Sunday, December 12, 2010

Lévay on Qubits & Black Hole Horizons













The BPS black hole solutions of the STU model of N=2, D=4 supergravity can be recovered from N=8, D=4 supergravity and the N=2 magic supergravities for Freudenthal triple systems in which the off-diagonal components have been diagonalized by the reduced structure group. Under D=4 U-duality, this can always be done, with the reduced structure group being in general, E6(C). Therefore, any results clarifying the quantum information interpretation of the STU model will equally apply to the N=8, D=4 and N=2 magic supergravity BPS black hole solutions. This is the case in Péter Lévay and Szilárd Szalay's November 18th pre-print: STU attractors from vanishing concurrence. The abstract is as follows:

Concurrence is an entanglement measure characterizing the mixed state bipartite correlations inside of a pure state of an n-qubit system. We show that after organizing the charges and the moduli in the STU model of N=2, d=4 supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the pure state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.

2 comments:

ThePeSla said...

Hello,

pesla.blogspot.com

I find your binary pictures interesting but cannot see why anyone would connect such simple diagrams to "supergravity"

We can label orthogonal points like that to any number n of dimensions?

I do not see new mathematics of physics here.

kneemo said...

Hello,

The math and physics is not in the labels. It is in the invariants involved, which appear in both the quantum information side and the supergravity side, with different interpretations. On the supergravity side one has a quartic invariant, which is interpreted as an entanglement measure on the quantum information side for three qubits. Such a quartic invariant, in general, is invariant under E7 transformations, which generalizes the results for three qubit entanglement, which is normally described by SL(2,C)xSL(2,C)xSL(2,C). Hence, this is a new result in the physics of quantum information theory coming from supergravity. Specifically, it proves the existence of quantum mechanical systems (SUGRA extremal black holes) which transform as three entangled qubits under a generalized SLOCC group, E7.

Remember that with exceptional groups (G2, F4, E6, E7 and E8), their properties stem from structures based on composition algebras that only exist in dimensions 1, 2, 4 and 8 as vector spaces over R and C. Hence, such qubit/supergravity labellings do not work generally for n-dimensions.

The intimate and still mysterious relationship between composition algebras and supergravity goes back to the early days of supergravity, when Freund and others were classifying all consistent theories. See the classic paper in 1982 from Townsend and Kugo Supersymmetry and the Division Algebra.


Regards,

-K