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In this talk I'll be presenting the result of Beigi et.al. on achievability for rate equal to one-shot information spectrum divergence through collision relative entropy for one sender and one receiver classical-quantum channel, whose input is classical and output is quantum.

In the first part of the talk I'll draw a quick analogue between a probability distribution of a random variable and a quantum state described via density matrix. Then we'll look at typical set and an achievability proof for point to point discrete memory less classical channel (both input and output being classical) where the number of channel use is asymptotic, as a warm up.

In the second part we'll look at one-shot achievability proof for a classical point to point channel where the rate is given by hypothesis testing relative entropy and how is this related to information spectrum divergence.

Finally, we'll see Beige et.al achievability proof for a c-q channel.