Relating Entanglement to Quantum Communication

          @misc{ pirsa_PIRSA:07120015,
            doi = {10.48660/07120015},
            url = {https://pirsa.org/07120015},
            author = {Oppenheim, Jonathan},
            keywords = {Quantum Information},
            language = {en},
            title = {Relating Entanglement to Quantum Communication},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {dec},
            note = {PIRSA:07120015 see, \url{https://pirsa.org}}
          }
          

Abstract

Roughly speaking, the more Alice is entangled with Bob, the harder it is for her to send her state to Charlie. In particular, it will be shown that the squashed entanglement, a well known entanglement measure, gives the fastest rate at which a quantum state can be sent between two parties who share arbitrary side information. Likewise, the entanglement of formation and entanglement cost is shown to be the fastest rate at which a quantum state can be sent when the parties have access to side-information which is maximally correlated. A further restriction on the type of side-information implies that the rate of state transmission is given by the quantum mutual information. This suggests a new paradigm for understanding entanglement and other correlations in terms of quantum Shannon theroy. Different types of side-information correspond to different types of correlations with the squashed entanglement and the mutual information being two extremes. Furthermore, there is a dual paradigm: if one distributes the side-information as aliciously as possible so as to make the sending of the state as difficult as possible, one finds maximum rates which give interpretations to known quantities as well as new ones.