Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest (Hungary)
Recently it has been observed that the group E{sub 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{sub 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 that 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{sub 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.
- OSTI ID:
- 20935238
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 75, Issue 2; Other Information: DOI: 10.1103/PhysRevD.75.024024; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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