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The quantum sky of Majorana stars

L. L. Sanchez-Soto, A. B. Klimov, A. Z. Goldberg, G. Leuchs

TL;DR

This paper surveys the Majorana constellation, a geometric representation that encodes a pure spin $S$ state by $2S$ points on the unit sphere. It introduces the stellar function $f_\psi(z)$, shows how to recover state coefficients from the constellation via Vieta relations, and derives star dynamics under a differential SU(2) realization. It discusses quantumness through state multipoles, introduces the Kings of Quantumness and their connection to spherical designs and optimization problems like the Thomson problem. The combined algebraic–geometric framework provides an intuitive tool for quantum information tasks, entanglement classification, and metrology, with dynamical signatures in Majorana-star motion.

Abstract

Majorana stars, the $2S$ spin coherent states that are orthogonal to a spin-$S$ state, offer an elegant method to visualize quantum states. This representation offers deep insights into the structure, symmetries, and entanglement properties of quantum states, bridging abstract algebraic formulations with intuitive geometrical intuition. In this paper, we briefly survey the development and applications of the Majorana constellation, exploring its relevance in modern areas of quantum information.

The quantum sky of Majorana stars

TL;DR

This paper surveys the Majorana constellation, a geometric representation that encodes a pure spin state by points on the unit sphere. It introduces the stellar function , shows how to recover state coefficients from the constellation via Vieta relations, and derives star dynamics under a differential SU(2) realization. It discusses quantumness through state multipoles, introduces the Kings of Quantumness and their connection to spherical designs and optimization problems like the Thomson problem. The combined algebraic–geometric framework provides an intuitive tool for quantum information tasks, entanglement classification, and metrology, with dynamical signatures in Majorana-star motion.

Abstract

Majorana stars, the spin coherent states that are orthogonal to a spin- state, offer an elegant method to visualize quantum states. This representation offers deep insights into the structure, symmetries, and entanglement properties of quantum states, bridging abstract algebraic formulations with intuitive geometrical intuition. In this paper, we briefly survey the development and applications of the Majorana constellation, exploring its relevance in modern areas of quantum information.
Paper Structure (6 sections, 39 equations, 1 figure)

This paper contains 6 sections, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Majorana constellations
  3. Extracting information from the constellation
  4. Constellations and quantumness
  5. Stellar dynamics
  6. Concluding remarks

Figures (1)

  • Figure 1: Density plots of the $Q$ functions for the optimal Kings of Quantumness for the cases $S=3, 5, 6,$ and 10 (from left to right, blue indicates the zero values and red maximal ones). On top, we sketch the Majorana constellations.