Quantum data hiding in the presence of noise

When classical or quantum information is broadcast to separate receivers, there exist codes that encrypt the encoded data such that the receivers cannot recover it when performing local operations and classical communication, but they can decode reliably if they bring their systems together and perform a collective measurement. This phenomenon is known as quantum data hiding and hitherto has been studied under the assumption that noise does not affect the encoded systems. With the aim of applying the quantum data hiding effect in practical scenarios, here we define the data-hiding capacity for hiding classical information using a quantum channel. Using this notion, we establish a regularized upper bound on the data hiding capacity of any quantum broadcast channel, and we prove that coherent-state encodings have a strong limitation on their data hiding rates. We then prove a lower bound on the data hiding capacity of channels that map the maximally mixed state to the maximally mixed state (we call these channels "mictodiactic"---they can be seen as a generalization of unital channels when the input and output spaces are not necessarily isomorphic) and argue how to extend this bound to generic channels and to more than two receivers.Comment: 12 pages, accepted for publication in IEEE Transactions on Information Theor

Polar codes in network quantum information theory

Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information processing, for tasks such as classical communication, private classical communication, and quantum communication. In the present work, we apply the polar coding method to network quantum information theory, by making use of recent advances for related classical tasks. In particular, we consider problems such as the compound multiple access channel and the quantum interference channel. The main result of our work is that it is possible to achieve the best known inner bounds on the achievable rate regions for these tasks, without requiring a so-called quantum simultaneous decoder. Thus, our work paves the way for developing network quantum information theory further without requiring a quantum simultaneous decoder.Comment: 18 pages, 2 figures, v2: 10 pages, double column, version accepted for publicatio

A father protocol for quantum broadcast channels

A new protocol for quantum broadcast channels based on the fully quantum Slepian-Wolf protocol is presented. The protocol yields an achievable rate region for entanglement-assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of Marton's region for classical broadcast channels. The protocol can be adapted to yield achievable rate regions for unassisted quantum communication and for entanglement-assisted classical communication; in the case of unassisted transmission, the region we obtain has no independent constraint on the sum rate, only on the individual transmission rates. Regularized versions of all three rate regions are provably optimal.Comment: Typo in statement of Theorem 4 fixe