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Quantum Theory of Information for Python; pronounced "cutie pie". A package for performing calculations with quantum states and channels.

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QuTIpy

Quantum Theory of Information for Python pronounced "cutie pie". A package for performing calculations with quantum states and channels. It is comparable to the QETLAB package for MATLAB / Octave.

Requirements

The code requires Python 3, and apart from the standard numpy and scipy packages, it requires cvxpy if you want to run SDPs (e.g., for the diamond norm). It requires sympy for symbolic computations.

Installation

A simple pip install from the github repository will install the package in your system.

Quantum channels

The package comes with functions for commonly-used channels such as the depolarizing channel and the amplitude damping channel. One can also create an arbitrary Qubit Pauli channel as follows:

>>> Pauli_channel(px, py, pz)

where px, py, pz are the probabilities of the individual Pauli Matrices. The output of this function contains the Kraus operators of the channel as well as an isometric extension of the channel.

In order to apply a quantum channel to a quantum state rho, we can use the function apply_channel. First, let us define the following amplitude damping channel :

>>> K = amplitude_damping_channel(0.2)

The variable K contains the Kraus operators of the channel. Then,

>>> rho_out = apply_channel(K, rho)

gives the state at the output of the channel when the input state is rho.

Other functions include:

• Getting the Choi and natural representation of a channel from its Kraus representation
• Converting between the Choi, natural, and Kraus representations of a channel

Summary of other features

The package also contains functions for:

• Trace norm
• Fidelity and entanglement fidelity
• Random unitaries
• Clifford unitaries
• Generators of the su(d) Lie algebra(for d=2, this is the set of Pauli matrices)
• Discrete Weyl operators
• von Neumann entropy and relative entropy
• Renyi entropies
• Coherent information and Holevo information for states and channels

Acknowledgements

Thanks to Mark Wilde for suggesting the name for the package.

Quantum Theory of Information for Python; pronounced "cutie pie". A package for performing calculations with quantum states and channels.

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