Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions

Understand

We present an entanglement analysis of quantum superpositions corresponding to smooth, differentiable, real-valued (SDR) univariate functions.

• SDR functions are shown to be scalably approximated by low-rank matrix product states, for large system discretizations.
• We show that the maximum von-Neumann bipartite entropy of these functions grows logarithmically with the system size.
• This implies that efficient low-rank approximations to these functions exist in a matrix product state (MPS) for large systems.