Dear Pennylane supervisor,

Hi!

To see what happens when Amplitude is reduced in a Beam splitter system, I carried out the below calculation. I confirmed the intensity step. This intensity step could be due to

(1) rounding error in the calculation, (2) quantization of the real single photons, and other answers.

I appreciate it if you can explain what is the reason for this? In addition, where comes from the special value of 1.1E-16. Python program is as follows:

import pennylane as qml

from pennylane import numpy as np

import matplotlib.pyplot as plt

dev_exact2 = qml.device(“default.gaussian”, wires = 2)

@qml.qnode(dev_exact2)

def measurement(a, phi):

qml.Displacement(a, phi, wires = 0) # Implement displacement using PennyLane

return qml.expval(qml.X(0))

@qml.qnode(dev_exact2)

def measurement2(a, theta, alpha, phi):

qml.Displacement(a, theta, wires = 0) # We choose the initial to be a displaced vacuum

qml.CoherentState(alpha, phi, wires = 1) # Prepare coherent as second qumode

qml.Beamsplitter(np.pi / 4, 0, wires=[0, 1]) # Interfere both states

return qml.expval(qml.NumberOperator(0)), qml.expval(qml.NumberOperator(1)) # Read out N

pi=3.141592653589793238462643

count = 0

while count <=180:

a = 2.0E-08

theta = count*pi/180.

```
print("Theta: {}".format(count), "Detector 1: {}".format(measurement2(a, theta, a, 0)[0].numpy()), "|", "Detector 2: {}".format(measurement2(a, theta, a, 0)[1].numpy()))
count=count+1
```

print (“End of calculation”)

----- End of program ----

Thank you four your help,

Hiro