Error Exponent and Strong Converse for Quantum Soft Covering

How well can we approximate a classical-quantum channel output state by using a random codebook with a certain size? In this work, we study the quantum soft covering problem and establish exponential achievability and strong converse bounds on the expected trace distance between the codebook-induced state and the true state. When using independent and identically distributed random codebook or constant composition random codebook with a rate above the quantum mutual information I(X : B)
ρ
, we prove that the trace distances decay exponentially with error exponents expressed by the sandwiched Rényi and Augustin information. For a rate below I(X : B)
ρ
, we show that both the trace distances converge to 1 exponentially fast. The full manuscript can be found at [1].