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Hadamard quantum broadcast channels

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Abstract

We consider three different communication tasks for quantum broadcast channels, and we determine the capacity region of a Hadamard broadcast channel for these various tasks. We define a Hadamard broadcast channel to be such that the channel from the sender to one of the receivers is entanglement-breaking and the channel from the sender to the other receiver is complementary to this one. As such, this channel is a quantum generalization of a degraded broadcast channel, which is well known in classical information theory. The first communication task we consider is classical communication to both receivers, the second is quantum communication to the stronger receiver and classical communication to other, and the third is entanglement-assisted classical communication to the stronger receiver and unassisted classical communication to the other. The structure of a Hadamard broadcast channel plays a critical role in our analysis: The channel to the weaker receiver can be simulated by performing a measurement channel on the stronger receiver’s system, followed by a preparation channel. As such, we can incorporate the classical output of the measurement channel as an auxiliary variable and solve all three of the above capacities for Hadamard broadcast channels, in this way avoiding known difficulties associated with quantum auxiliary variables.

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Acknowledgements

We are grateful to Haoyu Qi for discussions related to the topic of this paper. QLW is supported by the NFSC (Grants Nos. 61272057, 61309029 and 61572081) and funded by the China Scholarship Council (Grant No. 201506470043). SD acknowledges support from the LSU Graduate School Economic Development Assistantship. MMW acknowledges support from the NSF under Award No. CCF-1350397.

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Authors and Affiliations

  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Qingle Wang

  2. Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803, USA

    Qingle Wang, Siddhartha Das & Mark M. Wilde

  3. Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    Mark M. Wilde

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  1. Qingle Wang
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  2. Siddhartha Das
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  3. Mark M. Wilde
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Correspondence to Mark M. Wilde.

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Wang, Q., Das, S. & Wilde, M.M. Hadamard quantum broadcast channels. Quantum Inf Process 16, 248 (2017). https://doi.org/10.1007/s11128-017-1697-5

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