【量子光学】 Quantum Optics 2 Quiz 4.3(10)

Quantum Optics 2课程第十次测验

第1题 (单选)

We call $\hat{P}_{\vec{u}}=\left|\vec{u}\right\rangle\left\langle\vec{u}\right|$ the projector associated to the eigenvalue +1 of a measurement with polarizer along the $\vec{u}$ axis.
How can be expressed the quantum observable $\hat{A}$ associated to a measurement of the polarization of photon $\nu_1$ along $\vec{x}$?

A) $\hat{A}=\hat{P}_{\vec{x}}$

B) $\hat{A}=\hat{P}_{\vec{x}}-\hat{P}_{\vec{y}}$

C) $\hat{A}=\hat{P}_{\vec{x}}+\hat{P}_{\vec{y}}$

第2题 (不定项选择)

Just after a measurement of the polarization of photon $\nu_1$ yielding +1, what is the quantum state $\left|\psi_M\right\rangle$ of the pair of photons initially in the state $\left|\psi\right\rangle$?

A) $\left|\psi_M\right\rangle=\hat{P}_{\vec{x}}\left|\psi\right\rangle$

B) $\left|\psi_M\right\rangle=\frac{\hat{P}_{\vec{x}}\left|\psi\right\rangle}{\left\langle\psi\right|\hat{P}_{\vec{x}}\left|\psi\right\rangle}$

C) $\left|\psi_M\right\rangle=\frac{\hat{P}_{\vec{x}}\left|\psi\right\rangle}{\left\langle\psi\right|(\hat{P}_{\vec{x}})^{-1}\hat{P}_{\vec{x}}\left|\psi\right\rangle}$

D) $\left|\psi_M\right\rangle=\hat{P}_{\vec{x}}\left|\psi\right\rangle-\hat{P}_{\vec{y}}\left|\psi\right\rangle$

第3题 (单选)

Considering a pair of photons in the EPR state $\left|\psi_{EPR}\right\rangle=\frac{1}{\sqrt{2}}(\left|x_1, x_2\right\rangle+\left|y_1, y_2\right\rangle)$, what is the quantum state $\left|\psi_M\right\rangle$ after this measurement?

A) $\left|\psi_M\right\rangle=\left|x_1, x_2\right\rangle$

B) $\left|\psi_M\right\rangle=\frac{1}{\sqrt{2}}\left|x_1, x_2\right\rangle$

C) $\left|\psi_M\right\rangle=\frac{1}{\sqrt{2}}(\left|x_1, x_2\right\rangle+\left|y_1, y_2\right\rangle)$

D) $\left|\psi_M\right\rangle=\frac{1}{\sqrt{2}}(\left|x_1, x_2\right\rangle-\left|y_1, y_2\right\rangle)$

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