T3Q3A Two photons moving in opposite directions along the y-axis are in the enta
ID: 3163209 • Letter: T
Question
T3Q3A
Two photons moving in opposite directions along the y-axis are in the entangled polarization state |Psi| = 1/Squareroot 2 (|VV> + |HH>), where V denotes vertical polarization relative to the z-axis, and H denotes horizontal polarization relative to the z-axis. The linear polarizations of the two photons are measured relative to different axes in the xz-plane. For photon 1, we use the axis n_1, whose direction is defined by theta = theta_1, where theta is the polar angle of spherical coordinates. For photon 2, we use the axis n_2, whose direction is defined by theta = theta_2. We define the following probabilities: P_VV is the probability that photon 1 gives vertical polarization relative to n_1 and photon 2 gives vertical polarization relative to n_2. P_HH is the probability that photon 1 gives horizontal polarization relative to n_1 and photon 2 gives horizontal polarization relative to n_2. P_VH is the probability that photon 1 gives vertical polarization relative to n_1 and photon 2 gives horizontal polarization relative to n_2. P_HV is the probability that photon 1 gives horizontal polarization relative to n_1 and photon 2 gives vertical polarization relative to n_2. (a) Explain carefully why P_VV+ P_HH + P_VH + P_HV = 1.Explanation / Answer
Here we have two particle system. So we have four basis states for this system.
they are HH, HV, VH and VV.
When we do the measurements in any axis of the polarizer, we need to find these four basis states only. With the change of basis i..e rotated from the original, the total probability remains same.
So the total probability must be equal to 1.
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