Nothing could be simpler
If we have a quantum system that has n_sites and n_levels, itertools.product provides a convenient way to enumerate the basis_states:
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import itertools n_sites=2 # 2 lattice sites n_levels=3 # 3 energy levels per lattice site basis_states = list(itertools.product(range(n_levels), repeat=n_sites)) |
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In [19]: list(itertools.product(range(n_levels), repeat=n_sites)) Out[19]: [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)] |
Here we discuss the meaning of a partial trace and show how to perform this operation. We provide explicit examples and a python implementation that is intended to be instructive, but is not (at all) optimized for efficiency.
We first consider the canonical example of two coupled two-level systems, sites a and b.
The basis states of this system are 
, 
, 
, 
, for 
and the density matrix is:
The reduced density matrix for one of these sites can be computed by the partial trace. For site a the reduced density matrix is:
$
\rho_{a} = \begin{bmatrix}
\rho_{00, 00} + \rho_{01,01} & \rho{10,10} + \rho{11
Here is something that you might want to do in python:
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def my_function(): for i,val in enumerate(data): print '{},{}'.format(i,val) |