Quantum Information Framework Enables Experimental Studies of Color Perception Based on 1920 and 1974 Axiomatization

The enduring mystery of how we perceive colour receives a novel approach thanks to work led by Roberto Leporini of the University of Bergamo, Edoardo Provenzi of the Université de Bordeaux, and Michel Berthier of the Université de La Rochelle. Building upon early theoretical foundations laid by Schrödinger and Resnikoff, this team proposes a new framework for understanding colour perception using the principles of quantum information. Their research moves beyond traditional quantum mechanics, employing ‘rebits’ rather than ‘qubits’, and demonstrates that this alternative approach does not impede the design of experiments to validate the model. The team successfully translates perceptual attributes of colour into a quantifiable form using qubit density matrices, opening new avenues for rigorous experimental investigation into the fundamental processes of colour vision.

Quantum Perception Mirrors Measurement Process

This research presents a quantum mechanical model of colour perception, building upon earlier theoretical work and connecting the abstract mathematics of quantum information theory with how we see colour. Scientists argue that colour perception isn’t simply about wavelengths of light, but is fundamentally shaped by the observer and the act of measurement, mirroring principles found in quantum mechanics. The team translates concepts like density matrices and quantum effects into the language of colour perception, creating a more rigorous and potentially testable model. The foundation of this work lies in the concept of a rebit, a two-level quantum system, and its mathematical representation using Jordan algebras, allowing them to model chromatic opposition, such as red versus green.

Scientists then translate this rebit-based model into the language of qubit density matrices and quantum effects, utilising well-established tools from quantum information theory. A central tenet of the model is that colour perception is observer-dependent; the act of observing light influences the perceived colour, similar to how measurement collapses a quantum wave function. The research demonstrates how to calculate key perceptual attributes, hue, saturation, and brightness, using quantum mechanical tools, expressing these attributes as quantum operators and measurements. The team defines an operational framework for conducting experiments to test their model, including light stimuli, observer characteristics, and measurement types. They propose experiments involving entangled photons, suggesting that certain entanglement effects would be difficult to explain using classical theories of colour perception. This work offers a new perspective on colour vision, moving beyond the traditional view of it as a purely physiological process, and provides a mathematically rigorous framework allowing for precise predictions and testable hypotheses, potentially challenging classical theories and fostering interdisciplinary research connecting physics, neuroscience, and psychology.

Rebits Validate Quantum Colour Perception Model

Scientists developed a framework for experimentally testing a new quantum model of colour perception, addressing a key challenge: validating a theory that utilises ‘rebits’ while standard quantum mechanics relies on ‘qubits’. The team demonstrates that this difference does not prevent the implementation of experimental protocols, allowing for rigorous testing of the model’s predictions. The study revisits the theoretical underpinnings of the quantum model, defining perceptual attributes using the language of quantum information. To achieve this, the team devised a method for computing perceptual attributes using qubit states and effects, effectively translating rebit concepts into measurable qubit quantities.

This translation involved mapping theoretical constructs onto experimental observables, enabling the design of an operational framework for conducting colour perception experiments. Despite the general impossibility of determining the density matrix of a composite system using only local measurements, by focusing on specific experimental scopes, they successfully expressed colourimetric concepts defined within the rebit framework using density matrices associated with qubit states. This innovative approach allows researchers to probe the predictions of the new colour perception model using standard quantum mechanical tools and techniques.

Quantum Perception Modelled with Jordan Algebras

This research presents a novel quantum mechanical model of colour perception, building upon concepts established in the early 20th century and refined through recent theoretical advances. Scientists demonstrate how perceived colours can be mathematically described using the principles of quantum mechanics, specifically through the use of density matrices and effects within a Jordan algebra framework. The core of the model interprets perceived colours not as simple coordinates in a colour space, but as the result of measurements performed on chromatic states, linking perception to the duality between quantum states and effects. The team developed a mathematical framework where effects, representing perceptual measurements, are defined as elements within a specific mathematical space, bounded between the null and the identity matrix.

These effects parameterise state transformations called Lüdners operations, crucial for describing how a perceived colour changes after a measurement. The geometry of this effect space is consistent with established colour solid models. Crucially, the model demonstrates that the change in a chromatic state due to a measurement can be computed using a three-dimensional Lorentz boost, a concept borrowed from special relativity. Researchers show that the post-measurement state, representing the perceived colour, is directly related to the original chromatic state and the expectation value of the effect.

This relationship is expressed through a formula that fuses the chromatic information of the state with the measurement outcome. In the case of achromatic effects, representing shades of grey, the model predicts that the post-measurement state is identical to the original state, meaning no chromatic information is altered. This work provides a formal framework for describing colourimetric perceptual attributes, associating emitted light with generalized states, perceptual measurements with effects, and the measurement outcome with the resulting generalized state, linking the quantum properties of light with the subjective experience of colour perception.

Colour Perception Mapped to Qubit States

This research successfully establishes a connection between a theoretical model of colour perception and practical experimental implementation. Building upon earlier work that formalised colour as a mathematical space, the team demonstrates how perceptual attributes of colour can be computed using standard qubit states and effects, rather than the more complex rebit systems initially proposed. This achievement provides an operational framework for designing experiments to test the predictions of the quantum colour perception model, bridging the gap between abstract theory and empirical investigation. The work confirms the mathematical foundations of colour perception, aligning the perceptual colour space with the geometry of real symmetric matrices and the spin factor. By translating the model into terms accessible through qubit technology, the researchers circumvent potential experimental difficulties associated with rebit systems, opening avenues for direct testing of the model’s predictions. Further work is needed to design and conduct specific experiments, but this study provides a crucial theoretical and computational foundation for such investigations, likely focusing on translating these computational results into concrete experimental protocols and validating the model through human psychophysical studies.