BLACK HOLES AND QUBITS

Abstract

We establish a correspondence between the entanglement measures of qubits in quantum information theory and the Bekenstein-Hawking entropy of black holes in string theory. Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary M. J. Duff, “String triality, black hole entropy and Cayley’s hyperdeterminant,” Phys. Rev. D 76, 025017 (2007) [arXiv:hep-th/0601134] R. Kallosh and A. Linde, “Strings, black holes, and quantum information,” Phys. Rev. D 73, 104033 (2006) [arXiv:hep-th/0602061]. P. Levay, “Stringy black holes and the geometry of entanglement,” Phys. Rev. D 74, 024030 (2006) [arXiv:hep-th/0603136]. M. J. Duff and S. Ferrara, “E7 and the tripartite entanglement of seven qubits,” Phys. Rev. D 76, 025018 (2007) [arXiv:quant-ph/0609227]. P. Levay, “Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane,” Phys. Rev. D 75, 024024 (2007) [arXiv:hep-th/0610314]. Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary M. J. Duff and S. Ferrara, “E6 and the bipartite entanglement of three qutrits,” Phys. Rev. D 76, 124023 (2007) [arXiv:0704.0507 [hep-th]]. P. Levay, “A three-qubit interpretation of BPS and non-BPS STU black holes,” Phys. Rev. D 76, 106011 (2007) [arXiv:0708.2799 [hep-th]]. L. Borsten, D. Dahanayake, M. J. Duff, W. Rubens and H. Ebrahim, “Wrapped branes as qubits,” Phys.Rev.Lett.100:251602,2008 arXiv:0802.0840 [hep-th]. P. Levay, M. Saniga and P. Vrana, “Three-Qubit Operators, the Split Cayley Hexagon of Order Two and Black Holes,” arXiv:0808.3849 [quant-ph]. Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary Black holes and entanglement 1) BLACK HOLES AND ENTANGLEMENT Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary BH/qubit correspondence Quantum entanglement lies at the heart of quantum information theory, with applications to quantum computing, teleportation, cryptography and communication. In the apparently separate world of quantum gravity, the Bekenstein-Hawking entropy of black holes has also occupied center stage. Despite their apparent differences, recent work has established a correspondence between the tripartite entanglement measure of three qubits and the macroscopic entropy of the four-dimensional 8-charge STU black hole of N = 2 supergravity. Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary BH/qubit correspondence The measure of tripartite entanglement of three qubits (Alice, Bob and Charlie), known as the 3-tangle τABC , and the entropy S of the 8-charge STU black hole of supergravity are related by: S = π 2 √ τABC Duff: hep-th/0601134 Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary Further developments Further papers have written a more complete dictionary, which translates a variety of phenomena in one language to those in the other: For example, one can relate the classification of three-qubit entanglements to the classification of supersymmetric black holes as in the following table: Black holes and entanglement Qubits STU black holes N = 8 case Wrapped D3-branes and 3 qubits Wrapped M2-branes and 2 qutrits Summary