A general pure 1-qubit state can be written as a ZX-diagram like this:
Correspondingly, for a general pure 2-qubit state:
How can a general pure 3-qubit state be written as a ZX-diagram?
Two things to consider:
Use only 14 parametrized spiders as an $n$-qubit state can be parametrized by $2^{n+1} - 2$ real parameters (ignoring the global phase, of course).
If possible, provide a representation that is symmetric in permutations of the qubits
My approach so far
For the 2-qubit case, the approach
- Singular Value decomposition on 1-to-1 qubit map
- Wire bending a.k.a. Choi–Jamiołkowski isomorphism
proved to be ideal.
The corresponding approach for the 3-qubit case gave me (ingoing wire not bent yet):
However, there are 16 instead of 14 parameters and this looks far from symmetric. I am stuck at this point. Any help?
