The standard example of data hiding states in quantum information is given by the pair of the symmetric and antisymmetric states (Werner states).
In this paper, we show that the phenomenon of data hiding is generic: it is witnessed by any generic pair of states in sufficiently large dimension. However, a notable difference is that for generic states the data hiding property (against separable measurement) does not follow from the positive partial transpose obstruction; in this sense they differ from Werner states.
Our arguments rely on volume and mean width estimates.
aubrun (arrobas) math. univ-lyon1. fr