  The concept of symmetric extendibility has recently drawn attention in the
context of tolerable error rates in quantum cryptography, where it can be used
to decide whether quantum states shared between two parties can be purified by
means of entanglement purification with one-way classical communication only.
Unfortunately, at present there exists no simple general criterion to decide
whether a state possesses a symmetric extension or not. In this article we
derive criteria for symmetric extendibility within subclasses of all two-qudit
states. Using these criteria, we can completely solve the problem for a
two-parameter family of two-qudit states, which includes the isotropic states
as a subclass.
