# Macroscopic superpositions require tremendous measurement devices

## TL;DR

This paper demonstrates that detecting macroscopic quantum superpositions demands measurement devices exponentially larger than the superposition itself, making such detection practically infeasible at large scales, unless relative degrees of freedom are used.

## Contribution

It provides a fundamental analysis of the measurement limitations for macroscopic superpositions, emphasizing the necessity of enormous measurement devices and proposing a workaround using relative degrees of freedom.

## Key findings

- Detecting macroscopic superpositions requires devices quadratically larger than the superposition.
- For cat-sized superpositions, measurement devices would need to be Earth-sized.
- Using superpositions in relative degrees of freedom can bypass measurement size limitations.

## Abstract

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.