Entanglement without distillable secret key

Constructs an entangled state on $\mathbb C^{10}\otimes\mathbb C^{10}$ with zero distillable secret key for the specified local-instrument protocols that complete almost surely. These allow joint local processing and authenticated two-way public communication, with no other shared private resource and an eavesdropper holding the input purification and public record. A trace-preserving PPT channel on $M_{21}(\mathbb C)$ whose square is not entanglement breaking disproves Christandl's PPT-square conjecture.