analysis

# QuTiP 分析与测量 ## 期望值 ### 基本期望值 python from qutip import * import numpy as np # 单个算符 psi = coherent(N, 2) n_avg = expect(num(N), psi) # 多个算符 ops = [num(N), destroy(N), create(N)] results = expect(ops, psi) # 返回列表 ### 密度矩阵的期望值 python # 适用于纯态和密度矩阵 rho = thermal_dm(N, 2) n_avg = expect(num(N), rho) ### 方差 python # 计算可观测量方差 var_n = variance(num(N), psi) # 手动计算 var_n = expect(num(N)**2, psi) - expect(num(N), psi)**2 ### 含时期望值 python # 在时间演化期间 result = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)]) n_t = result.expect[0] # 每个时刻 ⟨n⟩ 的数组 ## 熵度量 ### Von Neumann 熵 python from qutip import entropy_vn # 密度矩阵熵 rho = thermal_dm(N, 2) S = entropy_vn(rho) # 返回 S = -Tr(ρ log₂ ρ) ### 线性熵 python from qutip import entropy_linear # 线性熵 S_L = 1 - Tr(ρ²) S_L = entropy_linear(rho) ### 纠缠熵 python # 针对二分系统 psi = bell_state('00') rho = psi.proj() # 对子系统 B 求偏迹以获得约化密度矩阵 rho_A = ptrace(rho, 0) # 纠缠熵 S_ent = entropy_vn(rho_A) ### 互信息 python from qutip import entropy_mutual # 针对二分态 ρ_AB I = entropy_mutual(rho, [0, 1]) # I(A:B) = S(A) + S(B) - S(AB) ### 条件熵 python from qutip import entropy_conditional # S(A|B) = S(AB) - S(B) S_cond = entropy_conditional(rho, 0) # 给定子系统 1 的子系统 0 的熵 ## 保真度与距离度量 ### 态保真度 python from qutip import fidelity # 两个态之间的保真度 psi1 = coherent(N, 2) psi2 = coherent(N, 2.1) F = fidelity(psi1, psi2) # 返回 [0, 1] 之间的值 ### 过程保真度 python from qutip import process_fidelity # 两个过程（超算符）之间的保真度 U_ideal = (-1j * H * t).expm() U_actual = mesolve(H, basis(N, 0), [0, t], c_ops).states[-1] F_proc = process_fidelity(U_ideal, U_actual) ### 迹距离 python from qutip import tracedist # 迹距离 D = (1/2) Tr|ρ₁ - ρ₂| rho1 = coherent_dm(N, 2) rho2 = thermal_dm(N, 2) D = tracedist(rho1, rho2) # 返回 [0, 1] 之间的值 ### Hilbert-Schmidt 距离 python from qutip import hilbert_dist