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  • Open Access

Transition from statistical to hardware-limited scaling in photonic quantum state reconstruction

Attila Baumann1, Zsolt Kis2, János Koltai1, and Gábor Vattay1,*

  • 1Institute for Physics and Astronomy, Eötvös Loránd University, Pázmány Péter s 1/A, 1117 Budapest, Hungary
  • 2Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, Konkoly-Thege Miklós út 29-33, 1117 Budapest, Hungary

  • *Contact author: gabor.vattay@ttk.elte.hu
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Phys. Rev. A 114, 023709 – Published 10 August, 2026

DOI: https://doi.org/10.1103/3gsc-krrq

Abstract

The theoretical efficiency of classical shadow tomography is predicated on a perfect Haar-random unitary ensemble, yet this mathematical ideal remains physically unattainable in near-term hardware. Here, we report the experimental characterization of a hardware-induced systematic error floor on integrated photonic processors: an operational Hardware Horizon, where the reconstruction error undergoes a sharp crossover. While the error initially obeys the predicted statistical scaling O(M−1/2) in a variance-dominated regime, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group, marking a transition to a bias-dominated regime. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this device-specific noise floor imposes a systematic saturation limit that statistical accumulation cannot overcome. These findings establish that the utility of shadow tomography on NISQ (noisy intermediate-scale quantum) hardware is defined by a specific scaling law involving hardware parameters, necessitating active compensation strategies to bridge the gap between theoretical purity and the noisy reality of integrated photonics.

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Phys. Rev. A 114, 023709– Published 10 August, 2026
  • Received 28 November 2025
  • Accepted 29 June 2026
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