Figure 1. Adaptive quantum protocol.

The first step is the preparation of the initial separable state of a and b by some adaptive LOCC Λ₀. After the preparation of the local registers, there is the first transmission: Alice picks a system from her local register a₁∈a, so that the register is updated as a→aa₁; system a₁ is sent through the channel , with Bob getting the output b₁; Bob includes the output in his local register, which is updated as b₁b→b; finally, Alice and Bob apply another adaptive LOCC Λ₁ to their registers a,b. In the second transmission, Alice picks and sends another system a₂∈a through channel with output b₂ for Bob. The parties apply a further adaptive LOCC Λ₂ to their registers and so on. This procedure is repeated n times, with output state for the Alice's and Bob's local registers.