Directly Measuring a Multiparticle Quantum Wave Function via Quantum Teleportation

We propose a new method to directly measure general multi-particle quantum wave function, single matrix element in density matrix, by teleportation. The is embedded virtual logical qubit and nondestructively teleported physical for readout. experimentally implement this the wavefunction of photonic mixed state beyond photon using observable first time. Our also provides an exponential advantage over standard tomography measurement complexity fully characterize sparse state.