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We consider wavefunctions which are non-negative in some tensor productbasis. We study what possible teleportation can occur in such wavefunctions,giving a complete answer in some cases (when one system is a qubit) and partialanswers elsewhere. We use this to show that a one-dimensional wavefunctionwhich is non-negative and has zero correlation length can be written in a"coherent Gibbs state" form, as explained later. We conjecture that such holdsin higher dimensions. Additionally, some results are provided on possibleteleportation in general wavefunctions, explaining how Schmidt coefficientsbefore measurement limit the possible Schmidt coefficients after measurement,and on the absence of a "generalized area law"\cite{genarealaw} even forHamiltonians with no sign problem.  One of the motivations for this work is an attempt to prove a conjectureabout ground state wavefunctions which have an "intrinsic" sign problem thatcannot be removed by any quantum circuit. We show a weaker version of this,showing that the sign problem is intrinsic for commuting Hamiltonians in thesame phase as the double semion model under the technical assumption that TQO-2holds\cite{tqo2}.

How Quantum Are Non-Negative Wavefunctions?