Commit 306f34e3 by Orkun Şensebat

Merge branch 'tobi'

parents ca05f27b 324727cd
Pipeline #466094 passed with stage
in 1 minute and 2 seconds
 import numpy as np import math class ObservationStation: def __init__(self, T): self.T = T def set_a(self, a): self.a = a def execute(self, phi, r): c = math.cos(2 * (self.a - phi)) s = math.sin(2 * (self.a - phi)) x = np.sign(c) t_star = r * self.T * s ** 2 return x, t_star def generate_phis(): phi1 = np.random.rand() * 2 * np.pi phi2 = phi1 + np.pi / 2 return phi1, phi2 def simulate(): M = 100 N = int(1e6) a = np.array([0, 1/4, 1/8, 3/8]) * np.pi W = 1 T = 1000 station = (ObservationStation(T), ObservationStation(T)) # conducts EPRB experiment M times for _ in range(M): results = np.zeros((N, 4, 2), dtype=np.int8) import matplotlib.pyplot as plt import time # settings N = int(1e6) T_0 = 1000 W = 1 showPlots = True def simulate(phi1, phi2): # generate random phis thetas = np.empty((N, 2), dtype=np.float32) thetas[:, 0] = np.random.rand(N) * 2 * np.pi thetas[:, 1] = thetas[:, 0] + np.pi / 2 # generate random number for timestamp rs = np.random.rand(N) # calculate outcome of observation station x1 = (np.cos(2 * (phi1 - thetas[:, 0])) >= (2*np.random.rand(N) -1)).reshape(N, 1) t1 = T_0 * rs * np.sin(2 * (phi1 - thetas[:, 0])) ** 2 x2 = (np.cos(2 * (phi2 - thetas[:, 1])) >= (2*np.random.rand(N) -1)).reshape(N, 1) t2 = T_0 * rs * np.sin(2 * (phi2 - thetas[:, 1])) ** 2 # determine which events are conincidences (1) and which not (0) coincidences = np.abs(t1 - t2) < W # zip measurement outcome together x1x2 = np.concatenate((x1, x2), axis=1) counts = np.empty((2, 4), dtype=np.int32) counts[0, 0] = np.sum(np.all(x1x2 == np.array([0, 0]), axis=1), axis=0) counts[0, 1] = np.sum(np.all(x1x2 == np.array([0, 1]), axis=1), axis=0) counts[0, 2] = np.sum(np.all(x1x2 == np.array([1, 0]), axis=1), axis=0) counts[0, 3] = np.sum(np.all(x1x2 == np.array([1, 1]), axis=1), axis=0) counts[1, 0] = np.sum(np.all(x1x2 == np.array([0, 0]), axis=1) == coincidences, axis=0) counts[1, 1] = np.sum(np.all(x1x2 == np.array([0, 1]), axis=1) == coincidences, axis=0) counts[1, 2] = np.sum(np.all(x1x2 == np.array([1, 0]), axis=1) == coincidences, axis=0) counts[1, 3] = np.sum(np.all(x1x2 == np.array([1, 1]), axis=1) == coincidences, axis=0) E_all = np.sum(counts, axis=1).astype(float) E_12 = (counts[:, 0] - counts[:, 1] - counts[:, 2] + counts[:, 3]).astype(float) E_1 = (counts[:, 0] + counts[:, 1] - counts[:, 2] - counts[:, 3]).astype(float) E_2 = (counts[:, 0] - counts[:, 1] + counts[:, 2] - counts[:, 3]).astype(float) if (np.all(E_all > 0)): E_12 /= E_all E_1 /= E_all E_2 /= E_all # iterates through all pairs of settings for p in range(4): # selects a unique pair of settings from all possible settings station[0].set_a(a[int(p/2)]) station[1].set_a(a[2+p%2]) # simulates 10^6 events for n in range(N): #if n%1000 == 0: # print(p, n) phi = generate_phis() for s in range(2): r = np.random.rand() x, t_star = station[s].execute(phi[s], r) results[n, p, s] = x # alternative approach to simulating 10^6 events return E_12, E_1, E_2 # calculates absolute X products = np.prod(results, axis=2) products[:, 2] *= -1 sums = np.sum(products, axis=1) X_abs = np.abs(sums) if np.any(X_abs >= 2): print(f'|X| <= 2 is violated with |x| = {X_abs.max()}') else: print(f'|X| <= 2 is satisfied with |x| = {X_abs.max()}') simulate() def try_all_configs(n_configs): E_12 = np.empty((n_configs, 2), dtype=np.float32) E_1 = np.empty((n_configs, 2), dtype=np.float32) E_2 = np.empty((n_configs, 2), dtype=np.float32) for i in range(n_configs): phi1 = 0 phi2 = i * 2 * np.pi / n_configs E_12_, E_1_, E_2_ = simulate(phi1, phi2) E_12[i, :] = E_12_ E_1[i, :] = E_1_ E_2[i, :] = E_2_ x = np.linspace(0, 360, n_configs) plt.figure() plt.plot(x, E_12[:, 0]) plt.show() # correlation phi = np.linspace(0, 360, n_configs) phi_theory = np.linspace(0, 360, n_configs*100) theory = -np.cos(2 * phi_theory * (2 * np.pi / 360)) plt.figure() plt.xlabel(r'$\Delta \varphi$') plt.ylabel(r'$$') plt.plot(phi_theory, theory, '.', markersize=1, color='orange') plt.plot(phi, E_12[:, 0], 'o', color='blue') #plt.savefig('correlation.pdf') if showPlots: plt.show() plt.close() # product of expectation values line = np.zeros(phi_theory.shape) plt.figure() plt.xlabel(r'\Delta \varphi') plt.ylabel(r'$$') plt.ylim([-1, 1]) plt.xticks([0, 45, 90, 135, 180, 225, 270, 305, 360]) plt.plot(phi_theory, line, '.', markersize=1, color='orange') plt.plot(phi, E_1[:, 0]*E_2[:, 0], 'o', color='blue') #plt.savefig('expectation_value.pdf') if showPlots: plt.show() plt.close() start = time.time() try_all_configs(32) duration = time.time() - start print(f'simulation took {round(duration, 2)} seconds') \ No newline at end of file
 import example import eprb
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