diff --git a/docs/conf.py b/docs/conf.py index 2740d087e..331f3f5bb 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -18,11 +18,11 @@ # -- Project information ----------------------------------------------------- project = "toqito" -copyright = "2020-2024, Toqito Contributors" -author = "Contributors to Toqito" +copyright = "2020-2024, toqito Contributors" +author = "Contributors to toqito" # The full version, including alpha/beta/rc tags -release = "1.0.8" +release = "1.0.9" # -- General configuration --------------------------------------------------- diff --git a/main.py b/main.py new file mode 100644 index 000000000..abf4bad5e --- /dev/null +++ b/main.py @@ -0,0 +1,140 @@ +import numpy as np + +from toqito.matrices import standard_basis +from toqito.nonlocal_games import ExtendedNonlocalGame +from toqito.rand import random_povm +from toqito.states import trine + +import numpy as np +from toqito.matrices import standard_basis +from toqito.state_props import concurrence +e_0, e_1 = standard_basis(2) +e_00, e_11 = np.kron(e_0, e_0), np.kron(e_1, e_1) +u_vec = 1 / np.sqrt(2) * (e_00 + e_11) +rho = u_vec @ u_vec.conj().T +print(np.around(concurrence(rho), decimals=2)) + +eps = 0.5 +print(np.around(1/3 * (2 + np.sqrt(1 - eps**2)), decimals=3)) + + +exit() + +e_0, e_1 = standard_basis(2) +ep = (e_0 + e_1) / np.sqrt(2) +em = (e_0 - e_1) / np.sqrt(2) + +dim = 2 +num_alice_out, num_bob_out = 2, 2 +num_alice_in, num_bob_in = 3, 3 + +povms = random_povm(dim=dim, num_inputs=num_alice_in, num_outputs=num_alice_out) + +print(povms[:,:,0,0] + povms[:,:,0,1]) +print(ep @ ep.conj().T + em @ em.conj().T) +exit() + +pred_mat = np.zeros([dim, dim, num_alice_out, num_bob_out, num_alice_in, num_bob_in]) +pred_mat[:, :, 0, 0, 0, 0] = povms[:, :, 0, 0] +pred_mat[:, :, 0, 0, 1, 1] = povms[:, :, 1, 0] +pred_mat[:, :, 0, 0, 2, 2] = povms[:, :, 2, 0] + +pred_mat[:, :, 1, 1, 0, 0] = povms[:, :, 0, 1] +pred_mat[:, :, 1, 1, 1, 1] = povms[:, :, 1, 1] +pred_mat[:, :, 1, 1, 2, 2] = povms[:, :, 2, 1] + +prob_mat = 1 / 3 * np.identity(3) + +game = ExtendedNonlocalGame(prob_mat, pred_mat, reps=1) +unent = game.unentangled_value() +print(f"{unent=}") +lb = game.quantum_value_lower_bound() +print(f"{lb=}") +ns = game.nonsignaling_value() +print(f"{ns=}") + +exit() + +e_0, e_1 = standard_basis(2) +e_p = (e_0 + e_1) / np.sqrt(2) +e_m = (e_0 - e_1) / np.sqrt(2) + +dim = 2 +num_alice_out, num_bob_out = 2, 2 +num_alice_in, num_bob_in = 2, 2 + +pred_mat = np.zeros([dim, dim, num_alice_out, num_bob_out, num_alice_in, num_bob_in]) + +#pred_mat[:, :, 0, 1, 0, 0] = e_0 @ e_0.conj().T +#pred_mat[:, :, 1, 0, 0, 0] = e_0 @ e_0.conj().T +pred_mat[:, :, 1, 1, 0, 0] = e_0 @ e_0.conj().T + +pred_mat[:, :, 0, 0, 0, 1] = e_1 @ e_1.conj().T +#pred_mat[:, :, 1, 0, 0, 1] = e_1 @ e_1.conj().T +pred_mat[:, :, 1, 1, 0, 1] = e_1 @ e_1.conj().T + +pred_mat[:, :, 0, 0, 1, 0] = e_p @ e_p.conj().T +#pred_mat[:, :, 0, 1, 1, 0] = e_p @ e_p.conj().T +pred_mat[:, :, 1, 1, 1, 0] = e_p @ e_p.conj().T + +pred_mat[:, :, 0, 0, 1, 1] = e_m @ e_m.conj().T +#pred_mat[:, :, 0, 1, 1, 1] = e_m @ e_m.conj().T +#pred_mat[:, :, 1, 0, 1, 1] = e_m @ e_m.conj().T + +prob_mat = 1 / 2 * np.identity(2) +#prob_mat = np.array([[1/4, 1/4], [1/4, 1/4]]) + +game = ExtendedNonlocalGame(prob_mat, pred_mat, reps=2) +res = game.unentangled_value() +#res = game.nonsignaling_value() +#res = game.quantum_value_lower_bound() +print(res) + +#res = game.nonsignaling_value() +#res = game.commuting_measurement_value_upper_bound() +#res = game.quantum_value_lower_bound() + +exit() +dim = 2 +num_in = 3 +num_out = 2 +pred_mat = np.zeros([dim, dim, num_out, num_out, num_in, num_in], dtype=complex) + +e0, e1 = standard_basis(2) + +theta_1 = 1/4 * np.arccos((121 + 52 * np.sqrt(13))/(477)) +theta_2 = 1/4 * np.arccos((-431 + 4 * np.sqrt(13))/(477)) +alpha_0 = -theta_1 +alpha_1 = theta_2 +beta_0 = (np.pi/2) - theta_2 +beta_1 = theta_1 +def M(theta): + return np.array([ + [np.cos(theta)**2, np.cos(theta) * np.sin(theta)], + [np.sin(theta) * np.cos(theta), np.sin(theta)**2] + ]) + +# V(0,0|x,y): +pred_mat[:, :, 0, 0, 1, 1] = M(alpha_0) +pred_mat[:, :, 0, 0, 2, 2] = np.identity(dim) - M(alpha_0) + +# V(0,1|x,y): +pred_mat[:, :, 0, 1, 0, 0] = M(alpha_1) +pred_mat[:, :, 0, 1, 1, 1] = np.identity(dim) - M(alpha_1) + +# V(1,0|x,y): +pred_mat[:, :, 1, 0, 0, 0] = M(beta_0) +pred_mat[:, :, 1, 0, 1, 1] = np.identity(dim) - M(beta_0) + +# V(1,1|x,y): +pred_mat[:, :, 1, 1, 0, 0] = M(beta_1) +pred_mat[:, :, 1, 1, 2, 2] = np.identity(dim) - M(beta_1) + +prob_mat = 1 / 3 * np.identity(3) + +game = ExtendedNonlocalGame(prob_mat, pred_mat) +res = game.unentangled_value() +#res = game.nonsignaling_value() +#res = game.commuting_measurement_value_upper_bound() +#res = game.quantum_value_lower_bound() +print(res) diff --git a/poetry.lock b/poetry.lock new file mode 100644 index 000000000..3c5182960 --- /dev/null +++ b/poetry.lock @@ -0,0 +1,2023 @@ +# This file is automatically @generated by Poetry 1.8.3 and should not be changed by hand. + 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