How to obtain partial transpose of a 5*5 matrix?

Questions
1

I have a 5*5 matrix as follow

Open in Wolfram Cloud ↗

its a density matrix of a quantum state. suppose the quantum state is as follow:

|w> = |10000>+|01000>+|00100>+|00010>+|00001>

I want to obtain the partial transpose of the matrix (THE PERES PARTIAL TRANSPOSITION MATRIX)

note: there are 5 partial transpose matrix for a 5*5 matrix. I want all of them.
I don’t know if there is a command in Mathematica for it?

2

I’m guessing that the Transpose function will work (look at the documentation for the various alternate forms), but I don’t know exactly what is meant by “the Peres partial transposition matrix”. If you provided some examples of expected output it would be easier to help you.

3

w = Total[
QuantumState /@ {“10000”, “01000”, “00100”, “00010”, “00001”}];
s = QuantumPartialTranspose[w, {2}];
s[“DensityMatrix”] // MatrixForm

QuantumPartialTranspose[state,{j}] with j the qubit with respect to which you do the partial transpose

Note the density matrix of w is a 2^5x2^5 matrix.