須鎗 弘樹

The mathematical concept ''lifting'' which stems from ''compound state'' and ''transition expectation'' could have been applied to optical communication processes and quantum Markov chains. In the latest study of Lifting for the optical communication processes it was succesful to rigorously derive the error probability and SNR for quantum amplifier processes. In this paper the mutual entropy for quantum amplifier processes which is one of the most important efficiencies concerning the channel capacity is rigorously derived from the concept of ''lifting'' and its computational results of the mutual entropy are discussed.

Mutual entropy was introduced in classical communication theories to measure how much information can be transmitted from an input system to an output system. It has been expanded to quantum systems and applied to various physical models. By contrast, quantum Markov chains, introduced as an extension of classical Markov chains have been used to explain the irreversibility of observed systems. In [1], a physical model used frequently in quantum optics was applied to a quantum Markov chain. The Stinespring-Kraus expression was derived to discuss mutual entropy on quantum Markov chains. Mutual entropy was then computed and irreversibility was examined using numerical experiments. To further the ongoing research, mean mutual entropy is applied here to the same quantum Markov chain as the previous one; necessary discussion is included.