Transition from Statistical to Hardware-Limited Scaling in Photonic Quantum State Reconstruction

TL;DR

This paper experimentally reveals a fundamental accuracy limit in photonic quantum state reconstruction caused by hardware imperfections, showing a phase transition from statistical to hardware-limited scaling and emphasizing the need for active error compensation.

Contribution

It introduces the concept of a 'Hardware Horizon' in photonic quantum tomography, demonstrating a phase transition in reconstruction error due to hardware-induced spectral distortions.

Findings

Error scales as M^{-1/2} initially

Error saturates at a hardware-dependent floor

Active compensation is necessary to improve accuracy

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 discovery of a fundamental accuracy bound on integrated photonic processors: a ``Hardware Horizon'' where the reconstruction error undergoes a sharp phase transition. While the error initially obeys the predicted statistical scaling $\mathcal{O}(M^{-1/2})$, it abruptly saturates at a floor determined by the spectral distortions of the realized unitary group. By deriving a phenomenological error model, we decouple the competing mechanisms of static coherent spectral distortion and dynamic decoherence, demonstrating that this intrinsic noise floor imposes a hard bound 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.