Impossibility of creating a superposition of unknown quantum states

TL;DR

This paper explores the fundamental limits of quantum superposition, demonstrating that creating a superposition of unknown states violates core principles and leads to impossible tasks in quantum and no-signaling theories.

Contribution

It shows that a protocol for superposing unknown quantum states would contradict established no-go theorems, revealing fundamental constraints in quantum theory.

Findings

Superposing unknown states implies violation of no-go theorems.

Such a protocol enables forbidden state discrimination and cloning.

Results highlight fundamental limitations in quantum superposition.

Abstract

The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability. The implications of this result, however, remain poorly understood so far. In this paper we show that the existence of a protocol that superposes two unknown pure states with nonzero probability (allowed to vary over input states) leads to violation of other no-go theorems. In particular, such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden not only in quantum theory but in no-signaling theories as well.