# Distinguishing two preparations for same pure state leads to signalling

## TL;DR

The paper proves that it is impossible to distinguish different preparation methods for the same pure quantum state, and doing so could enable signaling, highlighting fundamental limits in quantum state preparation and communication.

## Contribution

It introduces a novel impossibility result linking indistinguishability of preparations to no-signaling, extending to bipartite entangled states.

## Key findings

- Distinguishing preparations for a pure state is impossible.
- Distinguishing preparations can lead to signaling.
- Extension to bipartite states shows similar impossibility.

## Abstract

Pure state of a physical system can be prepared in an infinite number of ways. Here, we prove that given a pure state of a quantum system it is impossible to distinguish two preparation procedures. Further, we show that if we can distinguish two preparation procedures for the same pure state then that can lead to signalling. This impossibility result is different than the no measurement without disturbance and the no-cloning. Extending this result for a pure bipartite entangled state entails that the impossibility of distinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing two preparations for a pure bipartite state.