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arxiv: 2508.08998 · v2 · submitted 2025-08-12 · 🪐 quant-ph

Realizing the Petz Recovery Map on an NMR Quantum Processor

Gayatri Singh , Ram Sagar Sahani , Vinayak Jagadish , Lea Lautenbacher , Nadja K. Bernardes , Kavita Dorai This is my paper

Pith reviewed 2026-05-18 23:23 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Petz recovery mapquantum noiseNMR quantum processorduality quantum computingamplitude dampingphase dampingreference state
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The pith

The Petz recovery map can be realized on an NMR quantum processor as a reference-state-dependent recovery channel.

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

This paper shows how the Petz recovery map, a theoretical prescription for reversing quantum noise that depends on a chosen reference state, can be physically implemented using the duality quantum computing algorithm on a nuclear magnetic resonance quantum processor. Tests on amplitude damping and phase damping noise with tuned reference states reveal better recovery when the reference matches the noise and weaker recovery when it does not. The experimental fidelities match theoretical predictions closely, indicating that the map functions as a workable physical channel.

Core claim

The authors implement the Petz recovery map via the duality quantum computing algorithm on an NMR quantum processor for single-qubit amplitude damping and phase damping channels, obtaining close quantitative agreement between measured recovery fidelities and theoretical predictions across families of reference states and thereby establishing the map as a physically realizable, reference-state-dependent recovery channel.

What carries the argument

The Petz recovery map, a reference-state-dependent quantum channel that reverses the effects of a given noise process.

If this is right

  • Recovery fidelity increases when the reference state is chosen to match the noise model.
  • The method supplies an experimental benchmark for testing state-adapted recovery on near-term quantum hardware.
  • The same approach can validate recovery performance for other single-qubit noise channels.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Optimal reference-state selection may become a practical lever for improving error mitigation on small devices.
  • The technique could be tested on multi-qubit systems or different hardware platforms to check whether quantitative agreement persists.

Load-bearing premise

The duality quantum computing algorithm faithfully implements the Petz recovery map on the NMR hardware without unaccounted physical errors or decoherence that would invalidate the observed agreement with theory.

What would settle it

Repeating the experiment for a well-matched reference state and finding recovery fidelities that deviate substantially from the theoretical predictions would falsify faithful physical realization of the map.

Figures

Figures reproduced from arXiv: 2508.08998 by Gayatri Singh, Kavita Dorai, Lea Lautenbacher, Nadja K. Bernardes, Ram Sagar Sahani, Vinayak Jagadish.

Figure 1
Figure 1. Figure 1: FIG. 1: (Color online) [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (Color online) Schematic of the quantum circuit used to implement the damping channel and the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (Color online) NMR pulse sequence used to [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (Color online) Experimental results for the AD [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (Color online) Experimental results showing the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

The Petz recovery map is a central construct in quantum information theory, providing an explicit, channel-aware prescription for reversing the effects of noise. Unlike standard quantum operations, the Petz map is intrinsically dependent on a chosen reference state, which makes its physical implementation and experimental validation particularly challenging. Here, we report an experimental realization of Petz recovery maps on a nuclear magnetic resonance (NMR) quantum processor using the duality quantum computing (DQC) algorithm. We investigate two paradigmatic single-qubit noise models: amplitude damping and phase damping, and construct corresponding families of Petz recovery maps for varying reference states. By systematically tuning the reference state, we experimentally demonstrate the state-adapted nature of Petz recovery, observing both enhanced recovery when the reference state is well matched and fidelity degradation for mismatched choices. Our experimental results show close quantitative agreement with theoretical predictions, providing direct evidence that the Petz recovery map constitutes a physically realizable, reference-state-dependent recovery channel rather than a purely formal inverse of noise. This work bridges the gap between the abstract information-theoretic formulation of Petz recovery and its implementation on a realistic quantum platform, and establishes an experimental benchmark for testing noise-adapted recovery strategies on near-term quantum devices.

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

1 major / 2 minor

Summary. The manuscript reports an experimental realization of the Petz recovery map on an NMR quantum processor via the duality quantum computing algorithm. For amplitude-damping and phase-damping channels, the authors construct reference-state-dependent Petz maps, tune the reference state, and measure recovery fidelities that exhibit close quantitative agreement with theoretical predictions, thereby demonstrating the state-adapted character of the map.

Significance. If the DQC implementation is shown to faithfully reproduce the theoretical Petz channel without dominant contamination from native NMR relaxation or control errors, the work would provide the first direct experimental evidence that the Petz map is a physically realizable, reference-state-dependent recovery operation. This would bridge abstract quantum information theory with near-term hardware and supply a concrete benchmark for noise-adapted recovery protocols.

major comments (1)
  1. [Results section] Results section: The claim of 'close quantitative agreement' with theory for tuned reference states is load-bearing for the central assertion of faithful Petz-map realization, yet the manuscript provides neither error bars on the reported fidelities, details of the fidelity metric, process-tomography characterization of the implemented channel, nor bounds on the contribution of T1/T2 relaxation and RF inhomogeneity during the DQC circuit. Without these, it remains possible that the observed state dependence arises from unaccounted hardware effects rather than the intended map.
minor comments (2)
  1. [Abstract] The abstract states that two noise models were investigated but does not indicate the number of experimental repetitions or the specific NMR sample used; adding these would improve reproducibility assessment.
  2. Figure captions could explicitly state whether theoretical curves are overlaid on experimental data points to facilitate direct visual comparison of the quantitative agreement.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive critique of our manuscript on the experimental realization of reference-state-dependent Petz recovery maps. We have revised the manuscript to strengthen the quantitative validation of our results and to address concerns about potential hardware contributions.

read point-by-point responses

  1. Referee: [Results section] Results section: The claim of 'close quantitative agreement' with theory for tuned reference states is load-bearing for the central assertion of faithful Petz-map realization, yet the manuscript provides neither error bars on the reported fidelities, details of the fidelity metric, process-tomography characterization of the implemented channel, nor bounds on the contribution of T1/T2 relaxation and RF inhomogeneity during the DQC circuit. Without these, it remains possible that the observed state dependence arises from unaccounted hardware effects rather than the intended map.

    Authors: We agree that explicit error bars, a clear definition of the fidelity metric, and quantitative bounds on systematic errors strengthen the central claim. In the revised manuscript we have added statistical error bars to all fidelity plots, obtained from repeated experimental runs with standard deviation. The fidelity is the standard Uhlmann state fidelity, now defined explicitly in the Methods section together with the precise formula used for comparison with theory. Full process tomography of the recovery channel was not performed in the original data set because the experiment targets specific input states rather than a complete channel characterization; however, we have added a supplementary analysis that reconstructs the effective action of the DQC circuit on the relevant subspace and confirms consistency with the theoretical Petz map. We have also included new bounds on T1/T2 relaxation and RF inhomogeneity, derived from independent calibration measurements performed on the same spectrometer, showing that their cumulative effect during the DQC sequence is below 4 % and cannot reproduce the observed reference-state dependence. These additions appear in the revised Results section and a new supplementary note. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental implementation with independent theoretical benchmarks

full rationale

The paper is an experimental demonstration of realizing the Petz recovery map via the duality quantum computing algorithm on NMR hardware for amplitude and phase damping channels. It reports quantitative agreement between measured fidelities and pre-existing theoretical predictions for varying reference states, without deriving the Petz map, its properties, or any load-bearing result from the experimental data itself. No equations reduce predictions to fitted inputs, no self-citation chains justify uniqueness, and the central claim rests on external theory plus hardware implementation rather than self-referential construction. This is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard quantum channel theory and the assumption that DQC can realize the Petz map; no new free parameters or invented entities are introduced beyond the experimental platform.

axioms (1)
  • domain assumption The duality quantum computing algorithm can be used to implement the Petz recovery map on NMR hardware
    Invoked to justify the experimental construction of the recovery channel.

pith-pipeline@v0.9.0 · 5765 in / 1107 out tokens · 29982 ms · 2026-05-18T23:23:00.630301+00:00 · methodology

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