Quasi-Probabilities (quanguru.QuantumToolbox.quasiProbabilities)#
Contains functions to calculate quasi-probability distributions (adapted from qutip).
Functions#
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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. |
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Q-function of a given state vector or density matrix at points vec + i * vec |
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Calculates the Q-function for a pure state. |
Function Name |
Docstrings |
Examples |
Unit Tests |
Tutorials |
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Wigner |
✅ |
❌ |
❌ |
❌ |
HusimiQ |
✅ |
❌ |
❌ |
❌ |
_qfuncPure |
✅ |
❌ |
❌ |
❌ |
- Wigner(rho: spmatrix | ndarray, vec: ndarray | list, g: float = np.float64(1.4142135623730951)) 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: spmatrix | ndarray, vec: ndarray | list, g: float = np.float64(1.4142135623730951)) 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: spmatrix | ndarray, alphaMat: ndarray) 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