A no-go result on the purification of quantum states

TL;DR

This paper proves a fundamental no-go theorem showing that it is impossible to purify quantum states without losing some initial information, impacting quantum information processing and state management.

Contribution

The paper establishes a no-go result for quantum state purification, demonstrating the inherent limitations in transferring mixedness without information loss.

Findings

Purification transfer cannot be perfect; some information loss is unavoidable.

The minimal loss is determined by the initial state's properties.

Implications for quantum information protocols and correlations.

Abstract

The information encoded in a quantum system is generally spoiled by the influences of its environment, leading to a transition from pure to mixed states. Reducing the mixedness of a state is a fundamental step in the quest for a feasible implementation of quantum technologies. Here we show that it is impossible to "transfer" part of such mixedness to a "trash" system without losing some of the initial information. Such loss is lower-bounded by a value determined by the properties of the initial state to purify. We discuss this interesting phenomenon and its consequences for general quantum information theory, linking it to the information theoretical primitive embodied by the quantum state-merging protocol and to the behaviour of general quantum correlations.