Four-qubit entanglement: lessons of a black hole

Recent investigations have established an analogy between the entropy of four-dimensional supersymmetric black holes in string theory and entanglement in quantum information theory. Examples include: (1) $N=2$ STU black holes and the tripartite entanglement of three qubits (2-state systems), where the common symmetry is $[SL(2){]}^{3}$ and (2) $N=8$ black holes and the tripartite entanglement of seven qubits where the common symmetry is ${E}_{7}\ensuremath{\supset}[SL(2){]}^{7}$. Here we present another example: $N=8$ black holes (or black strings) in five dimensions and the bipartite entanglement of three qutrits (3-state systems), where the common symmetry is ${E}_{6}\ensuremath{\supset}[SL(3){]}^{3}$. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic ${E}_{6}$ invariant. Similar analogies exist for magic $N=2$ supergravity black holes in both four and five dimensions.Recent investigations have established an analogy between the entropy of four-dimensional supersymmetric black holes in string theory and entanglement in quantum information theory. Examples include: (1) $N=2$ STU black holes and the tripartite entanglement of three qubits (2-state systems), where the common symmetry is $[SL(2){]}^{3}$ and (2) $N=8$ black holes and the tripartite entanglement of seven qubits where the common symmetry is ${E}_{7}\ensuremath{\supset}[SL(2){]}^{7}$. Here we present another example: $N=8$ black holes (or black strings) in five dimensions and the bipartite entanglement of three qutrits (3-state systems), where the common symmetry is ${E}_{6}\ensuremath{\supset}[SL(3){]}^{3}$. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic ${E}_{6}$ invariant. Similar analogies exist for magic $N=2$ supergravity black holes in both four and five dimensions.

arXiv:0704.0507Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsDec 19, 200751 citations

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

Péter Lévay

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 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 ${E}_{7(7)}$ 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.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 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 ${E}_{7(7)}$ 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.

arXiv:hep-th/0610314Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJan 19, 200757 citations

Entanglement Entropy and Black Hole

Shinji Mukohyama A

Progress of Theoretical Physics SupplementJan 31, 20000 citations

Entanglement of Matter Qubits at a Distance

E. Zipper, Marcin Kurpas

Journal of Computational and Theoretical NanoscienceJul 22, 20101 citation

N=2

STU black holes and the tripartite entanglement of three qubits (2-state systems), where the common symmetry is

[SL(2){]}^{3}

and (2)

N=8

black holes and the tripartite entanglement of seven qubits where the common symmetry is ${E}_{7}\ensuremath{\supset}[SL(2){]}^{7}$. Here we present another example:

N=8

black holes (or black strings) in five dimensions and the bipartite entanglement of three qutrits (3-state systems), where the common symmetry is ${E}_{6}\ensuremath{\supset}[SL(3){]}^{3}$. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic

{E}_{6}

invariant. Similar analogies exist for magic

N=2

supergravity black holes in both four and five dimensions.

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 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}_{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.