| """Full propagator checks of multistage photon survival and finite dwell. |
| |
| No physical measurements are represented by this script. |
| """ |
| from pathlib import Path |
| import json |
| import numpy as np |
| from scipy.linalg import expm |
|
|
| rng=np.random.default_rng(8102028) |
| max_telescope=0.;max_two=0.;max_bound_violation=0. |
| for case in range(250): |
| b=rng.normal(size=3);x=rng.normal(size=3) |
| U0=np.dot(b,b);n0=b/np.sqrt(U0) |
| actual=n0.copy();ideal=n0.copy();rbound=0.;Uprev=U0 |
| for j in range(12): |
| n=b/np.linalg.norm(b);pulse=rng.normal();a=pulse*n |
| b=b+np.cross(x,a);x=x+a |
| U=np.dot(b,b);nn=b/np.sqrt(U);P=np.outer(nn,nn) |
| gamma=rng.uniform(.2,2);dwell=rng.uniform(.01,2) |
| M=expm(-gamma*U*(np.eye(3)-P)*dwell/2) |
| actual=M@actual;ideal=P@ideal |
| eps=np.exp(-gamma*U*dwell/2) |
| rbound+=eps*np.sqrt(U0*(U-Uprev)/(Uprev*U)) |
| Uprev=U |
| theo=U0/U |
| max_telescope=max(max_telescope,abs(np.dot(ideal,ideal)-theo)) |
| max_bound_violation=max(max_bound_violation,abs(np.dot(actual,actual)-theo)-2*rbound) |
| assert abs(np.dot(actual,actual)-theo)<=2*rbound+1e-12 |
| for case in range(100): |
| gamma=rng.uniform(.1,2);t1,t2=rng.uniform(0,3,size=2) |
| n1=np.array([0.,1.,1.])/np.sqrt(2);n2=np.array([0.,1.,0.]) |
| M1=expm(-gamma*2*(np.eye(3)-np.outer(n1,n1))*t1/2) |
| M2=expm(-gamma*4*(np.eye(3)-np.outer(n2,n2))*t2/2) |
| psi=M2@M1@np.array([0.,0.,1.]) |
| e=np.exp(-gamma*t1) |
| pred=((1-e)**2+(1+e)**2*np.exp(-4*gamma*t2))/4 |
| err=abs(np.dot(psi,psi)-pred);max_two=max(max_two,err) |
| assert err<1e-12 |
| result={'seed':8102028,'multistage_histories':250,'stages_per_history':12,'two_stage_checks':100,'max_ideal_telescope_residual':max_telescope,'max_two_stage_residual':max_two,'maximum_error_bound_violation':max_bound_violation,'status':'all checks passed; exact formulas concern the defined loss protocol'} |
| out=Path(__file__).resolve().parent/'results';out.mkdir(exist_ok=True) |
| (out/'quantum_protocol_check.json').write_text(json.dumps(result,indent=2)+'\n') |
| print(json.dumps(result,indent=2)) |
|
|
