Quantum Entropy

To run each python script, run: python file_name.py on the command line.

Classical Shannon functions

shannon.py

• Contains Shannon definitions and its inequalities.
• Has function that generates random probability distributions.
• Contains definitions of all Shannon and non-Shannon inequalities.

separate_probs.py Separates joint probability distributions into marginal distributions (and smaller joint distributions). Works up to 4 random variables.

Von Neumann functions

entropy.py Contains Von Neumann definitions and quantum inequalities.

entangle.py

• Contains definitions of Bell states and GHZ states
• Has functions that check for entanglement in quantum states.

evolution.py

• Functions of unitary evolution and unitary time evolution.
• Functions of quantum noisy channels: bit-flip, phase-flip, bit-phase-flip and depolarising channels.
• Has functions that check unitality, partial trace preservations and change of entropy of a quantum state when it passes through the quantum channels.

non_shannon_quantum.py Contains definitions of the non-Shannon inequalities.

partial_trace.py Contains function that computes partial trace for 2,3,4 and 5 qubit and qutrit systems.

generate_random_quantum.py

• Has functions that generate unitary, hermitian and density matrices (pure and mixed states).
• Different methods to generate mixed states.

Testing

run_classical_tests.py Runs Shannon and non-Shannon inequalities tests once. Uses pytest, so to run script, run pytest --verbose run_classical_tests.py on the command line.

quantum_tests.py Has functions to used for testing all the Von Neumann and non-Shannon inequalities.

extensive_testing.py Uses functions in quantum_tests.py to run tests all Von Neumann and non-Shannon inequalities. Running script runs goes through all inequalities and prints result in the command line. Uses similar syntax to pytest.

print_tests.py Runs tests below and prints to command line. Tests:

• Number of entangled states in mixed states generated
• All non-Shannon inequalities for the different generate functions, 100,000 times run.
• Non-Shannon inequality fir GHZ states.

Other

graphs.py

• Plots probability against average entropy difference (for 1000 states) for each quantum channel
• Plots avg. difference with method of generation for Zhang-Yeung inequality

utils.py Useful additional functions