Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane

TL;DR

This paper explores the deep connection between seven-qubit entanglement, the Fano plane geometry, and black hole entropy in string theory, revealing a duality and extending the quantum-information/black-hole analogy.

Contribution

It demonstrates that a special type of seven-qubit entanglement is fully represented by the Fano plane geometry and relates this to black hole entropy in supergravity theories.

Findings

Entanglement structure encoded in Fano plane geometry.

Dual relationship between tripartite and quadripartite subsystems.

Extension of quantum information and black hole entropy analogy.

Abstract

Recently it has been observed that the group $E_7$ can be used to describe a special type of quantum entanglement of seven qubits partitioned into seven tripartite systems. Here we show that this curious type of entanglement is entirely encoded into the discrete geometry of the Fano plane. We explicitly work out the details concerning a qubit interpretation of the $E_7$ generators as representatives of tripartite protocols acting on the 56 dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric black holes in four-dimensional string theory. We point out there is a dual relationship between entangled subsystems containing three and four tripartite systems. This relationship is reflected in the structure of the expressions for the black hole entropy in the N=4 and N=2 truncations of the $E_{7(7)}$ symmetric area form of N=8 supergravity. We conjecture that a similar picture based on other qubit systems might hold for black hole solutions in magic supergravities.