DensityMatrix.partial_transpose does not preserve input dimensions

[diemilio]

Environment

• Qiskit Terra version: to be released in 0.24.0
• Python version: 3.10
• Operating system: MacOS

What is happening?

The partial_transpose should return a density matrix of the same dimensionality as the input DensityMatrix object. When the dimensions are for systems different than qubits, the dimensions are currently not preserved.

How can we reproduce the issue?

For in the following example, the dimensions of the output density matrix ρ2 are (9,) but they should be (3,3).

>>> import numpy as np
>>> from qiskit.quantum_info import Statevector, DensityMatrix
>>> ψ = Statevector(np.array([1,0,0,0,1,0,0,0,1])*1/np.sqrt(3),dims=(3,3))
>>> ρ1 = DensityMatrix(ψ)
>>> ρ1.dims()
(3, 3)
>>> ρ2 = ρ1.partial_transpose([0])
>>> ρ2.dims()
(9,)

What should happen?

It should be an easy fix. The function should return:

return DensityMatrix(rho, dims=self.dims())

instead of just:

return DensityMatrix(rho)

Any suggestions?

No response

[jakelishman]

Thanks, Diego. Would you like to make the PR as well?

[diemilio]

Hi @jakelishman. Will do.

[pranay1990]

Thank you @diemilio for bringing this to our attention