Quasi-Probabilities (quanguru.QuantumToolbox.quasiProbabilities)#

Contains functions to calculate quasi-probability distributions (adapted from qutip).

Functions#

Wigner(rho, vec[, g])

An iterative method to evaluate the Wigner functions for the states |m \rangle \langle n| and use them in a weighted sum to calculate Wigner function of any arbitrary state.

HusimiQ(state, vec[, g])

Q-function of a given state vector or density matrix at points vec + i * vec

_qfuncPure(psi, alphaMat)

Calculates the Q-function for a pure state.

Function Name

Docstrings

Examples

Unit Tests

Tutorials

Wigner

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HusimiQ

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_qfuncPure

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Wigner(rho: Union[scipy.sparse._base.spmatrix, numpy.ndarray], vec: Union[numpy.ndarray, list], g: float = 1.4142135623730951) → numpy.ndarray[source]#

An iterative method to evaluate the Wigner functions for the states |m \rangle \langle n| and use them in a weighted sum to calculate Wigner function of any arbitrary state.

The Wigner function is calculated as W = \sum_{mn} \rho_{mn} W_{mn} where W_{mn} is the Wigner function for the density matrix |m \rangle \langle n|.

In this implementation, for each row m, Wlist contains the Wigner functions Wlist = [0, ..., W_{mm} , ..., W_{mN} ]. As soon as one W_{mn} Wigner function is calculated, the corresponding contribution is added to the total Wigner function, weighted by the corresponding element in the density matrix \\rho_{mn}.

Parameters

  • rho (Matrix) – Density matrix or ket state.

  • vec (ndOrList) – An array (or list) to define the (coarse-grained) Phase space. This creates a square grid of the phase space.

  • g (float) – Scaling factor for a = 0.5 * g * (x + iy), default g = sqrt(2).

Returns

Values representing the Wigner-function calculated over the specified range [vec, vec].

Return type

ndarray

Examples

# TODO

HusimiQ(state: Union[scipy.sparse._base.spmatrix, numpy.ndarray], vec: Union[numpy.ndarray, list], g: float = 1.4142135623730951) → numpy.ndarray[source]#

Q-function of a given state vector or density matrix at points vec + i * vec

Parameters

  • rho (Matrix) – density matrix or ket state

  • vec (ndOrList) – An array (or list) to define the (coarse-grained) Phase space. This creates a square grid of the phase space.

  • g (float) – Scaling factor for a = 0.5 * g * (x + iy), default g = sqrt(2).

Returns

Values representing the Q-function calculated over the specified range [vec, vec].

Return type

array

Examples

# TODO

_qfuncPure(psi: Union[scipy.sparse._base.spmatrix, numpy.ndarray], alphaMat: numpy.ndarray) → numpy.ndarray[source]#

Calculates the Q-function for a pure state.

Parameters

  • psi (Matrix) – a pure state

  • vec (ndOrList) – an array (or list) to define the (coarse-grained) Phase space. This creates a square grid of the phase space.

  • g (float) – Scaling factor for a = 0.5 * g * (x + iy), default g = sqrt(2).

Returns

Values representing the Q-function calculated over the specified range [vec, vec].

Return type

array

Examples

# TODO

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