Constraints on correlations in multiqubit systems

TL;DR

This paper investigates the structure of correlations in multiqubit quantum systems, revealing how odd and even correlations are interconnected and how this understanding can aid in state determination and entanglement detection.

Contribution

It introduces a novel analysis dividing correlations into odd and even components, showing their interdependence and applications in state identification and invariants.

Findings

Pure multi-qubit states with an odd number of qubits are uniquely determined by their odd correlations.

The correlation components are often mutually determining, revealing deep structural insights.

The approach simplifies entanglement detection and identifies invariants under certain Hamiltonian evolutions.

Abstract

The set of correlations between particles in multipartite quantum systems is larger than those in classical systems. Nevertheless, it is subject to restrictions by the underlying quantum theory. In order to better understand the structure of this set, a possible strategy is to divide all correlations into two components, depending on the question of whether they involve an odd or an even number of particles. For pure multi-qubit states we prove that these two components are inextricably interwoven and often one type of correlations completely determines the other. As an application, we prove that all pure qubit states with an odd number of qubits are uniquely determined among all mixed states by the odd component of the correlations. In addition, our approach leads to invariants under the time evolution with Hamiltonians containing only odd correlations and can simplify entanglement detection.