Super-activation conjecture for mean random correlated secrecy capacity

An arbitrarily varying wiretap channel (AVWC) is a pair $(\mathfrak W,\mathfrak V)$ of finite arbitrarily varying channels, with legitimate channel family $\mathfrak W$ and eavesdropper channel family $\mathfrak V$. Let $C^{\mathrm{mean}}_{\mathrm{S,ran}}(\mathfrak W,\mathfrak V)$ denote its mean random secrecy capacity.

Super-activation conjecture. There exist pairs $(\mathfrak W_1,\mathfrak V_1)$ and $(\mathfrak W_2,\mathfrak V_2)$ of finite AVWCs such that

$$C^{\mathrm{mean}}_{\mathrm{S,ran}}(\mathfrak W_1,\mathfrak V_1)=C^{\mathrm{mean}}_{\mathrm{S,ran}}(\mathfrak W_1,\mathfrak V_1)=0,$$

but

$$C^{\mathrm{mean}}_{\mathrm{S,ran}}(\mathfrak W_1\otimes\mathfrak W_2,\mathfrak V_1\otimes\mathfrak V_2)>0.$$

This conjectures super-activation for mean random correlated secrecy capacity: two AVWCs with zero individual capacity could have a positive capacity when used jointly. The repeated first pair in the stated zero-capacity condition is reproduced exactly from the source; it may be a typographical error for $C^{\mathrm{mean}}_{\mathrm{S,ran}}(\mathfrak W_2,\mathfrak V_2)$.