Mixed-state certification of quantum capacities for noisy communication channels

We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.

Figure 1

Detectable quantum capacity for the qubit depolarizing channel vs $p$ for the mixed input state as in Eq. (24) with $d=2$ and fidelity $F=0.98$ (dashed), $F=0.95$ (dotted), $F=0.9$ (dot-dashed), along with the hashing bound (solid line) achieved for $F=1$.

Figure 2

Detectable quantum capacity for the qubit erasure channel vs erasure probability $p$ for the mixed input state as in Eq. (24) with $d=2$ and fidelity $F=0.98$ (dashed), $F=0.95$ (dotted), $F=0.9$ (dot-dashed), along with the exact quantum capacity (solid line) achieved for $F=1$.