  We give for the first time a diagrammatic calculational tool of quantum
entanglement. We present a pedagogical and simple mechanical implementation of
quantum entanglement or "spooky action at a distance" to give a tangible
realization of this weird quantum mechanical concept alien to classical
physics. When two or more particles are correlated in a certain way, no matter
how far apart they are in space, their states remain correlated. Their
correlation, which is instantaneous, does not seem to involve any communication
which is limited by the speed of light. The same mechanical implementation
demonstrates the fundamental physical limits of any computational processes.
The analytical derivations of calculational entangled basis states are given
and their corresponding diagrammatic representations give an efficient aid in
determining the calculational entangled basis states. A quantum Fourier
transform for the two-state diagrams representing entangled basis states
('renormalized qubits') can also be formulated. Our results seem to advocate
the idea that quantum entanglement generates the extra dimensions of the
gravitational theory, indeed quantum entanglement is related to deep issues in
the unification of general relativity and quantum mechanics. This extra
dimensions of spacetime entanglement are currently being speculated in the
literature.
