在此論文中，我們討論了量子力學中的量子態如何演化到熱力學中的熱平衡態，主要是以熵的觀點來探討。為了要比較量子態和熱平衡態，在論文中我們使用了一個簡單的模型來描述熵在不同系統中的形式。其中在量子力學理論中，可用縮減密度矩陣(reduced density matrix)來計算子系統的熵。我們推論: 如整個系統的量子態始於一個純態(pure state)，則由於時間演化算符的么正性質，整個系統的熵將會維持為零；而有限的熵將將由區域性的測量 (local measurement)而獲得。主要的原因在於部分對角和( partial trace)會破壞時間演化算符的么正性質。並且我們運用了一種破壞么正性質的方法提出了如何產生多量子位元的W態(W state)。其主要方法是有條件的測量熱儲。 基於模型中的平移不變性和條件測量，W態的保真度(Fidelity)在某些特定的條件下將可以提高到最大值。

We discuss how the state in quantum dynamics evolves toward thermal equilibrium in the entropic perspective. For comparing the evolution in semi-classical dynamics which
can be expected directly by thermal equilibrium and in quantum dynamics, we set up a simple model to calculate the entropies. In the quantum dynamical region, the reduced density matrix is adopted to derive the entropy of subsystems. We find that the entropy of the whole system would be kept to zero in quantum dynamics due to the unitary time evolution operator, if the system starts with a pure state. The finite entropy would be gained from the reduced density matrix associated with local measurement . The main cause is that the partial tracing operator would break the unitary property of the entropy for subsystems. We apply the method of the tracing out the heat bath and propose a model for generating W state in multi-qubits with fermion particles. The method is the conditional measurement for the common quantum well. From the non-unitary property of the conditional measurement and the translational symmetry of this model, the W state can be made in these qubits with high fidelity.

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