Computational Progress towards Maximum Distinguishability of Bell States by Linear Evolution and Local Measurement

Many quantum information protocols rely on the ability to distinguish between entangled quantum states known as Bell states. However, theoretical limits exist on the maximal distinguishability of these entangled states using linear evolution and local measurement (LELM) devices. In the case of two particles entangled in multiple qubit variables, the maximum number of distinguishable Bell states is known. However, in the more general case of two particles entangled in multiple qudit variables, only an upper bound is known under additional assumptions. I have written software in Matlab andMathematica to explore computationally the maximum number of Bell states that can be distinguished in the case of two particles entangled in a qutrit variable, and the case of two particles entangled in both a qutrit and qubit variable. Using code I have written in Mathematica, I have reduced the number of cases to check for sets of 9 qubit⊗qutrit Bell states from 94, 143, 280 to 10, 365. Further work needs to be done to computationally check these cases for distinguishability by an LELM apparatus.