須鎗 弘樹

1994年, Bell研のShorは公開鍵暗号の基礎である素因数分解を量子コンピュータ上で多項式時間で解くことのできるアルゴリズムを発見した.この発見を機に, 量子コンピュータの研究が一躍脚光をあびることとなった.そして, 今日まで多くの研究者が「古典的な計算機では膨大な計算量を要する問題を量子コンピュータで解くと, どれほどその計算量が減少するか」という問題に挑んでいる.本論文では, 組合せ最適化問題を解くために, その組合せ最適化問題の目的関数の値すべてを多項式時間で計算できる量子回路を構成する.

Jaynes-Cummingsモデルにおける原子の振舞いは, これまでに遷移確率やエントロピー等を用いて多くの解析や議論がなされてきた.本論文では, 状態変換を表す量子力学的チャネルを用いてJaynes-Cummingsモデルを記述し, そのチャネルに対して, von Neumannエントロピー及び量子相互エントロピーを導出し, これらを用いてこのモデルにおける原子の状態の変化及び非可逆性について議論する.

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.