Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An Operational Quantum Information Framework for Experimental Studies on Color Perception

Roberto Leporini, Edoardo Provenzi, Michel Berthier

TL;DR

The paper addresses validating a real-field quantum-information model of color perception by translating Hering’s rebit framework into the conventional qubit formalism. It develops an operational route where emitted light and observers are described by qubit density matrices and Lüders updates, enabling concrete computations of brightness, lightness, saturation, and hue. Key contributions include explicit mappings from rebit states/effects to qubit states/effects, definitions of perceptual attributes in the qubit setting, and a practical experimental framework. The work enables empirical tests of a real-quantum theory of color perception and opens avenues for exploring quantum-like center–surround interactions in vision.

Abstract

Starting from the foundational axiomatization of the perceptual color space initiated by Schrödinger in 1920 and eventually refined by Resnikoff in 1974, Berthier, Provenzi and their collaborators have recently proposed a reformulation of perceptual color attributes within the framework of quantum information. Their work is based on the Jordan algebra formalism of quantum theories and, more specifically, on a quantum system described by a spin factor over the field of real numbers. This theoretical framework is not that of ordinary quantum mechanics, mainly because it requires dealing with rebits, whereas the latter uses qubits. The aim of this paper is to show that this difference in no way hinders the implementation of experimental protocols for testing the validity of the predictions of the color perception model. In particular, we show how to compute the quantum information based perceptual attributes of perceived colors in terms of qubit density matrices.

An Operational Quantum Information Framework for Experimental Studies on Color Perception

TL;DR

The paper addresses validating a real-field quantum-information model of color perception by translating Hering’s rebit framework into the conventional qubit formalism. It develops an operational route where emitted light and observers are described by qubit density matrices and Lüders updates, enabling concrete computations of brightness, lightness, saturation, and hue. Key contributions include explicit mappings from rebit states/effects to qubit states/effects, definitions of perceptual attributes in the qubit setting, and a practical experimental framework. The work enables empirical tests of a real-quantum theory of color perception and opens avenues for exploring quantum-like center–surround interactions in vision.

Abstract

Starting from the foundational axiomatization of the perceptual color space initiated by Schrödinger in 1920 and eventually refined by Resnikoff in 1974, Berthier, Provenzi and their collaborators have recently proposed a reformulation of perceptual color attributes within the framework of quantum information. Their work is based on the Jordan algebra formalism of quantum theories and, more specifically, on a quantum system described by a spin factor over the field of real numbers. This theoretical framework is not that of ordinary quantum mechanics, mainly because it requires dealing with rebits, whereas the latter uses qubits. The aim of this paper is to show that this difference in no way hinders the implementation of experimental protocols for testing the validity of the predictions of the color perception model. In particular, we show how to compute the quantum information based perceptual attributes of perceived colors in terms of qubit density matrices.

Paper Structure

This paper contains 10 sections, 71 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Hering's rebit of color perception
  3. Perceived colors and measurements in the quantum framework
  4. The quantum information of perceived colors
  5. Perceived colors from the qubit point of view
  6. From rebit generalized states and effects to qubit states and effects
  7. Color measurements with qubit states and effects
  8. Computing perceptual attributes with qubit states and effects
  9. The operational framework
  10. Conclusions and future perspectives

Figures (3)

  • Figure 1: The double cone representing the effect space can be interpreted as the color solid of actually perceived colors inside the infinite cone $\overline{\mathcal{L}^+}$.
  • Figure 2: Geometric representation of the set $\mathcal{E}_1$ opened in half at its basis.
  • Figure 3: Left: geometric representation of the set $\mathcal{E}_2$ inside the Bloch sphere. Right: the equatorial basis of the double cone corresponds to the Bloch disk with Hering's opponency.