We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such as generated in previous experiments this is not a stringent restriction, for macroscopic superpositions of the size of a cat the required effort quickly becomes intractable, requiring measurement devices of the size of the Earth. We illustrate our results using macroscopic superposition states of photons, spins, and position. Finally, we also show how this limitation can be circumvented by dealing with superpositions in relative degrees of freedom.
Measurement devices are often treated within quantum mechanics as classical systems, with no intrinsic uncertainty, capable of resolving each degree of freedom with unlimited precision. Whereas this is a very good approximation when the measurement device is way larger than the quantum system of interest, it quickly becomes problematic when considering quantum superpositions of larger and larger size. Using the fundamental symmetries of physical laws only, we show that, in many relevant cases, the size of the measurement device has to be quadratically larger than the size of the macroscopic superposition in question in order for this to hold. Moreover, if this is not the case the superposition in question cannot be distinguished form a mere classical mixture. Within a simplified model, our result shows that in order to observe a cat in a superposition of facing the right way up or upside-down one requires a measurement device whose size is equal to the whole Earth.
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