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We study information transmission over quantum channels in the one shot setting. We primarily consider multiterminal channels and develop several tools to send quantum information over these channels.
Our first contribution is a generalisation of the well known decoupling theorem, to the setting of multiple senders, which immediately allows us to design encoders and decoders for entanglement transmission over the quantum multiple access channel, among other applications. However, these results are non-smooth, in the sense that they do not recover the best known asymptotic iid bounds.
To overcome this issue, we develop two new techniques which we believe will be useful in other contexts as well ;
i. Successive cancellation decoding for entanglement transmission codes
ii. Quantum Rate Splitting
Finally, we tackle the problem of sending private classical information over the quantum MAC in the presence of an eavesdropper. Nothing was known about this problem, even in the asymptotic iid setting, due to a famous open problem that becomes a bottleneck for most coding strategies. This problem is known as 'simultaneous smoothing'. We overcome this issue by developing a new successive cancellation covering lemma, which allows us to recover the ideal rate region in the asymptotic iid setting. We also recover a non-trivial rate region in the one shot setting by using our new covering lemma in conjunction with our quantum rate splitting technique