10 research outputs found
Superqubits
We provide a supersymmetric generalization of n quantum bits by extending the
local operations and classical communication entanglement equivalence group
[SU(2)]^n to the supergroup [uOSp(1|2)]^n and the stochastic local operations
and classical communication equivalence group [SL(2,C)]^n to the supergroup
[OSp(1|2)]^n. We introduce the appropriate supersymmetric generalizations of
the conventional entanglement measures for the cases of and . In
particular, super-Greenberger-Horne-Zeilinger states are characterized by a
nonvanishing superhyperdeterminant.Comment: 16 pages, 4 figures, 4 tables, revtex; minor corrections, version
appearing in Phys. Rev.
Wrapped branes as qubits
Recent work has established a correspondence between the tripartite
entanglement measure of three qubits and the macroscopic entropy of the
four-dimensional 8-charge STU black hole of supergravity. Here we consider the
configurations of intersecting D3-branes, whose wrapping around the six compact
dimensions T^6 provides the microscopic string-theoretic interpretation of the
charges, and associate the three-qubit basis vectors |ABC>, (A,B,C=0 or 1) with
the corresponding 8 wrapping cycles. In particular, we relate a well-known fact
of quantum information theory, that the most general real three-qubit state can
be parameterized by four real numbers and an angle, to a well-known fact of
string theory, that the most general STU black hole can be described by four
D3-branes intersecting at an angle.Comment: Version appearing in Phys. Rev. Lett, includes Type IIA description
as well as Type II
Four-qubit entanglement from string theory
We invoke the black hole/qubit correspondence to derive the classification of
four-qubit entanglement. The U-duality orbits resulting from timelike reduction
of string theory from D=4 to D=3 yield 31 entanglement families, which reduce
to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references
adde
Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
One would often like to know when two a priori distinct extremal black
p-brane solutions are in fact U-duality related. In the classical supergravity
limit the answer for a large class of theories has been known for some time.
However, in the full quantum theory the U-duality group is broken to a discrete
subgroup and the question of U-duality orbits in this case is a nuanced matter.
In the present work we address this issue in the context of N=8 supergravity in
four, five and six dimensions. The purpose of this note is to present and
clarify what is currently known about these discrete orbits while at the same
time filling in some of the details not yet appearing in the literature. To
this end we exploit the mathematical framework of integral Jordan algebras and
Freudenthal triple systems. The charge vector of the dyonic black string in D=6
is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified
by a set of two arithmetic U-duality invariants. Similarly, the black hole
(string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge
canonical form, again uniquely fixed by a set of three arithmetic U-duality
invariants. The situation in four dimensions is less clear: while black holes
preserving more than 1/8 of the supersymmetries may be fully classified by
known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield
increasingly subtle orbit structures, which remain to be properly understood.
However, for the very special subclass of projective black holes a complete
classification is known. All projective black holes are E_{7(7)}(Z) related to
a four or five charge canonical form determined uniquely by the set of known
arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the
charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to
appear in Class. Quantum Gra
Black holes admitting a Freudenthal dual
The quantised charges x of four dimensional stringy black holes may be
assigned to elements of an integral Freudenthal triple system whose
automorphism group is the corresponding U-duality and whose U-invariant quartic
norm Delta(x) determines the lowest order entropy. Here we introduce a
Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although
distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the
requirement that \tilde{x} be integer restricts us to the subset of black holes
for which Delta(x) is necessarily a perfect square. The issue of higher-order
corrections remains open as some, but not all, of the discrete U-duality
invariants are Freudenthal invariant. Similarly, the quantised charges A of
five dimensional black holes and strings may be assigned to elements of an
integral Jordan algebra, whose cubic norm N(A) determines the lowest order
entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a
perfect cube, for which A**=A and which leaves N(A) invariant. The two
dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde
Freudenthal triple classification of three-qubit entanglement
We show that the three-qubit entanglement classes: (0) Null, (1) Separable
A-B-C, (2a) Biseparable A-BC, (2b) Biseparable B-CA, (2c) Biseparable C-AB, (3)
W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a
Freudenthal triple system defined over the Jordan algebra C+C+C. We also
compute the corresponding SLOCC orbits.Comment: 11 pages, 2 figures, 6 tables, revtex; minor corrections, references
added; version appearing in Phys. Rev.