Normalized non-redundant vector tomographic portraits of spin states

TL;DR

This paper introduces a new normalized vector tomographic portrait for spin states, providing a complete geometric interpretation and generalization to higher spins, with explicit constructions for spin 1/2.

Contribution

It develops a non-redundant, normalized four-component vector tomographic portrait for spin states, including dequantizer and quantizer, and generalizes to higher spins with geometric insights.

Findings

Complete description of spin 1/2 states using four-component vectors

Explicit construction of dequantizers and quantizers for spin 1/2

Generalization to higher spin states with geometric interpretation

Abstract

Non-redundant and normalized four-component vector tomographic portrait fully describing the states of spin 1/2 quantum particles was introduced. Dequantizer and quantizer for such portrait were found, and generalization to the case of spin (2^N-1)/2 was done (N is a natural number). It was shown that such a portrait is completely defined by a thriple of non-complanar vectors with the lengthes equal or less then unity. A clear geometric interpretation of the choice of parameters for finding normalized dequantizers and quantizers is presented and numerical examples of such dequantizers and quantizers for spin 1/2 are given.