Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane
Abstract
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 56dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric black holes in fourdimensional 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.
 Authors:
 Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H1521 Budapest (Hungary)
 Publication Date:
 OSTI Identifier:
 20935238
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024024; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; ENTROPY; FOURDIMENSIONAL CALCULATIONS; MANYDIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS; STRING MODELS; STRING THEORY; SUPERGRAVITY; SUPERSYMMETRY
Citation Formats
Levay, Peter. Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.024024.
Levay, Peter. Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane. United States. doi:10.1103/PHYSREVD.75.024024.
Levay, Peter. Mon .
"Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane". United States.
doi:10.1103/PHYSREVD.75.024024.
@article{osti_20935238,
title = {Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane},
author = {Levay, Peter},
abstractNote = {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 56dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric black holes in fourdimensional 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.},
doi = {10.1103/PHYSREVD.75.024024},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

We show that for tripartite quantum pure states of qubits, all the kinds of entanglement in terms of stochastic local operations and classical communications classification are experimentally measurable by simple projective measurements, provided that four copies of the composite quantum system are available. In particular, the entanglement of reduced density matrices, even though they are mixed states, can be exactly determined in experiment. Concurrence of assistance is also shown to be measurable by introducing an interesting equation with explicit physical meanings.

Entanglement and optimal strings of qubits for memory channels
We investigate the problem of enhancement of mutual information by encoding classical data into entangled input states of arbitrary length and show that while there is a threshold memory or correlation parameter beyond which entangled states outperform the separable states, resulting in a higher mutual information, this memory threshold increases toward unity as the length of the string increases. These observations imply that encoding classical data into entangled states may not enhance the classical capacity of quantum channels. 
Entanglement entropy of two black holes and entanglement entropic force
We study the entanglement entropy S{sub C} of the massless free scalar field on the outside region C of two black holes A and B whose radii are R{sub 1} and R{sub 2} and how it depends on the distance r(>>R{sub 1},R{sub 2}) between two black holes. If we can consider the entanglement entropy as thermodynamic entropy, we can see the entropic force acting on the two black holes from the r dependence of S{sub C}. We develop the computational method based on that of Bombelli et al. to obtain the r dependence of S{sub C} of scalar fields whosemore » 
Distortion of Schwarzschildantide Sitter black holes to black strings
Motivated by the existence of black holes with various topologies in fourdimensional spacetimes with a negative cosmological constant, we study axisymmetric static solutions describing any large distortions of Schwarzschildantide Sitter black holes parametrized by the mass m. Under the approximation such that m is much larger than the antide Sitter radius, it is found that a cylindrically symmetric black string is obtained as a special limit of distorted spherical black holes. Such a prolonged distortion of the event horizon connecting a Schwarzschildantide Sitter black hole to a black string is allowed without violating both the usual black hole thermodynamics andmore » 
Nonabelian black holes and black strings in higher dimensions
We review the properties of static, higher dimensional black hole solutions in theories where nonabelian gauge fields are minimally coupled to gravity. It is shown that black holes with hyperspherically symmetric horizon topology do not exist in d>4, but that hyperspherically symmetric black holes can be constructed numerically in generalized EinsteinYangMills models. 5dimensional black strings with horizon topology S{sup 2}xS{sup 1} are also discussed. These are socalled undeformed and deformed nonabelian black strings, which are translationally invariant and correspond to 4dimensional nonabelian black holes trivially extended into one extra dimensions. The fact that black strings can be deformed, i.e. axiallymore »