A probability distribution
over the four possible
two-bit configurations
(00,01,10 and 11) is
correlated or it is not.
For systems with more
than two bits, describing
the ways one can correlate
the various parts is far
more complicated.
In this talk I will
describe how one can qualify
the correlations among N
bits by a knot of N links,
where a subset of bits is
correlated if and only if the
corresponding subset of
links are unsplittable.
This result is established
by representing both the
correlations and the knots
as a collection of subsets
of {1,...,N}. We thus
obtain a way of enumerating
the different ways one can
correlate N bits, although
a closed formula for the
total number of possibilities is
not yet known.
We will also mention that the same results
also hold
for the ways one can
entangle N qubits (where we use
distillable entanglement as
our criterion). Hence we
generalize an observation
by P.K. Aravind about the
correspondance between GHZ
entangled states and
the "Borromean
rings" knot.
For this talk, no prior knowledge about
quantum
mechanics or knot theory is
required, but a familiarity
with basic probability
theory is helpful.
