Entanglement with zero distillable secret key in local dimension ten

We construct an entangled state on ${\mathbb{C}}^{10}\otimes {\mathbb{C}}^{10}$ with zero distillable secret key for the local-instrument protocols specified here. They allow joint processing of all copies and unlimited two-way public communication, with the input as the only shared private resource and an eavesdropper holding a purification and the complete public record. The construction also disproves the unrestricted two-map PPT-composition conjecture. A separate trace-preserving PPT channel on $M_{21}(\mathbb{C})$ has a square that is not entanglement breaking.