Triples¶

`XY_to_channel_Abc`	The method to compute the A,b,c triple of a channel based on its X, Y, and d parameters in the Wigner representation.
`amplifier_Abc`	The `(A, b, c)` triple of an amplifier.
`attenuator_Abc`	The `(A, b, c)` triple of an attenuator.
`attenuator_kraus_Abc`	The entire family of Kraus operators of the attenuator (loss) channel as a single `(A, b, c)` triple.
`bargmann_eigenstate_Abc`	The Abc triple of a Bargmann eigenstate.
`bargmann_to_quadrature_Abc`	The `(A, b, c)` triple of the multi-mode kernel \(\langle \vec{p}\|\vec{z} \rangle\) between bargmann representation with ABC Ansatz form and quadrature representation with ABC Ansatz.
`bargmann_to_wigner_Abc`	The Abc triple of the Bargmann to Wigner/Husimi transformation.
`beamsplitter_gate_Abc`	The `(A, b, c)` triple of a tensor product of a two-mode beamsplitter gate.
`coherent_state_Abc`	The `(A, b, c)` triple of a pure coherent state.
`displaced_squeezed_vacuum_state_Abc`	The `(A, b, c)` triple of a displaced squeezed vacuum state.
`displacement_gate_Abc`	The `(A, b, c)` triple of a tensor product of a displacement gate.
`displacement_map_s_parametrized_Abc`	The `(A, b, c)` triple of a multi-mode `s`-parametrized displacement map.
`fock_damping_Abc`	The `(A, b, c)` triple of a Fock damper.
`gaussian_random_noise_Abc`	The triple (A, b, c) for the gaussian random noise channel.
`gdm_state_Abc`	The A,b,c parameters of a Gaussian mixed state that is defined by the action of a Guassian on a thermal state.
`gket_state_Abc`	The A,b,c parameters of a Gaussian Ket (Gket) state.
`homodyne_projector_Abc`	The `(A, b, c)` triple of a homodyne projector.
`identity_Abc`	The `(A, b, c)` triple of a tensor product of identity gates.
`quadrature_eigenstates_Abc`	The `(A, b, c)` triple of a quadrature eigenstate.
`rotation_gate_Abc`	The `(A, b, c)` triple of of a tensor product of a rotation gate.
`sauron_state_Abc`	The A,b,c parametrization of Sauron states.
`squeezed_vacuum_state_Abc`	The `(A, b, c)` triple of a squeezed vacuum state.
`squeezing_gate_Abc`	The `(A, b, c)` triple of a squeezing gate.
`thermal_state_Abc`	The `(A, b, c)` triple of a thermal state.
`two_mode_squeezed_vacuum_state_Abc`	The `(A, b, c)` triple of a two mode squeezed vacuum state.
`twomode_squeezing_gate_Abc`	The `(A, b, c)` triple of a tensor product of a two-mode squeezing gate.
`vacuum_state_Abc`	The `(A, b, c)` triple of a tensor product of vacuum states on `n_modes`.

XY_to_channel_Abc¶

mrmustard.physics.triples.XY_to_channel_Abc(X, Y, d=None)[source]¶

The method to compute the A,b,c triple of a channel based on its X, Y, and d parameters in the Wigner representation.

Parameters:

X (RealMatrix) – The X matrix of the channel
Y (RealMatrix) – The Y matrix of the channel
d (ComplexVector | None) – The d (displacement) vector of the channel – if None, we consider it as 0

Returns:

The A,b,c triple of the channel.

Return type:

tuple[ComplexMatrix, ComplexVector, ComplexScalar]

amplifier_Abc¶

mrmustard.physics.triples.amplifier_Abc(gain)[source]¶

The (A, b, c) triple of an amplifier.

Parameters:: gain (float | Sequence[float]) – The values of the gains.
Returns:: The (A, b, c) triple of the amplifier channel.
Raises:: ValueError – If g is smaller than 1.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

attenuator_Abc¶

mrmustard.physics.triples.attenuator_Abc(transmissivity)[source]¶

The (A, b, c) triple of an attenuator.

Parameters:: transmissivity (float | Sequence[float]) – The values of the transmissivities.
Returns:: The (A, b, c) triple of the attenuator channel.
Raises:: ValueError – If eta is larger than 1 or smaller than 0.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

attenuator_kraus_Abc¶

mrmustard.physics.triples.attenuator_kraus_Abc(eta)[source]¶

The entire family of Kraus operators of the attenuator (loss) channel as a single (A, b, c) triple. The last index is the “bond” index which should be summed/integrated over.

Parameters:: eta (float | Sequence[float]) – The value of the transmissivity.
Returns:: The (A, b, c) triple of the kraus operators of the attenuator (loss) channel.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

bargmann_eigenstate_Abc¶

mrmustard.physics.triples.bargmann_eigenstate_Abc(alpha)[source]¶

The Abc triple of a Bargmann eigenstate.

Parameters:: alpha (complex | Sequence[complex]) – The eigenvalue of the Bargmann eigenstate.
Returns:: The (A, b, c) triple of the Bargmann eigenstate.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

bargmann_to_quadrature_Abc¶

mrmustard.physics.triples.bargmann_to_quadrature_Abc(n_modes, phi)[source]¶

The (A, b, c) triple of the multi-mode kernel \(\langle \vec{p}|\vec{z} \rangle\) between bargmann representation with ABC Ansatz form and quadrature representation with ABC Ansatz. The kernel can be considered as a Unitary-like component: the out_ket wires are related to the real variable \(\vec{p}\) in quadrature representation and the in_ket wires are related to the complex variable \(\vec{z}\).

If one wants to transform from quadrature representation to Bargmann representation, the kernel will be the dual of this component, but be careful that the inner product will then have to use the real integral.

Parameters:

n_modes (int) – The number of modes.
phi (float | Sequence[float]) – The quadrature angle. 0 corresponds to the x quadrature, and \(\pi/2\) to the p quadrature.

Returns:

The (A, b, c) triple of the map from bargmann representation with ABC Ansatz to quadrature representation with ABC Ansatz.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

bargmann_to_wigner_Abc¶

mrmustard.physics.triples.bargmann_to_wigner_Abc(s, n_modes)[source]¶

The Abc triple of the Bargmann to Wigner/Husimi transformation.

Parameters:

s (float) – The s parameter of this channel. The case s=-1 corresponds to Husimi, s=0 to Wigner, and s=1 to Glauber P function.
n_modes (int) – The number of modes.

Returns:

The Abc triple of the Bargmann to Wigner/Husimi transformation.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

beamsplitter_gate_Abc¶

mrmustard.physics.triples.beamsplitter_gate_Abc(theta, phi=0)[source]¶

The (A, b, c) triple of a tensor product of a two-mode beamsplitter gate.

Parameters:

theta (float | Sequence[float]) – The transmissivity parameters.
phi (float | Sequence[float]) – The phase parameters.

Returns:

The (A, b, c) triple of the beamsplitter gate.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

coherent_state_Abc¶

mrmustard.physics.triples.coherent_state_Abc(alpha)[source]¶

The (A, b, c) triple of a pure coherent state.

Parameters:: alpha (complex | Sequence[complex]) – The complex displacement.
Returns:: The (A, b, c) triple of the pure coherent state.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

displaced_squeezed_vacuum_state_Abc¶

mrmustard.physics.triples.displaced_squeezed_vacuum_state_Abc(alpha=0, r=0, phi=0)[source]¶

The (A, b, c) triple of a displaced squeezed vacuum state.

Parameters:

alpha (complex | Sequence[complex]) – The complex displacement.
r (float | Sequence[float]) – The squeezing magnitudes.
phi (float | Sequence[float]) – The squeezing angles.

Returns:

The (A, b, c) triple of the squeezed vacuum state.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

displacement_gate_Abc¶

mrmustard.physics.triples.displacement_gate_Abc(alpha)[source]¶

The (A, b, c) triple of a tensor product of a displacement gate.

Parameters:: alpha (complex | Sequence[complex]) – The displacement in the complex phase space.
Returns:: The (A, b, c) triple of the displacement gate.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

displacement_map_s_parametrized_Abc¶

mrmustard.physics.triples.displacement_map_s_parametrized_Abc(s, n_modes)[source]¶

The (A, b, c) triple of a multi-mode s-parametrized displacement map.

Math:

D_s(vec{gamma}^*, vec{gamma}) = e^{frac{s}{2}|vec{gamma}|^2} D(vec{gamma}^*, vec{gamma}) = e^{frac{s}{2}|vec{gamma}|^2} e^{frac{1}{2}|vec{z}|^2} e^{vec{z}^*vec{gamma} - vec{z} vec{gamma}^*}.

Parameters:

s (float | Sequence[float])
n_modes (int)

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

The indices of the final triple correspond to the variables \((\gamma_1^*, \gamma_2^*, ..., z_1, z_2, ..., \gamma_1, \gamma_2, ..., z_1^*, z_2^*, ...)\) of the Bargmann function of the s-parametrized displacement map, and correspond to out_bra, in_bra, out_ket, in_ket wires.

Parameters:

s (float | Sequence[float]) – The phase space parameter
n_modes (int) – the number of modes for this map.

Returns:

The (A, b, c) triple of the multi-mode s-parametrized dispalcement map \(D_s(\gamma)\).

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

fock_damping_Abc¶

mrmustard.physics.triples.fock_damping_Abc(damping)[source]¶

The (A, b, c) triple of a Fock damper.

Parameters:: damping (float | Sequence[float]) – The damping parameter.
Returns:: The (A, b, c) triple of the Fock damping operator.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

gaussian_random_noise_Abc¶

mrmustard.physics.triples.gaussian_random_noise_Abc(Y)[source]¶

The triple (A, b, c) for the gaussian random noise channel.

Parameters:: Y (RealMatrix) – the Y matrix of the Gaussian random noise channel.
Returns:: The (A, b, c) triple of the Gaussian random noise channel.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

gdm_state_Abc¶

mrmustard.physics.triples.gdm_state_Abc(beta, symplectic)[source]¶

The A,b,c parameters of a Gaussian mixed state that is defined by the action of a Guassian on a thermal state.

Parameters:

beta (ComplexVector) – the list of betas corresponding to the temperatures of the initial thermal state
symplectic (RealMatrix) – the symplectic matrix of the Gaussian

Returns:

The (A,b,c) triple of the resulting Gaussian DM state.

gket_state_Abc¶

mrmustard.physics.triples.gket_state_Abc(symplectic)[source]¶

The A,b,c parameters of a Gaussian Ket (Gket) state. This is simply a Gaussian acted on the vacuum.

Parameters:: symplectic (RealMatrix) – the symplectic representation of the Gaussian
Returns:: The (A,b,c) triple of the Gket state.

homodyne_projector_Abc¶

mrmustard.physics.triples.homodyne_projector_Abc(bs_theta, bs_phi, homodyne_angle, homodyne_outcome, hbar=None)[source]¶

The (A, b, c) triple of a homodyne projector.

Parameters:

bs_theta (float | RealMatrix) – The values of the beamsplitter angles.
bs_phi (float | RealMatrix) – The values of the beamsplitter phases.
homodyne_angle (float | RealMatrix) – The values of the homodyne angles.
homodyne_outcome (float | RealMatrix) – The values of the homodyne outcomes.
hbar (float | None) – The value of hbar to use. If None, settings.HBAR is used.

Returns:

The (A, b, c) triple of the homodyne projector.

Return type:

tuple[ComplexMatrix, ComplexVector, ComplexScalar]

identity_Abc¶

mrmustard.physics.triples.identity_Abc(n_modes)[source]¶

The (A, b, c) triple of a tensor product of identity gates.

Parameters:: n_modes (int) – The number of modes.
Returns:: The (A, b, c) triple of the identities.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

quadrature_eigenstates_Abc¶

mrmustard.physics.triples.quadrature_eigenstates_Abc(x, phi)[source]¶

The (A, b, c) triple of a quadrature eigenstate.

Parameters:

x (float | Sequence[float]) – The quadrature eigenvalues.
phi (float | Sequence[float]) – The quadrature angles.

Returns:

The (A, b, c) triple of the quadrature eigenstate.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

rotation_gate_Abc¶

mrmustard.physics.triples.rotation_gate_Abc(theta)[source]¶

The (A, b, c) triple of of a tensor product of a rotation gate.

Parameters:: theta (float | Sequence[float]) – The rotation angles.
Returns:: The (A, b, c) triple of the rotation gate.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

sauron_state_Abc¶

mrmustard.physics.triples.sauron_state_Abc(n, epsilon)[source]¶

The A,b,c parametrization of Sauron states. These are Fock states written as a linear superposition of a ring of coherent states.

Parameters:

n (int) – The number of photons.
epsilon (float) – The size of the ring. The approximation is exact in the limit for epsilon that goes to zero.

Returns:

The (A, b, c) triple of the sauron state.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

squeezed_vacuum_state_Abc¶

mrmustard.physics.triples.squeezed_vacuum_state_Abc(r, phi=0.0)[source]¶

The (A, b, c) triple of a squeezed vacuum state.

Parameters:

r (float | Sequence[float]) – The squeezing magnitudes.
phi (float | Sequence[float]) – The squeezing angles.

Returns:

The (A, b, c) triple of a squeezed vacuum state.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

squeezing_gate_Abc¶

mrmustard.physics.triples.squeezing_gate_Abc(r, phi=0)[source]¶

The (A, b, c) triple of a squeezing gate.

Parameters:

r (float | Sequence[float]) – The squeezing magnitudes.
phi (float | Sequence[float]) – The squeezing angles.

Returns:

The (A, b, c) triple of the squeezing gate.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

thermal_state_Abc¶

mrmustard.physics.triples.thermal_state_Abc(nbar)[source]¶

The (A, b, c) triple of a thermal state.

Parameters:: nbar (float | Sequence[float]) – The average number of photons.
Returns:: The (A, b, c) triple of the thermal state.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

two_mode_squeezed_vacuum_state_Abc¶

mrmustard.physics.triples.two_mode_squeezed_vacuum_state_Abc(r, phi=0)[source]¶

The (A, b, c) triple of a two mode squeezed vacuum state.

Parameters:

r (float | Sequence[float]) – The squeezing magnitudes.
phi (float | Sequence[float]) – The squeezing angles.

Returns:

The (A, b, c) triple of the squeezed vacuum state.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

twomode_squeezing_gate_Abc¶

mrmustard.physics.triples.twomode_squeezing_gate_Abc(r, phi=0)[source]¶

The (A, b, c) triple of a tensor product of a two-mode squeezing gate.

Parameters:

r (float | Sequence[float]) – The squeezing magnitudes.
phi (float | Sequence[float]) – The squeezing phase.

Returns:

The (A, b, c) triple of the two mode squeezing gate.

Return type:

tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

vacuum_state_Abc¶

mrmustard.physics.triples.vacuum_state_Abc(n_modes)[source]¶

The (A, b, c) triple of a tensor product of vacuum states on n_modes.

Parameters:: n_modes (int) – The number of modes.
Returns:: The (A, b, c) triple of the vacuum states.
Return type:: tuple[mrmustard.utils.typing.ComplexMatrix, mrmustard.utils.typing.ComplexVector, mrmustard.utils.typing.ComplexScalar]

code/physics/triples

Download Python script

Download Notebook

View on GitHub

Triples¶

XY_to_channel_Abc¶

amplifier_Abc¶

attenuator_Abc¶

attenuator_kraus_Abc¶

bargmann_eigenstate_Abc¶

bargmann_to_quadrature_Abc¶

bargmann_to_wigner_Abc¶

beamsplitter_gate_Abc¶

coherent_state_Abc¶

displaced_squeezed_vacuum_state_Abc¶

displacement_gate_Abc¶

displacement_map_s_parametrized_Abc¶

fock_damping_Abc¶

gaussian_random_noise_Abc¶

gdm_state_Abc¶

gket_state_Abc¶

homodyne_projector_Abc¶

identity_Abc¶

quadrature_eigenstates_Abc¶

rotation_gate_Abc¶

sauron_state_Abc¶

squeezed_vacuum_state_Abc¶

squeezing_gate_Abc¶

thermal_state_Abc¶

two_mode_squeezed_vacuum_state_Abc¶

twomode_squeezing_gate_Abc¶

vacuum_state_Abc¶

Contents