Quantum communication with zero-capacity channels

          @misc{ pirsa_PIRSA:08090021,
            doi = {10.48660/08090021},
            url = {https://pirsa.org/08090021},
            author = {Yard, Jon},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum communication with zero-capacity channels},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {sep},
            note = {PIRSA:08090021 see, \url{https://pirsa.org}}
          }
          

Abstract

A quantum channel models a physical process in which noise is added to a quantum system via interaction with its environment. Protecting quantum systems from such noise can be viewed as an extension of the classical communication problem introduced by Shannon sixty years ago. A fundamental quantity of interest is the quantum capacity of a given channel, which measures the amount of quantum information which can be protected, in the limit of many transmissions over the channel. In this talk, I will show that certain pairs of channels, each with a capacity of zero, can have a strictly positive capacity when used together, implying that the quantum capacity does not completely characterize a channel\'s ability to transmit quantum information. As a corollary, I will show that a commonly used lower bound on the quantum capacity - the coherent information, or hashing bound - is an overly pessimistic benchmark against which to measure the performance of quantum error correction because the gap between this bound and the capacity can be arbitrarily large.