# 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 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.

- Authors:

- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1521 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; FOUR-DIMENSIONAL CALCULATIONS; MANY-DIMENSIONAL 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 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.},

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}

}