Stringy Black Holes and the Geometry of Entanglement

Abstract

Recently striking multiple relations have been found between pure state 2 and 3-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theory. In particular we show that finding the frozen values of the moduli in the calculation of the macroscopic entropy in the STU model, is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of finding the optimal local distillation protocol of a GHZ state from an arbitrary pure three-qubit state. These results and a geometric classification of STU black holes BPS and non-BPS can be described in the elegant language of twistors. Finally an interesting connection between the black hole entropy and the average real entanglement of formation is established.

34 pages, 6 figures

References in corpus (3)

• Strings, Black Holes, and Quantum Information
• On the geometry of a class of N-qubit entanglement monotones
• Observations on the Darboux coordinates for rigid special geometry

Cited by in corpus (22)

• Charge Orbits of Symmetric Special Geometries and Attractors
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Strings, Black Holes, and Quantum Information
• Black holes admitting a Freudenthal dual
• E_7 and the tripartite entanglement of seven qubits
• Erice Lectures on Black Holes and Attractors
• Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes
• Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane
• On the Black-Hole/Qubit Correspondence
• E_6 and the bipartite entanglement of three qutrits
• Attractors with Vanishing Central Charge
• Wrapped branes as qubits
• Attractors in Black
• A three-qubit interpretation of BPS and non-BPS STU black holes
• Black Hole Entropy and Finite Geometry
• Holographic entanglement entropy of de Sitter braneworld
• Four curious supergravities
• Geometric phases and Bloch sphere constructions for SU(N), with a complete description of SU(4)
• More on N=8 Attractors
• Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions
• STU attractors from vanishing concurrence
• Black hole entropy and quantum information