Visualization of superposition of macroscopically distinct states

Abstract

We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more Hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the $XY$ model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes nonnegative (hence, becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.