# Non-holonomic tomography II: Detecting correlations in multiqudit systems

## TL;DR

This paper extends the use of partial determinants in quantum tomography to detect various SPAM correlations in multiqudit systems, providing scalable methods with topological foundations.

## Contribution

It introduces new methods for detecting SPAM correlations using partial determinants, with a focus on scalable approaches and their topological relationships.

## Key findings

- Methods for detecting measurement-measurement correlations.
- Complete classification scheme for SPAM correlation detection methods.
- Scalable methods with settings scaling as O(d^4).

## Abstract

In the context of quantum tomography, quantities called a partial determinants\cite{jackson2015detecting} were recently introduced. PDs (partial determinants) are explicit functions of the collected data which are sensitive to the presence of state-preparation-and-measurement (SPAM) correlations. In this paper, we demonstrate further applications of the PD and its generalizations. In particular we construct methods for detecting various types of SPAM correlation in multiqudit systems | e.g. measurement-measurement correlations. The relationship between the PDs of each method and the correlations they are sensitive to is topological. We give a complete classification scheme for all such methods but focus on the explicit details of only the most scalable methods, for which the number of settings scale as $\mathcal{O}(d^4)$. This paper is the second of a two part series where the first paper[2] is about theoretical perspectives of the PD and its interpretation as a holonomy.