Error Exponent and Strong Converse for Quantum Soft Covering

Understand

How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem.

• Namely, we use a random codebook with codewords independently sampled from a prior distribution and send it through a classical-quantum channel to approximate the target state.
• When using a random codebook sampled from an independent and identically distributed prior with a rate above the quantum mutual information, we show that the expected trace distance between the codebook-induced state and the target state decays with exponent given by the sandwiched R\'enyi information.
• On the other hand, when the rate of the codebook size is below the quantum mutual information, the trace distance converges to one exponentially fast.