  Quantum entanglement emerges naturally in interacting quantum systems and
plays a central role in quantum information processing. Remarkably, it is
possible to generate entanglement even in the absence of direct interactions:
provided that which path information is erased, weak spin-state dependent light
scattering can be used to project two distant spins onto a maximally entangled
state upon detection of a single photon. Even though this approach is
necessarily probabilistic, successful generation of entanglement is heralded by
the photon detection event. Here, we demonstrate heralded quantum entanglement
of two quantum dot heavy-hole spins separated by 5 meters using single-photon
interference. Thanks to the long coherence time of hole spins and the efficient
spin-photon interface provided by self-assembled quantum dots embedded in leaky
microcavity structures, we generate 2300 entangled spin pairs per second, which
represents an improvement approaching three orders of magnitude as compared to
prior experiments. Delayed two-photon interference scheme we developed allows
for efficient verification of quantum correlations. Our results lay the
groundwork for the realization of quantum networks in semiconductor
nanostructures. Combined with schemes for transferring quantum information to a
long-lived memory qubit, fast entanglement generation we demonstrate could also
impact quantum repeater architectures.
