Evidence of Uncollapsed Quantum Amplitudes After Consecutive Measurements

Two of the most common interpretations of quantum mechanics disagree about the fate of quantum amplitudes after measurement, but this difference has not yet led to predictions that could distinguish between the two. In the standard collapse picture (e.g., implied by the Copenhagen interpretation), measurements destroy unrealized amplitudes without leaving a memory. Instead, in the relative-state picture, the measurement device only reflects one of the potential outcomes, even though it is part of an entangled state that continues to harbor the unrealized amplitudes. This is theoretically possible because a measurement device cannot be a reliable diagnostic of the joint quantum state. Here, we experimentally demonstrate---using single-photon measurements of an arbitrary quantum state---that these two pictures make different predictions when three or more consecutive measurements are performed on the same quantum system. An analysis of the joint density matrix of the three measurement devices reveals their coherence and supports the unitary theory of quantum measurement. When decoherence of the devices is explicitly introduced, their joint density matrix is consistent with what a collapse theory would predict. This work sheds light on the dynamics of consecutive quantum measurements and offers new insights into the interpretation of quantum mechanics and the measurement problem.