# Qubit representation of qudit states: correlations and state reconstruction

## TL;DR

This paper introduces a qubit-based geometric representation of qudit states, revealing quantum correlations and inequalities useful for state reconstruction, exemplified through qutrit systems.

## Contribution

It presents a novel qubit decomposition method for qudit states, enabling geometric visualization and correlation analysis for improved state reconstruction.

## Key findings

- Qudit states can be represented in the Bloch sphere using qubit decomposition.
- Quantum correlations between qubits are linked to nonnegativity conditions of the qudit state.
- New inequalities for density matrix components are derived and used for state classification.

## Abstract

A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the qudit state imply the existence of quantum correlations between the qubits which compose it. These correlations are used to define new inequalities which the density matrices components must satisfy. The importance of such inequalities in the reconstruction of a qudit state is addressed. As an example of the general procedure the qubit decomposition of a qutrit system is shown, which allows a classification of the qutrit states by fixing their invariants ${\rm Tr}(\hat{\rho}^2)$, ${\rm Tr}(\hat{\rho}^3)$.