  Quantum entanglement is a key resource, which grants quantum systems the
ability to accomplish tasks that are classically impossible. Here, we apply
Feynman's sum-over-histories formalism to interacting bipartite quantum systems
and introduce entanglement measures for bipartite quantum histories. Based on
the Schmidt decomposition of the matrix comprised of the Feynman propagator
complex coefficients, we prove that bipartite quantum histories are entangled
if and only if the Schmidt rank of this matrix is larger than 1. The proposed
approach highlights the utility of using a separable basis for constructing the
bipartite quantum histories and allows for quantification of their entanglement
from the complete set of experimentally measured sequential weak values. We
then illustrate the non-classical nature of entangled histories with the use of
Hardy's overlapping interferometers and explain why local hidden variable
theories are unable to correctly reproduce all observable quantum outcomes. Our
theoretical results elucidate how the composite tensor product structure of
multipartite quantum systems is naturally extended across time and clarify the
difference between quantum histories viewed as projection operators in the
history Hilbert space or viewed as chain operators and propagators in the
standard Hilbert space.
