2017/07/31 by Eneet Kaur, Mark M. Wilde, Mark M Wilde · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Amortized analysis #Bounded function #Channel (broadcasting) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Upper and lower bounds #Wireless Communication Security Techniques #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1088/1751-8121/aa9da7
published as Journal of Physics A, vol. 51, no. 3, page 035303, January 2018 · v3: 38 pages, 5 figures, accepted for publication in Journal of Physics A
openalex created_date 2017/07/31 · openalex publication_date 2017/11/28 · arxiv created 2017/12/19 · arxiv updated 2017/12/20 · openalex updated_date 2026/08/05
Abstract This paper defines the amortized entanglement of a quantum channel as the largest difference in entanglement between the output and the input of the channel, where entanglement is quantified by an arbitrary entanglement measure. We prove that the amortized entanglement of a channel obeys several desirable properties, and we also consider special cases such as the amortized relative entropy of entanglement and the amortized Rains relative entropy. These latter quantities are shown to be single-letter upper bounds on the secret-key-agreement and PPT-assisted quantum capacities of a quantum channel, respectively. Of especial interest is a uniform continuity bound for these latter two special cases of amortized entanglement, in which the deviation between the amortized entanglement of two channels is bounded from above by a simple function of the diamond norm of their difference and the output dimension of the channels. We then define approximately teleportation- and positive-partial-transpose-simulable (PPT-simulable) channels as those that are close in diamond norm to a channel which is either exactly teleportation- or PPT-simulable, respectively. These results then lead to single-letter upper bounds on the secret-key-agreement and PPT-assisted quantum capacities of channels that are approximately teleportation- or PPT-simulable, respectively. Finally, we generalize many of the concepts in the paper to the setting of general resource theories, defining the amortized resourcefulness of a channel and the notion of ν -freely-simulable channels, connecting these concepts in an operational way as well.