Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes

TL;DR

This paper uses finite geometry to connect three- and four-qubit observables, revealing new insights into Mermin's magic pentagrams and their relation to black hole physics.

Contribution

It introduces a bijective mapping between three- and four-qubit observables using Clifford algebra and explores its implications for quantum contextuality and black hole-qubit correspondence.

Findings

Mapped 135 three-qubit heptads to four-qubit observables

Analyzed symplectic group actions on the mapped sets

Connected quantum contextuality structures to black hole physics

Abstract

We invoke some ideas from finite geometry to map bijectively 135 heptads of mutually commuting three-qubit observables into 135 symmetric four-qubit ones. After labeling the elements of the former set in terms of a seven-dimensional Clifford algebra, we present the bijective map and most pronounced actions of the associated symplectic group on both sets in explicit forms. This formalism is then employed to shed novel light on recently-discovered structural and cardinality properties of an aggregate of three-qubit Mermin's 'magic' pentagrams. Moreover, some intriguing connections with the so-called black-hole--qubit correspondence are also pointed out.