1. Realization of efficient quantum gates with a superconducting qubit-qutrit circuit | Scientific Reports (nature.com)
   

• 疊加態的布洛赫球表示位於赤道上的點。這是因為疊加態的狀態不是經典位（0或1），而是介於兩者之間的狀態。赤道上的點代表了這種連續性和疊加性。
  

• 
  

•  which basis vectors correspond to the poles is arbitrary; it could be any other orthogonal basis.

2. Two-Qubit Systems:

對於 2 量子位系統，我們可以使用其自己的布洛赫球來表示每個量子位。 兩個量子位的組合狀態可以使用它們各自狀態的張量積來描述。 2 量子位純態的布洛赫球體表示涉及三個單位 2 球體和一個相位因子。 三個球體中的兩個對應於每個量子位的布洛赫球體，第三個球體參數化糾纏的程度和相位（例如並發）

• For 2-qubit systems, we can represent each qubit using its own Bloch sphere.

• The combined state of the two qubits can be described using a tensor product of their individual states.

• The Bloch sphere representation for 2-qubit pure states involves three unit 2-spheres and a phase factor.

• Two of the three spheres correspond to the Bloch spheres of each qubit, and the third sphere parameterizes the degree and phase of entanglement (e.g., concurrence).

In summary, while the Bloch sphere is most commonly associated with single-qubit states, it can be extended to represent 2-qubit pure states as well. The visualization becomes less useful for higher-level quantum systems, but it remains a powerful tool for understanding qubit states and their properties12. If you have any more questions or need further clarification, feel free to ask! 😊