Compatibility of partial_transpose in Qiskit

Question

I need to calculate the negativity of a density matrix; in doing so on Qiskit I stuck on the problem of computing the partial transpose for a problem of compatibility.

Basically I extract my density matrix from a circuit via the Aer simulator in the following way:

circuit.append(SaveDensityMatrix(size, label = f'pho_%.1f' % (label)), [i for i in qubits])

aer_sim = Aer.get_backend('aer_simulator')
t_qc = transpile(circuit, aer_sim)
qobj = assemble(t_qc)
results = aer_sim.run(qobj, shots = 1).result()
counts = results.get_counts()

density_matrix = results.data()['pho_%.1f' % (i)]

the object resulting from this has the type :

qiskit_aer.backends.compatibility.DensityMatrix

How can I use the method partial_transpose described here as qiskit.quantum_info.DensityMatrix.partial_transpose?

https://qiskit.org/documentation/stubs/qiskit.quantum_info.DensityMatrix.partial_transpose.html

Answer 1

For calculating the negativity measure of a density matrix, there is a function for this in the toqito quantum information package here. It accepts a numpy array of the density matrix, so this is compatible with your Qiskit code (you can cast the rho as a numpy array). The source code also contains the implementation for how to compute the partial transpose.

Answer 2

Assume that the subsystems to be transposed are the first two qubits, that is, qubits with indexes 0 and 1. Then you can simply get the partially transposed density matrix as follows:

rho = density_matrix.partial_transpose([0, 1])

# Display rho:
from qiskit.visualization import array_to_latex
array_to_latex(rho)