One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event and there is no way to distinguish between them, interference occurs. It is often assumed that distinguishing information in the preparation, evolution, or measurement of a system is sufficient to destroy interference. However, it is still possible for photons in distinguishable, separable states to interfere due to the indistinguishability of paths corresponding to possible exchange processes. Here we experimentally measure an interference signal that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.
Interference effects are known to have a dependence upon indistinguishability of path. For this reason, it is accepted that different sources of a system cannot interfere if they have distinguishable states. We present an analysis of interference that predicts the allowance of interference between distinguishable states under the strict condition that the preparation has no distinguishability of path that results from the distinguishability of the states of the possible sources. This leads us to a new analysis of the quantum eraser experiment. In Principle Indistinguishability of paths In the history of interference effects in quantum mechanics it is dogmatically accepted in the literature that interference will only occur if there is no distinguishing information of path. For the classic double slit interference effect it is often argued that the knowledge of the system’s passage through one of the slits will lead to the result of non-interference, and only in the preparation where there is no such knowledge will the interference be measured. The reason for which interference effects require that the preparation be one where there is no implied knowledge of path is because any knowledge of path would imply a different state description. Knowledge of path could only be possible if the state of the system was not the superposition of states which allows for both paths. This can be loosely stated by
The complementarity principle of quantum mechanics relates qualitatively the visibility of quantum interference with path indistinguishability. A quantitative study was recently presented [Z. Y. Ou, Phys. Rev. A 74, 063808 (2006)]. Following the formalism of this study, we investigate another scheme for characterizing quantitatively the degree of temporal distinguishability of an
N-photon state, based on constructive quantum interference between an
N-photon and a single-photon state. This scheme is related to a generalized photon bunching effect in the form of a ``bump,'' in contrast to the ``dip'' for the destructive interference effect in the previous study. Generalization to other more complicated cases is straightforward and is much simpler than for the scheme of destructive interference in the previous study. A degree of (in)distinguishability is defined and can be determined experimentally by the measurement of the size of the constructive multiphoton interference effect.