5. The Classical-Quantum Channel

Zhihua Guo, Huaixin Cao

The aim of this paper is to discuss local quantum channels that preserve classical correlations. First, we give two equivalent characterizations of classical correlated states. Then we obtain the relationships among classical correlation-preserving local quantum channels, commutativity-preserving local quantum channels and commutativity-preserving quantum channels on each subsystem. Furthermore, for a two-qubit system, we show the general form of classical correlation-preserving local quantum channels.

Bob Coecke, Chris Heunen, Aleks Kissinger

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

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

Joseph M. Renes