Quantum Jumps Are More Quantum Than Quantum Diffusion

It was recently argued [Phys. Rev. Lett 108, 220402 (2012)] that the stochastic dynamics of an open quantum system are not inherent to the system, but rather depend on the existence and nature of a distant detector. The proposed experimental tests involved homodyne detection, giving rise to quantum diffusion, and required total efficiencies of well over 50%. Here we prove that for no system is it possible to demonstrate detector-dependence using diffusive-type detection of efficiency less than 50%. However, this no-go theorem does not apply to quantum jumps, and we propose a test involving a qubit, using different jump-type detectors, with a threshold efficiency of only 37%.