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I wonder how qubits interfere in interferometers when they are not in pure states. Let us take qubits with density matrix = Id/2. There lay at the center of the Bloch sphere.

Half of them can travel unchanged through the left arm. In the other arm they become ##UP_Z##. Then there is interference.

What is the density matrix of the result?

I can write ##\rho = Id/2 = (Id + a.\sigma)/4 + (Id - a.\sigma)/4 ##

which is a mixture of equiprobable pure states whith different "a" vectors. We know that we can add the amplitudes of pure states in interferometers. But is the result independent of the choice of the vector in the decomposition of ##\rho##?

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# Interference of a qubit

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