Nonexistence of a universal quantum machine to examine the precision of unknown quantum states

TL;DR

This paper proves a new fundamental limitation in quantum mechanics, showing that it is impossible to perfectly or unambiguously compare the closeness of multiple unknown quantum states with any non-trivial threshold, highlighting a collective impossibility.

Contribution

It introduces a novel collective impossibility theorem for comparing multiple unknown quantum states, expanding the understanding of fundamental limitations in quantum information processing.

Findings

Establishes a new impossibility result for quantum state comparison

Shows limitations on non-local quantum operations involving multiple states

Provides insights into the fundamental nature of quantum mechanics

Abstract

In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This impossibility is distinct from the existing impossibilities in that it is a "collective" impossibility on multiple quantum states while most other "no-go" theorems concern with only one single state each time, i.e., it is an impossibility on a non-local quantum operation. This novel impossibility may provide a new insight into the nature of quantum mechanics and it implies more limitations on quantum information tasks than the existing "no-go" theorems.