Strings, Black Holes, and Quantum Information

TL;DR

This paper explores deep connections between extremal black hole entropy in string theory and quantum entanglement measures in multi-qubit systems, revealing new insights into their mathematical and physical relationships.

Contribution

It establishes a novel correspondence between black hole entropy formulas and quantum entanglement invariants, linking string theory, supergravity, and quantum information theory.

Findings

Black hole entropy related to 2- and 3-qubit entanglement measures

Identification of black hole types with specific quantum states

Reduction of supergravity invariants to quantum entanglement hyperdeterminants

Abstract

We find multiple relations between extremal black holes in string theory and 2- and 3-qubit systems in quantum information theory. We show that the entropy of the axion-dilaton extremal black hole is related to the concurrence of a 2-qubit state, whereas the entropy of the STU black holes, BPS as well as non-BPS, is related to the 3-tangle of a 3-qubit state. We relate the 3-qubit states with the string theory states with some number of D-branes. We identify a set of "large" black holes with the maximally entangled GHZ-class of states and "small" black holes with separable, bipartite and W states. We sort out the relation between 3-qubit states, twistors, octonions, and black holes. We give a simple expression for the entropy and the area of stretched horizon of "small'' black holes in terms of a norm and 2-tangles of a 3-qubit system. Finally, we show that the most general expression for the black hole and black ring entropy in N=8 supergravity/M-theory, which is given by the famous quartic Cartan E_{7(7)} invariant, can be reduced to Cayley's hyperdeterminant describing the 3-tangle of a 3-qubit state.