Classical-Quantum Channel Coding (Message Transmission)

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under the attack of a malignant third party. These codes are robust to different kinds of channel uncertainties. To construct such universal codes, we invoke and generalize the properties of random codes for classical and quantum message transmission through quantum channels. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. In addition, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement. These include cases where the malignant jammer present in the arbitrarily varying channel model is classical (chooses channel states of the product form) and fully quantum (is capable of general attacks not necessarily of the product form).

Masahito Hayashi, Satoshi Ishizaka, Akinori Kawachi +2 more

Holger Boche, Gisbert Janßen, Sajad Saeedinaeeni

We derive universal codes for simultaneous transmission of classical messages and entanglement through quantum channels, possibly under attack of a malignant third party. These codes are robust to different kinds of channel uncertainty. We show these codes to be optimal by giving a multi-letter characterization of regions corresponding to capacity of compound quantum channels for simultaneously transmitting and generating entanglement with classical messages. Also, we give dichotomy statements in which we characterize the capacity of arbitrarily varying quantum channels for simultaneous transmission of classical messages and entanglement.

Masanori Ohya

Recently, much research has been carried out on the transmission capacity of the quantum channel, and there exists significant confusion. The transmission capacity of the quantum channel is the information transfer capability of the quantum channel itself and does not fundamentally depend on the messages to be treated classically or on the method of coding. Hence, it is incorrect to call the process of sending the message to be processed classically through a device (channel) designed in a quantum manner and restoring the classical signal again the “quantum process.” Since the actual daily messages are classical subjects, it is commonly carried out that such messages coded to quantum states are sent through a quantum configured channel and are restored. In this case, the transmission capability is considered on the composite channel consisting of the channel converting a classical state formed by a message to a quantum state, the quantum channel sending a quantum state to a quantum state, and the channel restoring a classical state from a quantum state. This is different from the transmission capability of the quantum channel itself. Mathematically, the conventional Shannon theory should be applied to the above composite channel since the input state and the output one are classical. The transmission capacity in this case is that of the classical-quantum-classical channel. In this paper, a method is discussed to systematically treat the transmission capacity of such channels. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(4): 69–75, 2001

Michael Reck, Klaus Mattle, Harald Weinfurter +1 more