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

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.

25 pages, one figure, published in the Oberwolfach Preprint Series (OWP-2013-17); a slightly extended version to appear in JHEP

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Cited by in corpus (16)

• Qubit Transport Model for Unitary Black Hole Evaporation without Firewalls
• Mermin pentagrams arising from Veldkamp lines for three qubits
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation
• Correlation Measure Equivalence in Dynamic Causal Structures of Quantum Gravity
• Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
• A finite geometric toy model of space-time as an error correcting code
• A Notable Relation between $N$-Qubit and $2^{N-1}$-Qubit Pauli Groups via Binary $\mathrm{LGr}(N,2N)$
• Four-qubit Systems and Dyonic Black Hole-Black Branes in Superstring Theory
• Smooth Entropy Transfer of Quantum Gravity Information Processing
• Stringy Dyonic Solutions and Clifford Structures
• Hexagons govern three-qubit contextuality
• A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals
• Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
• GoSam applications for automated NLO calculations
• Graph States and the Variety of Principal Minors