We present a protocol of remote nondestructive parity measurement (RNPM) on a
pair of quantum memories. The protocol works as a single module for key
operations such as entanglement generation, Bell measurement, parity check
measurement, and an elementary gate for extending one-dimensional cluster
states. The RNPM protocol is achieved by a simple combination of devices such
as lasers, optical fibers, beam splitters, and photon detectors. Despite its
simplicity, a quantum repeater composed of RNPM protocols is shown to have a
communication time that scales sub-exponentially with the channel length, and
it can be further equipped with entanglement distillation. With a reduction in
the internal losses, the RNPM protocol can also be used for generating cluster
states toward measurement-based quantum communication.Comment: 7 pages, 4 figure