Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions

We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.Comment: 38 pages, 1 figure. Fixed typos, added new example. Submitted to IEEE Tranactions on Information Theor

Quantum broadcast channels

We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for channels with a quantum input, where some of the messages transmitted are quantum instead of classical, in the sense that the parties establish bipartite or tripartite GHZ entanglement. We conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pairs of parties with the assistance of free classical communication.Comment: 15 pages; IEEE Trans. Inform. Theory, vol. 57, no. 10, October 201

Universal coding for transmission of private information

We consider the scenario in which Alice transmits private classical messages to Bob via a classical-quantum channel, part of whose output is intercepted by an eavesdropper, Eve. We prove the existence of a universal coding scheme under which Alice's messages can be inferred correctly by Bob, and yet Eve learns nothing about them. The code is universal in the sense that it does not depend on specific knowledge of the channel. Prior knowledge of the probability distribution on the input alphabet of the channel, and bounds on the corresponding Holevo quantities of the output ensembles at Bob's and Eve's end suffice.Comment: 31 pages, no figures. Published versio