicated to a Journal soon. Comments will be highly appreciated

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 92/100

The gist: The gist The comparison between Clifford and Haar scramblers yields equal mean fidelity but unequal fluctuations in black hole-inspired teleportation Model and Protocol The study investigates the

Key concepts

Quantum Magic (Non-stabilizerness)
This refers to a measure of how far a quantum state is from being perfectly stable or 'trivial.' In this context, it quantifies the resources available in a system that can be used for complex processes like teleportation. The paper uses specific diagnostics to track how this non-stabilizer resource is redistributed during the protocol.
Wormhole-Inspired Teleportation Protocol (WITP)
This is a five-stage process designed to simulate traversable wormhole teleportation using a doubled SYK system. It involves preparing states, scrambling them, inserting a message qubit, evolving the system, and extracting the information from the opposite side. The goal is to see if this complex quantum operation works.
Second-order Stabilizer Rényi Entropy (SRE)
This is a mathematical tool used as a diagnostic to measure non-stabilizerness in a quantum state. It helps quantify how much 'magic' or non-trivial structure exists in the system. The paper uses this to track the magic growth and its relationship with teleportation fidelity across different system sizes.

Terminology

Summary

The gist The comparison between Clifford and Haar scramblers yields equal mean fidelity but unequal fluctuations in black hole-inspired teleportation

Model and Protocol

The study investigates the dynamics of Quantum magic, formally known as non-stabilizerness, across the stages of the wormholeinspired teleportation protocol (WITP) in the Sachdev-Ye-Kitaev (SYK) model The WITP realizes traversable wormhole teleportation explicitly by inserting a message qubit into one side of a doubled SYK system, scrambling it, transmitting it through a doubletrace left-right coupling, and extracting it from the opposite side The protocol involves five stages: initial TFD preparation, backward scrambling, message insertion, forward evolution, double-trace coupling, and right-side extraction

Diagnostics and Numerical Methods

The central diagnostic is the secondorder stabilizer Rényi entropy (SRE), denoted as M2(ψ), which is defined as M2(ψ) = − log2 1/d X P ∈Pn 4 for an n-qubit pure state ψ⟩ The Haar-typical SRE is given by MHaar2 = log2(d + 3) − 2 ≈ n − 2 The computation of the SRE is performed using a Walsh-Hadamard acceleration, reducing complexity to O(4n · n) A key methodological contribution is the baseline-subtracted magic diagnostic δM2(tR) = M(g=g∗)2(tR) − M(g=0)2(tR), which isolates the coupling-induced redistribution of non-stabilizer resources from trivial magic growth

Results and Physical Interpretation

The central physical finding is that the relationship between non-stabilizerness and teleportation fidelity is qualitatively different in the two regimes In the gravitational regime (low temperature), fidelity rises concurrently with magic from early times, consistent with the sizewinding mechanism providing a structured channel for information transfer In contrast, in the peaked-size regime (high temperature), magic accumulates to nearHaar-typical values before teleportation onset The coupling plays a central role in channeling nonstabilizer resources into the teleportation signal, with a β-dependent amplitude The baseline-subtracted diagnostic δMpeak2 measures the coupling-induced magic at the moment of optimal teleportation, which is empirically positive across all temperatures studied

Conclusion

The comparison with two non-SYK control models reinforces this conclusion, demonstrating that raw non-stabilizerness is necessary but not sufficient for wormhole traversal Only the SYK model produces the structured magic redistribution that underlies successful teleportation, pointing to a qualitative distinction between holographic and nonholographic scrambling at the level of non-stabilizer resources The baseline-subtracted diagnostic reveals a twophase temporal structure in the coupling’s effect on magic: an initial suppression followed by a positive peak near the fidelity maximum whose amplitude decreases monotonically with inverse temperature This provides a quantitative link between the coupling-induced channeling of nonstabilizer resources and teleportation performance across the full temperature range The robustness of these features across Nmaj = 8, 10, and 12, together with the approximate collapse of the fidelity-magic trajectories under Haar normalization, suggests that the diagnostics introduced here capture physics that persists beyond the specific system sizes studied

How it works

The protocol-level magic diagnostics track nonstabilizerness through every stage of the WITP circuit, revealing physics that static or free-evolution diagnostics cannot access The comparison with a chaotic all-to-all random two-local (R2L) model and a magic-free Clifford scrambler demonstrates that structured magic redistribution, rather than the amount of nonstabilizerness, underlies successful wormhole traversal The SRE dips transiently at the fidelity peak in the peaked-size regime, marking the teleportation event in the time domain The comparison of normalized SRE M2/MHaar2 across system sizes suggests a degree of universality in the relationship between fractional magic saturation and teleportation performance The fidelity-magic trajectory distinguishes the gravitational and peaked-size regimes through a global, time-integrated feature The diagnostic contrast A is positive and increases from Nmaj = 8 to Nmaj = 10, providing quantitative evidence that the regime separation sharpens with increasing system size

Limitations

The O(4n) cost of exact SRE computation constrains the accessible system sizes The approximate Haar-normalized collapse in Fig. 6(b) is suggestive but not quantitatively sharp, and whether a true universal scaling function governs the fidelity-magic relationship in the large-N limit remains open questions The diagnostic contrast A increases with system size rather than decreasing, which provides quantitative evidence that the regime separation sharpens at larger Nmaj The fidelity-magic trajectory of Fig. 2 distinguishes the two regimes through a global, time-integrated feature, which is robust against finite-size fluctuations because it does not require resolving a narrow exponential growth window or extracting a scaling exponent from noisy data The protocol-level SRE analysis operates in the complementary regime where the 1/N expansion breaks down, and traditional holographic diagnostics lose resolution

Future Work

On the analytical side, extending the near-Clifford structure of the coupling to capture non-perturbative right-side evolution could yield a closed-form prediction for δMpeak2(β) Computing the operator size distribution and its correlation with the SRE directly would connect the magic diagnostic to the established size-winding framework at a microscopic level On the numerical side, extending the Haar-normalized collapse analysis to Nmaj = 12 or 14 using Monte Carlo SRE sampling methods would test whether this approximate collapse observed here tightens into a quantitative scaling function On the experimental side, these diagnostics are directly applicable to near-term quantum simulation platforms on which WITP dynamics have already been realized The SRE is measurable via randomized Pauli measurements, and the baseline subtraction requires only a comparison between two experimental runs with and without the coupling pulse, making the fidelity-magic trajectory and the channeling diagnostic δM2 experimentally accessible without additional overhead

References

[1] Subir Sachdev and Jinwu Ye. “Gapless spinfluid ground state in a random quantum heisenberg magnet”. Physical Review Letters 70, 3339–3342 (1993)

[2] Juan Maldacena and Douglas Stanford. “Remarks on the sachdev-ye-kitaev model”. Physical Review D 94, 106002 (2016)

[3] Alexei Kitaev. “A simple model of quantum holography (part 2)”. Entanglement in stronglycorrelated quantum matterPage 38 (2015)

[4] Juan Maldacena, Stephen H Shenker, and Douglas Stanford. “A bound on chaos”. Journal of High Energy Physics 2016, 1–17 (2016)

[5] Juan Maldacena, Douglas Stanford, and Zhenbin Yang. “Conformal symmetry and its breaking in two-dimensional nearly anti-de sitter space”. Progress of Theoretical and Experimental Physics 2016, 12C104 (2016)

[6] Alexei Kitaev and S Josephine Suh.

Improvements for AI systems

  1. Overall AI architecture should incorporate a Magic Channeling Module that dynamically adjusts coupling strength based on temperature regime to maximize teleportation fidelity, leveraging the finding that the double-trace coupling first suppresses and then channels non-stabilizer resources toward the teleportation signal.

  2. The system can perform regime-dependent resource allocation: in the gravitational (low temperature) regime, it should prioritize early magic accumulation for concurrent fidelity rise, whereas in the peaked-size (high temperature) regime, it should wait for magic to saturate near the Haar-typical value before teleportation onset.

  3. The AI can implement a diagnostic tool using baseline-subtracted magic diagnostic δM2(tR) = M(g=g∗)2(tR) − M(g=0)2(tR) to distinguish between generic scrambling and coupling-induced redistribution, allowing it to isolate the teleportation signal from background noise.

  4. The system can utilize Haar-normalized SRE M2/MHaar2 as a primary organizing variable for fidelity, enabling robust comparison across different system sizes where the approximate collapse of the fidelity-magic trajectories suggests a degree of universality in the relationship between fractional magic saturation and teleportation performance.

  5. The AI can utilize time-domain signatures: it should monitor for the magic transiently dips at the fidelity peak, marking the teleportation event in the time domain, specifically looking for this dip in the peaked-size regime as a direct indicator of successful wormhole traversal.

Abstract

Quantum information transfer between entangled black holes has inspired many-body teleportation protocols. We study such a protocol without assuming a gravitational dual and ask whether its fidelity requires nonstabilizerness, or magic, in the scrambling dynamics. Because the mean fidelity depends only on the third moments of the scrambler ensemble, zero-magic Clifford scramblers teleport on average as well as Haar-random unitaries. Solving the protocol exactly at infinite temperature, we find that typical Clifford scramblers approach perfect teleportation while the magic of the complete circuit vanishes as the inverse system size. The two ensembles nevertheless differ in their fluctuations: the exact Clifford fidelity variance decays only algebraically with system size, whereas the Haar variance is exponentially small. This separation characterizes the ensembles rather than magic itself, since magic added away from the message qubit can leave every fidelity statistic unchanged. With a decoder uncorrelated with the scrambler, every unitary 2-design leaves the mean fidelity at the no-transfer value, whatever its magic.

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