# Signaling versus distinguishing different superpositions of same pure quantum state

## TL;DR

This paper explores how distinguishing different superpositions or ensembles of quantum states, which result in the same state, can lead to signaling, highlighting fundamental limits in quantum state preparation and measurement.

## Contribution

It demonstrates that distinguishing superpositions of pure states with the same resulting state can imply signaling, regardless of the measurement's determinism or probabilistic nature.

## Key findings

- Distinguishing superpositions can lead to signaling.
- Signaling occurs regardless of measurement determinism.
- Implications for quantum state preparation and measurement protocols.

## Abstract

Different ensembles of quantum states can have the same average nonpure state. Distinguishing between such constructions, via different mixing procedures of the same nonpure quantum state, is known to entail signaling. In parallel, different superpositions of pure quantum states can lead to the same pure state. We show that the possibility of distinguishing between such preparations, via different interferometric setups leading to the same pure quantum state, also implies signaling. The implication holds irrespective of whether the distinguishing procedure is deterministic or probabilistic.