How quantum are non-negative wave functions? (Q2786615)

The phenomenon of interference relies on a cancellation between amplitudes of opposite sign. States, for which all amplitudes are non-negative in the computational basis from the perspective of quantum information theory, are investigated. It seems that the difficulty of estimating the ground state energy for Hamiltonians with no sign-problem becomes smaller. For such Hamiltonians it is quite possible that by some local quantum circuit, one might be able to bring the Hamiltonian to a form with no sign problem, simplifying the simulation. It is shown that a one-dimensional non-negative wavefunction with zero correlation length can be written in form of a ``coherent Gibbs state''. Possible teleportation of such wavefunctions are described and some results are presented for general wavefunction teleportation.