Parametrized Variational Quantum Tomography

TL;DR

This paper introduces a parametrized framework for quantum state tomography that unifies and extends existing methods, allowing controlled exploration of compatible states with improved fidelity to MaxEnt solutions.

Contribution

It generalizes Variational Quantum Tomography by interpolating between norms, enhancing reconstruction fidelity while maintaining computational efficiency.

Findings

The new method achieves higher fidelity to MaxEnt solutions.

Tuning hyperparameters controls the exploration of compatible states.

The approach remains computationally tractable.

Abstract

Quantum state tomography provides a fundamental framework for reconstructing quantum states. When the measurement data are not informationally complete, the observed statistics admit multiple compatible density matrices, making the reconstruction problem inherently underdetermined and calling for the selection of a meaningful estimator. Two well-established approaches to address this ambiguity are Maximum Entropy (MaxEnt) and Variational Quantum Tomography (VQT). A variant of VQT, named VQT$_\infty$, has been introduced to reproduce MaxEnt-like solutions. In this work, we generalize this approach by introducing a parametrized cost function that interpolates between the 1-norm and the infinity norm, thereby unifying VQT and VQT$_\infty$ within a single framework. By tuning the associated hyperparameters, the proposed method enables controlled exploration of the set of compatible density matrices. We show that this interplay yields reconstructed states with higher fidelity to the MaxEnt solution than those obtained via VQT$_\infty$ while preserving computational tractability.