Unentangled qubit states

thingiverse

Three-dimensional projection of all unentangled states in a two-qubit quantum system. Background: Consider a qubit in a state a|0> + b|1>, where a^2 + b^2 = 1, and another qubit similarly considered. The general state of a two-qubit system is represented by the state Ψ=x|00>+y|01>+z|10>+w|11>. This is a four-dimensional state. Now, a state is unentangled if there exist a, b, c, d such that Ψ=(a|0> + b|1>)⊗(c|0> + d|1>). I wrote a small script to map all points in the four-dimensional space where unentangled states occur. On taking a three-dimensional projection of this space, the shape turns out to be very cool and interesting, so I decided to 3D print it. Code: A MATLAB script to calculate unentangled states is included. If people are not comfortable with MATLAB (and Octave), I could port the script to Python, but generating STL files will be an issue. Let me know if anyone wants me to do it.