On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements

We begin with a detailed description of a low dimensional quantum channel (dA = 4, dE = 3) demonstrating the symmetric form of superactivation of one-shot zero-error quantum capacity. This means appearance of a noiseless (perfectly reversible) subchannel in the tensor square of a channel having no noiseless subchannels. Then we describe a quantum channel Φ such that Q̄0(Φ) = 0 and Q̄0(Φ⊗ Φ) ≥ log n for any n ≤ +∞. We also show that the superactivation of one-shot zero-error quantum capacity of a channel can be reformulated in terms of quantum measurements theory as appearance of an indistinguishable subspace for tensor product of two observables having no undistinguishable subspaces.