Quantum Tomography - Quantum Process Tomography - Standard Quantum Process Tomography

Standard Quantum Process Tomography

SQPT approaches this using linearly independent inputs, where is the dimension of the Hilbert space . For each of these input states, sending it through the process gives an output state which can be written as a linear combination of the, i.e. . By sending each through many times, quantum state tomography can be used to determine the coefficients experimentally.

Write

,

where is a matrix of coefficients. Then

.

Since form a linearly independent basis,

.

Inverting gives :

.

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