Loss of entanglement in quantum mechanics due to the use of realistic measuring rods

We show that the use of real measuring rods in quantum mechanics places a fundamental gravitational limit to the level of entanglement that one can ultimately achieve in quantum systems. The result can be seen as a direct consequence of the fundamental gravitational limitations in the measurements of length and time in realistic physical systems. The effect may have implications for long distance teleportation and the measurement problem in quantum mechanics.