866 B
866 B
Bell State
- quantum-state
- created by using hadamard-gate on the control bit of a controlled-not:
`\left(\operatorname{CNOT}_{1 \to 2}\right) \left(\mathbf{H} \otimes \mathbf{1}\right)` `\ket{\Phi^+} = \frac{1}{\sqrt{2}} \left[\ket{00} + \ket{11}\right]`from`\ket{00}``\ket{\Psi^+} = \frac{1}{\sqrt{2}} \left[\ket{01} + \ket{10}\right]`from`\ket{01}``\ket{\Phi^-} = \frac{1}{\sqrt{2}} \left[\ket{00} - \ket{11}\right]`from`\ket{10}``\ket{\Psi^-} = \frac{1}{\sqrt{2}} \left[\ket{01} - \ket{10}\right]`from`\ket{11}`- the four bell states form an orthonormal basis
- for an unentangled 2-qubit state
`\ket{\varphi} = \left(a\ket{0}+b\ket{1}\right)\otimes\left(c\ket{0}+d\ket{1}\right)`, the inner-product with any bell state is bounded`\braket{\varphi|\text{B}_{ij}} \leq \frac{1}{\sqrt{2}}`