A Mechanical Implementation and Diagrammatic Calculation of Entangled Basis States

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.