qfi_local_noise — Quantum Fisher information for many-body systems exposed to local noise

This code base was used to produce the numerical data in [Faist, Woods, Albert, Renes, Eisert, Preskill, <in preparation>].

Simple example usage:

import numpy as np
import numpy.linalg as npl
import scipy as sp
import scipy.linalg as spl
import qutip

from qfi_local_noise import (
    DitstringSuperpositionKet,
    DitstringActionHamiltonian,
    # QutipReducedOperatorCalculator,
    LocalKrausOperators,
    DitstringSuperpositionKetReducedPsiXiCalculator,
    #
    #compute_Fisher_information,
    #
    #compute_Eve_operators_leqk,
    compute_pinched_DF_lower_bound,
)


# GHZ state (|↑↑↑↑⟩ + |↓↓↓↓⟩)/√2
dsk = DitstringSuperpositionKet(
    4, 2,
    np.array([1, 1])/np.sqrt(2),
    np.array([[0,0,0,0],
              [1,1,1,1,]])
)

# Z+Z+Z+Z Hamiltonian
daH = DitstringActionHamiltonian(
    dsk,
    np.array([4, -4]),
)

# Local Kraus operators -- amplitude damping
p = 0.05
lko = LocalKrausOperators(
    [qutip.Qobj([[np.sqrt(1-p),0],[0,1]]),
     qutip.Qobj([[0,0],[np.sqrt(p),0]])]
)

# full setting --
dskrpxc = DitstringSuperpositionKetReducedPsiXiCalculator(
    dsk, daH, lko
)

# compute the bound --
DFlb, _ = compute_pinched_DF_lower_bound(dskrpxc, lko, k=2)

F_Alice = 4 * daH.variance()

F_Bob_ub = F_Alice - DFlb

print(f"Upper bound on Bob's quantum Fisher information w.r.t. time = {F_Bob_ub:.4g}")

phfaist/qfi_local_noise

qfi_local_noise — Quantum Fisher information for many-body systems exposed to local noise