The no-cloning theorem prevents creation of independent copies of a quantum state.
And if we use CX gates we create entangled copies, which are affected by each others measurement.
So, how does one create copies for quantum state tomography?
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1$\begingroup$ This article might help: arxiv.org/pdf/0912.3823.pdf $\endgroup$– OhadCommented Aug 10, 2022 at 15:24
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Generally, quantum state tomography is used study how well a fixed series of pulses are able to produce a desired quantum state. For example, in this paper, the authors propose and demonstrate pulse sequences to generate GHZ states with 2-7 nuclear spin qubits in diamond. They assess their ability to do this by repeatedly initializing the spin registers, running these sequences, and then measuring the output in different bases to eventually get a description of the full density matrix after their sequences to compare to the state they hoped to create.
