QuantumSimulator

This is a project to simulate Quantum Cryptography Protocols.

This project is a simplified simulation of qubits and polarizers, so it just work on a bidimensional space, what means that Qubits value will be always between [0,1] and the calculations will not take into account the complex part.

There is a BB84 transference protocol simulation to study the Qubits behaviours.

There are 2 classes and some functions to emulate the Quantum behaviour.

Classes

Qubit()

A Qubit can be created by default with a random state, or with specific data. You can call the class instance Qubit() to create a random Qubit, or introducing a valid state inside de constructor:

example_qubit = Qubit(alpha, beta)

Where:

∣α∣²+∣β∣²=1

Another way to generate a new qubit, is creating it from a regular bit using:

example_qubit = generateQubitFromBit(bit, polarizer)

Where bit must be equal 0 or 1 and polarizer must be an existing polarizer

A useful function is .quantumEntangle(qubit) where a qubit gets associated with another qubit following the paradox of EPR. To use it, 2 or more qubits must be defined:

qubit1 = Qubit()

qubit2 = Qubit()

qubit1.quantumEntangle(qubit2)

or

qubit2.quantumEntangle(qubit1)

To reflect a modification on the entangled qubits, in the one that has been modified, you have to use the function .quantumEntanglement():

qubit.quantumEntanglement()

Polarizer()

A Polarizer can be also created by default as a random polarizer (what means that its angle will be random 0 or 90), and can also be created by its constructor specifying the angle used (remember that this value must be 0 or 90):

example_polarizer = Polarizer()

or

example_polarizer = Polarizer(angle) Where angle must be equal 0 or 90

A useful and neccesary function in class Polarizer() is .polarize(qubit) used to measure a Qubit, e.g.:

qubit = Qubit()

polarizer = Polarizer()

polarizer.polarize(qubit)

Functions

createNQubits(n)

Returns a list of random Qubits given n (integer number > 0)

createNPolarizers(n)

Returns a list of random Polarizers given n (integer number > 0)

createNBits(n)

Returns a list of random Bits [0,1] given n (integer number > 0)

createNQubitsFromBits(bits, polarizers)

Returns a list of Qubits given a list of bits and a list of polarizers

polarizeQubits(qubits, polarizers)

Returns a list of measured qubits given a list of qubits and another of polarizers

duplicateQubit(qubit)

Returns a copy of a bit given a qubit (This function is really useful because after measure a Qubit, it completely changes and lose its original state, so in case that you need have a copy to study results, you must previously create a copy of the qubit)

protocol_bb84_simulation(n, mitm)

Generate a full QKD protocol simulation and returns an object with the attributes:

• a_bits (original bits generated)
• a_polarizers ("Alice" Sender polarizers)
• a_qubits ("Alice" Sender generated Qubits from the original bits)
• b_polarizers ("Bob" Receiver polarizers)
• b_bits ("Alice" Receiver generated Qubits after polarize "Alice" Sender qubits)

protocol_bb84_checker(qkd)

Returns an object which contains the percentage of similarity in qkd protocol (100% if there is not MiTM attack) and an array of bits corresponding with the rest of the available bits (the not checked ones) used as password