 Entanglement-assisted classical capacity

This is the supremum of reliable classical bits per use of a memoryless quantum channel when sender and receiver share unlimited prior quantum entanglement. If $|{\psi }_{\rho }{⟩}_{RA}$ purifies the input, let ${\omega }_{RB}=({\mathrm{id}}_R\otimes \mathcal{N})(|{\psi }_{\rho }⟩⟨{\psi }_{\rho }|)$. The single-letter capacity formula is ${\max }_{\rho }[S(\rho )+S(\mathcal{N}(\rho ))-S({\omega }_{RB})]$, the maximum quantum mutual information between reference and output. The preshared resource is independent of the message.

Entanglement-assisted classical capacity refers to the maximum rate at which classical information can be transmitted over a quantum channel when the sender and receiver share entanglement. This concept is an important aspect of quantum information theory, which explores the transmission and processing of information using quantum systems. In classical information theory, channels can be characterized by their capacity to transmit bits of information.