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EntangledPhotonMeasurement.py
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EntangledPhotonMeasurement.py
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import math
import random
from decimal import Decimal, ROUND_HALF_UP
class EntangledPhotonMeasurement:
def __init__(self, i00, i01, i10, i11):
# Initialize the state probabilities for the photons
self.p00 = i00
self.p01 = i01
self.p10 = i10
self.p11 = i11
# Check if probabilities add up to approximately 1 (within a small range)
check = self.p00 ** 2 + self.p01 ** 2 + self.p10 ** 2 + self.p11 ** 2
if check > 1.01 or check < 0.99:
print("Error: Probabilities must add up to 1")
def format_number(self, value):
# Format a number to two decimal places
return str(Decimal(value).quantize(Decimal('0.00'), rounding=ROUND_HALF_UP))
def square(self, value):
# Calculate the square of a value
return value * value
def set_independent_photon_angles(self, angle1, angle2):
# Set the photon state based on independent angles
r1 = math.radians(angle1)
r2 = math.radians(angle2)
self.p00 = math.cos(r1) * math.cos(r2)
self.p01 = math.cos(r1) * math.sin(r2)
self.p10 = math.sin(r1) * math.cos(r2)
self.p11 = math.sin(r1) * math.sin(r2)
def set_measurement_angles(self, angle1, angle2):
# Set the measurement angles for the photons
self.m1angle = angle1
self.m2angle = angle2
r1 = math.radians(angle1)
r2 = math.radians(angle2)
self.m00 = math.cos(r1) * math.cos(r2)
self.m01 = math.cos(r1) * math.sin(r2)
self.m10 = math.sin(r1) * math.cos(r2)
self.m11 = math.sin(r1) * math.sin(r2)
def report_measurement_probability(self):
# Compute and print measurement probabilities
# Store original measurement angles
original_p1angle = self.m1angle
original_p2angle = self.m2angle
# Calculate probability for measuring 11
prob11 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Set measurement angles for 01
self.set_measurement_angles(90 + original_p1angle, original_p2angle)
prob01 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Set measurement angles for 10
self.set_measurement_angles(original_p1angle, original_p2angle + 90)
prob10 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Set measurement angles for 00
self.set_measurement_angles(90 + original_p1angle, 90 + original_p2angle)
prob00 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Reset to original measurement angles
self.set_measurement_angles(original_p1angle, original_p2angle)
# Print the probabilities
print("Probability of 00 =", self.format_number(prob00))
print("Probability of 01 =", self.format_number(prob01))
print("Probability of 10 =", self.format_number(prob10))
print("Probability of 11 =", self.format_number(prob11))
too_small = 0.00001
if prob01 + prob11 > too_small:
print("Probability of Photon1 measured to be 1, given that Photon2 was measured to be 1 =", self.format_number(prob11 / (prob01 + prob11)))
if prob10 + prob00 > too_small:
print("Probability of Photon1 measured to be 1, given that Photon2 was measured to be 0 =", self.format_number(prob10 / (prob10 + prob00)))
if prob01 + prob11 > too_small:
print("Probability of Photon1 measured to be 0, given that Photon2 was measured to be 1 =", self.format_number(prob01 / (prob01 + prob11)))
if prob10 + prob00 > too_small:
print("Probability of Photon1 measured to be 0, given that Photon2 was measured to be 0 =", self.format_number(prob00 / (prob10 + prob00)))
if prob10 + prob11 > too_small:
print("Probability of Photon2 measured to be 1, given that Photon1 was measured to be 1 =", self.format_number(prob11 / (prob10 + prob11)))
if prob01 + prob00 > too_small:
print("Probability of Photon2 measured to be 1, given that Photon1 was measured to be 0 =", self.format_number(prob01 / (prob01 + prob00)))
if prob10 + prob11 > too_small:
print("Probability of Photon2 measured to be 0, given that Photon1 was measured to be 1 =", self.format_number(prob10 / (prob10 + prob11)))
if prob01 + prob00 > too_small:
print("Probability of Photon2 measured to be 0, given that Photon1 was measured to be 0 =", self.format_number(prob00 / (prob01 + prob00)))
def perform_measurement(self):
# Perform a measurement and update the photon states
# Store original measurement angles
original_p1angle = self.m1angle
original_p2angle = self.m2angle
# Calculate probability for measuring 11
prob11 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Set measurement angles for 01
self.set_measurement_angles(90 + original_p1angle, original_p2angle)
prob01 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Set measurement angles for 10
self.set_measurement_angles(original_p1angle, original_p2angle + 90)
prob10 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Set measurement angles for 00
self.set_measurement_angles(90 + original_p1angle, 90 + original_p2angle)
prob00 = self.square((self.p00 * self.m00) + (self.p01 * self.m01) + (self.p10 * self.m10) + (self.p11 * self.m11))
# Reset to original measurement angles
self.set_measurement_angles(original_p1angle, original_p2angle)
# Generate a random number to simulate measurement outcome
rand = random.random()
if rand < prob00:
angle1 = self.m1angle + 90
angle2 = self.m2angle + 90
self.set_independent_photon_angles(angle1, angle2)
print("-------------------------------------------------------")
print("Measured 00")
print("After measurement, the photon angles are", self.format_number(angle1), "and", self.format_number(angle2), "and the photon state is", self.format_number(self.p00), self.format_number(self.p01), self.format_number(self.p10), self.format_number(self.p11))
elif rand < prob00 + prob01:
angle1 = self.m1angle + 90
angle2 = self.m2angle
self.set_independent_photon_angles(angle1, angle2)
print("-------------------------------------------------------")
print("Measured 01")
print("After measurement, the photon angles are", self.format_number(angle1), "and", self.format_number(angle2), "and the photon state is", self.format_number(self.p00), self.format_number(self.p01), self.format_number(self.p10), self.format_number(self.p11))
elif rand < prob00 + prob01 + prob10:
angle1 = self.m1angle
angle2 = self.m2angle + 90
self.set_independent_photon_angles(angle1, angle2)
print("-------------------------------------------------------")
print("Measured 10")
print("After measurement, the photon angles are", self.format_number(angle1), "and", self.format_number(angle2), "and the photon state is", self.format_number(self.p00), self.format_number(self.p01), self.format_number(self.p10), self.format_number(self.p11))
else:
angle1 = self.m1angle
angle2 = self.m2angle
self.set_independent_photon_angles(angle1, angle2)
print("-------------------------------------------------------")
print("Measured 11")
print("After measurement, the photon angles are", self.format_number(angle1), "and", self.format_number(angle2), "and the photon state is", self.format_number(self.p00), self.format_number(self.p01), self.format_number(self.p10), self.format_number(self.p11))
if __name__ == "__main__":
# Compute probabilities. But we don't make any measurement. So the Photon state is not changed.
pairPrediction = EntangledPhotonMeasurement(0.707106, 0, 0, 0.707106)
pairPrediction.set_measurement_angles(90, 90)
pairPrediction.report_measurement_probability()
# Perform some measurements. Measurements will change the photon states.
for i in range(100):
pairExperiment = EntangledPhotonMeasurement(0.707106, 0, 0, 0.707106)
pairExperiment.set_measurement_angles(90, 90)
pairExperiment.perform_measurement()