Determining quantum correlations in bipartite systems - from qubit to qutrit and beyond

TL;DR

This paper discusses the increasing complexity of evaluating quantum correlations as the system dimension grows from qubits to higher-dimensional qudits, highlighting theoretical challenges and differences in state space geometry.

Contribution

It analyzes the fundamental differences in properties and measurement of quantum correlations between qubits and higher-dimensional systems, emphasizing the need for new approaches.

Findings

Qubit systems are simpler and well-understood.

Higher-dimensional systems exhibit complex geometry and measurement challenges.

No-go theorems limit generalizations of existing criteria.

Abstract

We advocate the step change in properties of discrete $d$-level quantum systems, between $d=2$ and $d\geq 3$. Qubit systems, or multipartite systems containing qubit subsystem, are exceptional in their relative simplicity. One faces a step in complexity in valuating measures of quantum correlations for qutrits and then other higher dimensional qudits. There is a growing number of arguments leading to such conclusion: recently found no-go theorem for generalization of the Peres-Horodecki's PPT criterion \cite{sko}, change in geometry of state spaces of qubit and higher degree qudits (the so called 'generalized Bloch ball' is not a ball anymore), restricted possibilities for diagonalization of correlation matrices for bipartite systems, more difficult way for handling the set of relevant families of orthogonal projectors.