def measure(qubits, basis):
    bit_stream = ""
    for q, b in zip(qubits, basis):
        if b == 'x':
            q *= complex(0.707, -0.707)
        bit_stream += str(np.random.choice([0,1], p=[round(pow(q.real, 2),1), round(pow(q.imag, 2),1)]))
    return bit_stream

def key_exchange(qubits, basisA, basisB) :
    measured_bits = measure(qubits, basisA)
    bs = ''
    for i in range(LENGTH) :
        if basisA[i] == basisB[i] :
            bs += measured_bits[i]
    return bs