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→Mixed state
量子比特和经典比特的一个重要区别是多个量子比特可以表现出量子纠缠。量子纠缠是两个或多个量子比特的非局域性质，它允许一组量子比特表达比经典系统更高的相关性。
量子比特和经典比特的一个重要区别是多个量子比特可以表现出量子纠缠。量子纠缠是两个或多个量子比特的非局域性质，它允许一组量子比特表达比经典系统更高的相关性。
===Mixed state===
===Mixed state混合状态===
A pure state is one fully specified by a single ket, <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\,</math> a coherent superposition as described above. Coherence is essential for a qubit to be in a superposition state. With interactions and [[decoherence]], it is possible to put the qubit in a [[Mixed state (physics)|mixed state]], a statistical combination or incoherent mixture of different pure states. Mixed states can be represented by points ''inside'' the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles <math>\phi </math> and <math>\theta </math>, as well as the length <math>r</math> of the vector that represents the mixed state.
A pure state is one fully specified by a single ket, <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle,\,</math> a coherent superposition as described above. Coherence is essential for a qubit to be in a superposition state. With interactions and [[decoherence]], it is possible to put the qubit in a [[Mixed state (physics)|mixed state]], a statistical combination or incoherent mixture of different pure states. Mixed states can be represented by points ''inside'' the Bloch sphere (or in the Bloch ball). A mixed qubit state has three degrees of freedom: the angles <math>\phi </math> and <math>\theta </math>, as well as the length <math>r</math> of the vector that represents the mixed state.
纯态是一个完全由单个ket指定的态，<math>|\psi\rangle=\alpha | 0\rangle+\beta | 1\rangle，\，</math>如上所述的相干叠加。相干是量子位元处于叠加态所必需的。通过相互作用和[[退相干]]，可以将量子位置于[[混合态（物理）|混合态]]，不同纯态的统计组合或非相干混合。混合状态可以用布洛赫球（或布洛赫球）“内部”的点来表示。混合量子比特态有三个自由度：角<math>\phi</math>和<math>\theta</math>，以及表示混合态的向量的长度<math>r</math>。
The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the <math>|\Phi^+\rangle</math> Bell state:
The simplest system to display quantum entanglement is the system of two qubits. Consider, for example, two entangled qubits in the <math>|\Phi^+\rangle</math> Bell state:
显示量子纠缠的最简单的系统是两个量子位的系统。例如，考虑两个处于 < math > | Phi ^ + rangle </math > Bell 态的纠缠量子比特:
显示量子纠缠的最简单的系统是两个量子位的系统。例如，考虑两个处于 < math > | Phi ^ + rangle </math > Bell 态的纠缠量子比特:
===Operations on pure qubit states===
===Operations on pure qubit states===