Experimental quantification of spatial correlations in quantum dynamics

TL;DR

This paper introduces a scalable, platform-independent method to quantify and analyze spatial correlations in quantum dynamics, demonstrated experimentally on a trapped ion system, with implications for quantum error correction.

Contribution

It derives a lower bound for a quantum correlation measure that does not require full process tomography and extends it to multipartite systems.

Findings

Successfully applied to a trapped ion quantum processor

Quantified spatial correlations in environmental noise

Method is scalable and applicable to various quantum platforms

Abstract

Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [\'A. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for two- and four-qubit systems. The method proposed and demonstrated in this work is scalable, platform-independent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures.