Steering in spin tomographic probability representation

TL;DR

This paper extends the concept of quantum steering from two-qubit systems to single qudit systems with spin 3/2 using tomographic probability representations, introducing new correlation functions and integral relations.

Contribution

It develops a framework for detecting quantum steering in single qudit states by translating two-qubit inequalities into the qudit context via tomographic probabilities.

Findings

Derived analogs of correlation functions for single qudit systems.

Established integral relations connecting two-qubit and single qudit correlation functions.

Applied tomographic probability representation to analyze steering properties.

Abstract

The steering property known for two qubit-state in terms of specific inequalities for correlation function is translated for the state of qudit with the spin $j=3/2$. Since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems. The tomographic probability representation for the qudit states is applied. The connection between the correlation function in two qubit system and the single qudit is presented in an integral form with a intertwining kernel calculated explicitly in tomographic probability terms.