  Quantum history states were recently formulated by extending the consistent
histories approach of Griffiths to the entangled superposition of evolution
paths and were then experimented with Greenberger--Horne--Zeilinger states.
Tensor product structure of history-dependent correlations was also recently
exploited as a quantum computing resource in simple linear optical setups
performing multiplane diffraction (MPD) of fermionic and bosonic particles with
remarkable promises. This significantly motivates the definition of quantum
histories of MPD as entanglement resources with the inherent capability of
generating an exponentially increasing number of Feynman paths through
diffraction planes in a scalable manner and experimental low complexity
combining the utilization of coherent light sources and photon-counting
detection. In this article, quantum temporal correlation and interference among
MPD paths are denoted with quantum path entanglement (QPE) and interference
(QPI), respectively, as novel quantum resources. Operator theory modeling of
QPE and counterintuitive properties of QPI are presented by combining
history-based formulations with Feynman's path integral approach. Leggett--Garg
inequality as temporal analog of Bell's inequality is violated for MPD with all
signaling constraints in the ambiguous form recently formulated by Emary. The
proposed theory for MPD-based histories is highly promising for exploiting QPE
and QPI as important resources for quantum computation and communications in
future architectures.
