# Characterizing quantum states via sector lengths

## TL;DR

This paper establishes tight bounds on sector lengths, which quantify k-partite correlations in multi-qubit states, and explores their applications to entanglement detection, monogamy, and quantum state representability.

## Contribution

It derives the first tight bounds on sector lengths for multi-qubit states and fully characterizes these bounds for two- and three-qubit systems, introducing new tools for quantum correlation analysis.

## Key findings

- Derived tight bounds on sector lengths in multi-qubit states.
- Complete characterization of sector lengths for two- and three-qubit systems.
- Proved a symmetrized strong subadditivity for linear entropy.

## Abstract

Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a three-particle system. A powerful tool to study correlation constraints is the notion of sector lengths. These quantify, for different $k$, the amount of $k$-partite correlations in a quantum state in a basis-independent manner. We derive tight bounds on the sector lengths in multi-qubit states and highlight applications of these bounds to entanglement detection, monogamy relations and the $n$-representability problem. For the case of two- and three qubits we characterize the possible sector lengths completely and prove a symmetrized version of strong subadditivity for the linear entropy.

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Source: https://tomesphere.com/paper/1905.06928