Entanglement transmission and generation under channel uncertainty: Universal quantum channel coding

Abstract

We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels, so that they are forced to use quantum codes that are reliable for the whole set of channels. This is precisely the quantum analog of the compound channel coding problem. We determine the entanglement transmission and entanglement-generating capacities of compound quantum channels and show that they are equal. Moreover, we investigate two variants of that basic scenario, namely the cases of informed decoder or informed encoder, and derive corresponding capacity results.

45 pages, no figures. Section 6.2 rewritten due to an error in equation (72) of the old version. Added table of contents, added section 'Conclusions and further remarks'. Accepted for publication in 'Communications in Mathematical Physics'

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• Quantum capacity of an amplitude-damping channel with memory
• Universal quantum state merging
• The invalidity of a strong capacity for a quantum channel with memory
• A hypothesis testing approach for communication over entanglement assisted compound quantum channel
• Entanglement-assisted capacities of compound quantum channels
• Simultaneous transmission of classical and quantum information under channel uncertainty and jamming attacks
• Universal coding for transmission of private information
• Universal random codes: Capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender
• Arbitrarily varying and compound classical-quantum channels and a note on quantum zero-error capacities
• Entanglement Transmission Capacity of Compound Channels
• Explicit decoders using fixed-point amplitude amplification based on QSVT
• Entanglement Transmission over Arbitrarily Varying Quantum Channels