| |
| """Static publication figures for the stated ideal models; no measured data.""" |
| from pathlib import Path |
| import math |
| import numpy as np |
| import matplotlib |
| matplotlib.use('Agg') |
| import matplotlib.pyplot as plt |
| from reproduce import gibbs, entropy_prob, entropy_matched_gibbs, q_work, lhs_work |
|
|
| ROOT = Path(__file__).resolve().parent |
| OUT = ROOT / 'figures' |
| OUT.mkdir(exist_ok=True) |
| plt.rcParams.update({'font.family':'DejaVu Sans','font.size':10,'axes.spines.top':False, |
| 'axes.spines.right':False,'savefig.dpi':190,'axes.titlesize':12}) |
| blue, teal, red, gray = '#294F8C', '#008B8B', '#B7494B', '#788490' |
|
|
| fig, axes = plt.subplots(1,2,figsize=(9.1,3.5),layout='constrained') |
| for ax, energies, beta, name in zip(axes,[np.array([0,1]),np.array([0,1,2])],[1.,1.],['Two levels','Three levels']): |
| tau=gibbs(energies,beta) |
| entropy=entropy_prob(tau) |
| infos=np.linspace(0,entropy,220) |
| work=[] |
| for info in infos: |
| _,cold=entropy_matched_gibbs(energies,max(0,entropy-info)) |
| work.append((tau-cold)@energies) |
| ax.plot(infos,work,color=blue,lw=2.3,label='Exact attainable frontier') |
| ax.plot(infos,infos/beta,color=gray,ls='--',label='Linear I / beta bound') |
| ax.set(xlabel='Receiver information (nats)',ylabel='Average gross work (gap units)',title=name+'; beta = 1') |
| ax.grid(alpha=.18) |
| axes[0].legend(loc='upper left',fontsize=8) |
| fig.suptitle('Finite thermal receivers: information does not supply unlimited work',fontsize=12) |
| fig.savefig(OUT/'frontier.png') |
| plt.close(fig) |
|
|
| r,p,a,Gamma,v,tau=.6,.05,.02,1e4,2e8,5e-6 |
| distance=np.linspace(0,12,350) |
| q=(1-2*p)*np.exp(-Gamma*(distance*1000/v+tau)) |
| theta=np.arctan2(q*np.sqrt(1-r*r),r) |
| work=np.array([q_work(r,float(x)) for x in q]) |
| bound=np.array([lhs_work(r,float(x)) for x in theta]) |
| qmin=max(1/math.sqrt(2),math.sqrt(4*a*(r+a)/(1-r*r))) |
| dmax=v*(math.log((1-2*p)/qmin)/Gamma-tau)/1000 |
| fig,axes=plt.subplots(1,2,figsize=(9.1,3.6),layout='constrained') |
| axes[0].plot(distance,work,color=blue,lw=2.3,label='Quantum gross work') |
| axes[0].plot(distance,bound,color=teal,lw=1.8,label='LHS bound; same controls') |
| axes[0].axhline(a,color=red,ls='--',label='Extraction cost') |
| axes[0].set(xlabel='Distance (km)',ylabel='Energy / epsilon',title='Cost and certification are separate gates') |
| axes[0].legend(fontsize=8) |
| axes[1].plot(distance,q,color=blue,lw=2.3,label='Remaining correlation q') |
| axes[1].axhline(qmin,color=red,ls='--',label='Joint threshold') |
| axes[1].axvline(dmax,color=gray,ls=':',label=f'Distance gate: {dmax:.2f} km') |
| axes[1].fill_between(distance,qmin,q,where=q>qmin,color=teal,alpha=.14) |
| axes[1].set(xlabel='Distance (km)',ylabel='Correlation visibility',title='Strict operating window in a chosen model') |
| axes[1].legend(fontsize=8) |
| for ax in axes: ax.grid(alpha=.18) |
| fig.suptitle('Illustration only: r=.6, p=.05, a=.02, Gamma=10,000 /s, overhead=5 us',fontsize=10) |
| fig.savefig(OUT/'causal_window.png') |
| plt.close(fig) |
|
|
| u=np.linspace(.001,2.3,300) |
| aa=np.cosh(2*u)/2 |
| work=(aa-1/(4*aa))/2 |
| bound=(aa-.5)/2 |
| adv=(1-1/(2*aa))/4 |
| fig,axes=plt.subplots(1,2,figsize=(9.1,3.4),layout='constrained') |
| axes[0].plot(u,work,color=blue,lw=2.2,label='Displacement work') |
| axes[0].plot(u,bound,color=teal,lw=1.8,label='Unsteerable benchmark') |
| axes[0].set(xlabel='Squeezing parameter u',ylabel='Energy / (hbar omega)',title='Gross conditional work grows with energy') |
| axes[1].plot(u,adv,color=blue,lw=2.2,label='Quantum excess') |
| axes[1].axhline(.25,color=red,ls='--',label='Quarter-quantum ceiling') |
| axes[1].set(xlabel='Squeezing parameter u',ylabel='Energy / (hbar omega)',title='Excess remains below a quarter quantum') |
| for ax in axes: ax.legend(fontsize=8); ax.grid(alpha=.18) |
| fig.savefig(OUT/'oscillator_scaling.png') |
| plt.close(fig) |
| print('Created three figures from ideal-model formulas.') |
|
|
