  In this paper we illuminate the relation between entanglement and secrecy by
providing the first example of a quantum state that is highly entangled, but
from which, nevertheless, almost no secrecy can be extracted. More precisely,
we provide two bounds on the bipartite entanglement of the totally
antisymmetric state in dimension d x d. First, we show that the amount of
secrecy that can be extracted from the state is low, to be precise it is
bounded by O(1/d). Second, we show that the state is highly entangled in the
sense that we need a large amount of singlets to create the state: entanglement
cost is larger than a constant, independent of d. In order to obtain our
results we use representation theory, linear programming and the entanglement
measure known as squashed entanglement. Our findings also clarify the relation
between the squashed entanglement and the relative entropy of entanglement.
