Non-holonomic tomography I: The Born rule as a connection between experiments

Abstract

In the context of quantum tomography, we recently introduced a quantity called a partial determinant \cite{jackson2015detecting}. PDs (partial determinants) are explicit functions of the collected data which are sensitive to the presence of state-preparation-and-measurment (SPAM) correlated errors. As such, PDs bypass the need to estimate state-preparation or measurement parameters individually. In the present work, we suggest a theoretical perspective for the PD. We show that the PD is a holonomy and that the notions of state, measurement, and tomography can be generalized to non-holonomic constraints. To illustrate and clarify these abstract concepts, direct analogies are made to parallel transport, thermodynamics, and gauge field theory. This paper is the first of a two part series where the second paper [2] is about scalable applications of the PD to multiqudit systems.

13 pages, 13 figures; This paper is 1 of 2 papers which are an updated version of a single paper, arXiv:1608.08067, that has been withdrawn

References in corpus (3)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Measuring measurement
• Measuring Measurement: Theory and Practice

Cited by in corpus (6)

• On the freedom in representing quantum operations
• Experimental demonstration of loop state-preparation-and-measurement tomography
• Non-holonomic tomography II: Detecting correlations in multiqudit systems
• Loop State-preparation-and-measurement tomography of a two-qubit system
• Detecting correlated errors in twin-field quantum key distribution
• Detecting false correlations: Uncovering a faked Bell-inequality violation