Calculations on Gaussian objects

This module contains functions for performing calculations on objects in the Gaussian representations.

Functions

CPTP(cov, means, X, Y, d, state_modes, ...)	Returns the cov matrix and means vector of a state after undergoing a CPTP channel.
XYd_dual(X, Y, d)	Returns the dual channel (X, Y, d).
amp_XYd(gain, nbar)	Returns the X, Y matrices and the d vector for the noisy amplifier channel.
beam_splitter_symplectic(theta, phi)	Symplectic matrix of a Beam-splitter gate.
compose_channels_XYd(X1, Y1, d1, X2, Y2, d2)	Returns the combined X, Y, and d for two CPTP channels.
controlled_X(g)	Controlled NOT gate of two-gaussian modes.
controlled_Z(g)	Controlled PHASE gate of two-gaussian modes.
displacement(x, y)	Returns the displacement vector for a displacement by \(alpha = x + iy\).
fidelity(mu1, cov1, mu2, cov2)	Returns the fidelity of two gaussian states.
gaussian_cov(symplectic[, eigenvalues])	Returns the covariance matrix of a Gaussian state.
general_dyne(cov, means, proj_cov[, ...])	Returns the results of a general-dyne measurement.
join_covs(covs)	Joins the given covariance matrices into a single covariance matrix.
join_means(means)	Joins the given means vectors into a single means vector.
log_negativity(cov)	Returns the log_negativity of a Gaussian state.
loss_XYd(transmissivity, nbar)	Returns the X, Y matrices and the d vector for the noisy loss (attenuator) channel.
mz_symplectic(phi_a, phi_b[, internal])	Symplectic matrix of a Mach-Zehnder gate.
noise_Y(noise)	Returns the X, Y matrices and the d vector for the additive noise channel (Y = noise * (\hbar / 2) * I)
number_cov(cov, means)	Returns the photon number covariance matrix given a Wigner covariance matrix and a means vector.
number_means(cov, means)	Returns the photon number means vector given a Wigner covariance matrix and a means vector.
partition_cov(cov, Amodes)	Partitions the covariance matrix into the A and B subsystems and the AB coherence block.
partition_means(means, Amodes)	Partitions the means vector into the A and B subsystems.
physical_partial_transpose(cov, modes)	Returns the covariance matrix that corresponds to applying the partial transposition on the density matrix of a given set of modes.
purity(cov)	Returns the purity of the state with the given covariance matrix.
quadratic_phase(s)	Quadratic phase single mode gate.
rotation_symplectic(angle)	Symplectic matrix of a rotation gate.
squeezed_vacuum_cov(r, phi)	Returns the real covariance matrix and real means vector of a squeezed vacuum state.
squeezing_symplectic(r, phi)	Symplectic matrix of a squeezing gate.
symplectic_eigenvals(cov)	Returns the sympletic eigenspectrum of a covariance matrix.
symplectic_inverse(S)	Returns the inverse of a symplectic matrix.
thermal_cov(nbar)	Returns the real covariance matrix and real means vector of a thermal state.
trace(cov, means, Bmodes)	Returns the covariances and means after discarding the specified modes.
two_mode_squeezed_vacuum_cov(r, phi)	Returns the real covariance matrix and real means vector of a two-mode squeezed vacuum state.
two_mode_squeezing_symplectic(r, phi)	Symplectic matrix of a two-mode squeezing gate.
vacuum_cov(num_modes)	Returns the real covariance matrix of the vacuum state.
vacuum_means(num_modes)	Returns the real covariance matrix and real means vector of the vacuum state.
von_neumann_entropy(cov)	Returns the Von Neumann entropy.

Variables

Matrix	ndarray(shape, dtype=float, buffer=None, offset=0,
Optional	Optional[X] is equivalent to Union[X, None].
Scalar	alias of Union[R, C, Z, N]
Sequence	A generic version of collections.abc.Sequence.
Tuple	Deprecated alias to builtins.tuple.
Union	Union type; Union[X, Y] means either X or Y.
Vector	ndarray(shape, dtype=float, buffer=None, offset=0,
math	A class to manage the different backends supported by Mr Mustard.
settings	A class containing various settings that are used by Mr Mustard throughout a session.

code/physics/utils/gaussian_calculations

 

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