Learning partial transpose signatures in qubit ququart states from a few measurements

TL;DR

This paper develops machine learning methods to classify the distillability of qubit-ququart quantum states using fewer measurements, enabling efficient high-dimensional quantum resource characterization without full state tomography.

Contribution

It introduces a machine learning framework leveraging learnable observables to classify quantum state distillability more efficiently than traditional methods.

Findings

Learnable observables outperform Collective Measurement Witnesses in classification accuracy.

All models effectively distinguish PPT from NPT states.

Differentiating NPT subclasses remains a complex challenge.

Abstract

Higher-dimensional quantum systems are attracting interest for improving quantum protocol performance by increasing memory space. Characterizing quantum resources of such systems is fundamental but experimentally costly. We tackle the first non-trivial example: a qubit-ququart system, focusing on partial-transpose spectral classification. Entanglement distillation extracts maximally entangled states from noisy resources, but determining distillability typically requires full state tomography, experimentally prohibitive for high-dimensional systems. We explore a machine learning framework to classify distillable bipartite quantum states using fewer measurements than complete tomography. Our approach employs the PPT criterion, categorizing states by negative eigenvalues in the partial transpose. We use various ML algorithms, including Support Vector Machines, Random Forest, and Artificial Neural Networks, with features from fixed measurements and learnable observables. Results show learnable observables consistently outperform Collective Measurement Witnesses methods. While all models distinguish between non-distillable (PPT) and distillable (NPT) states, differentiating NPT subclasses remains challenging, underscoring the intricate Hilbert space geometry. This work provides an experimentally friendly tool for distillability verification in high-dimensional quantum systems without full state reconstruction