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I have a state vector of a 16 qubit system. I want to get the wave function (in the form of a state vector) for half and quarter of this system. When I try to make a partial_trace to obtain the density matrix of a subsystem and represent this matrix as a state vector (by DensityMatrix.to_statevector()), I get the error "QiskitError: 'Density matrix is not a pure state'". Is it possible to obtain the wave function of a subsystem given the state vector of the system?

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  • $\begingroup$ Given a mixed state, there is no unique wave function that can be ascribed to it; the best you can do is a convex combination of wave functions $\endgroup$ Sep 16, 2023 at 16:03

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If you diagonalize the density matrix, the resulting eigenvectors are pure states of your mixture which gives the density matrix

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