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Given an entanglement measure $E$, the entanglement of a quantum channel isdefined as the largest amount of entanglement $E$ that can be generated fromthe channel, if the sender and receiver are not allowed to share a quantumstate before using the channel. The amortized entanglement of a quantum channelis defined as the largest net amount of entanglement $E$ that can be generatedfrom the channel, if the sender and receiver are allowed to share an arbitrarystate before using the channel. Our main technical result is that amortizationdoes not enhance the entanglement of an arbitrary quantum channel, whenentanglement is quantified by the max-Rains relative entropy. We prove thisstatement by employing semi-definite programming (SDP) duality and SDPformulations for the max-Rains relative entropy and a channel's max-Rainsinformation, found recently in [Wang et al., arXiv:1709.00200]. The mainapplication of our result is a single-letter, strong-converse, and efficientlycomputable upper bound on the capacity of a quantum channel for transmittingqubits when assisted by positive-partial-transpose preserving (PPT-P) channelsbetween every use of the channel. As the class of local operations andclassical communication (LOCC) is contained in PPT-P, our result establishes abenchmark for the LOCC-assisted quantum capacity of an arbitrary quantumchannel, which is relevant in the context of distributed quantum computationand quantum key distribution.

Amortization does not enhance the max-Rains information of a quantum channel