How Quantum Are Non-Negative Wavefunctions?

TL;DR

This paper investigates the nature of non-negative wavefunctions, their teleportation capabilities, and their relation to sign problems in quantum ground states, providing new insights into quantum state structure and limitations.

Contribution

It offers a complete characterization of teleportation in non-negative wavefunctions when one system is a qubit and introduces a coherent Gibbs state form for certain wavefunctions.

Findings

Non-negative wavefunctions with zero correlation length can be expressed as coherent Gibbs states.

Teleportation capabilities are constrained by the Schmidt coefficients before measurement.

Sign problems in certain Hamiltonians are shown to be intrinsic under specific conditions.

Abstract

We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a "coherent Gibbs state" form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, and on the absence of a "generalized area law"\cite{genarealaw} even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an "intrinsic" sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds\cite{tqo2}.