"""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))