Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions

09/18/2020
by   Adam Holmes, et al.
0

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. As a corollary, we show an upper bound on trace-distance approximation accuracy for a rank-2 MPS as Ω(log N/N), implying that these low-rank approximations can scale accurately for large quantum systems.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset