Maximal Privacy Without Coherence


Leung, D. (2014). Maximal Privacy Without Coherence. Perimeter Institute. https://pirsa.org/14030105


Leung, Debbie. Maximal Privacy Without Coherence. Perimeter Institute, Mar. 12, 2014, https://pirsa.org/14030105


          @misc{ pirsa_14030105,
            doi = {},
            url = {https://pirsa.org/14030105},
            author = {Leung, Debbie},
            keywords = {Quantum Information},
            language = {en},
            title = {Maximal Privacy Without Coherence},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {mar},
            note = {PIRSA:14030105 see, \url{https://pirsa.org}}


Privacy and coherence have long been considered closely related properties of a quantum state. Indeed, a coherently transmitted quantum state is inherently private. Surprisingly, coherent quantum communication is not always required for privacy: there are quantum channels that are too noisy to transmit quantum information but it can send private classical information. Here, we ask how different the private classical and the quantum capacities can be. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d) <= 1, and private classical capacity P(N_d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence.