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

@misc{citeulike:920093, 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.}, archivePrefix = {arXiv}, author = {L\évay, P\éter}, citeulike-article-id = {920093}, citeulike-linkout-0 = {http://arxiv.org/abs/hep-th/0610314}, citeulike-linkout-1 = {http://arxiv.org/pdf/hep-th/0610314}, day = {30}, eprint = {hep-th/0610314}, keywords = {black, e7, entanglement, entropy, fano, hole, plane, quantum, qubit}, month = {Oct}, posted-at = {2006-10-31 11:32:03}, priority = {2}, title = {Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane}, url = {http://arxiv.org/abs/hep-th/0610314}, year = {2006} }

TY - ELEC ID - citeulike:920093 L3 - citeulike-article-id:920093 N2 - 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. TI - Strings, black holes, the tripartite entanglement of seven qubits and the Fano plane KW - black KW - e7 KW - entanglement KW - entropy KW - fano KW - hole KW - plane KW - quantum KW - qubit AU - Lévay, Péter PY - 2006/Oct/30/ UR - http://arxiv.org/abs/hep-th/0610314 ER -