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

• 叠加态的布洛赫球表示位于赤道上的点。这是因为叠加态的状态不是经典位（0或1），而是介于两者之间的状态。赤道上的点代表了这种连续性和叠加性。
  

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

2. Two-Qubit Systems:

对于 2 量子位系统，我们可以使用其自己的布洛赫球来表示每个量子位。 两个量子位的组合状态可以使用它们各自状态的张量积来描述。 2 量子位纯态的布洛赫球体表示涉及三个单位 2 球体和一个相位因子。 三个球体中的两个对应于每个量子位的布洛赫球体，第三个球体参数化纠缠的程度和相位（例如并发）

• 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! 😊