No-go theorems for deterministic purification and probabilistic enhancement of coherence

TL;DR

This paper establishes fundamental limitations (no-go theorems) on the deterministic purification and probabilistic enhancement of quantum coherence, clarifying what is impossible in coherence manipulation within quantum resource theory.

Contribution

It introduces two no-go theorems that specify conditions under which coherence cannot be purified or enhanced, advancing understanding of quantum coherence manipulation constraints.

Findings

Deterministic purification is impossible if the state is a convex combination of incoherent and coherent states.

Provides a necessary and sufficient condition for probabilistic coherence enhancement via sSIO.

Establishes feasibility criteria for coherence manipulation in quantum systems.

Abstract

The manipulation of quantum coherence is one of the principal issues in the resource theory of coherence, with two critical topics being the purification and enhancement of coherence. Here, we present two no-go theorems for the deterministic purification of coherence and the probabilistic enhancement of coherence, respectively. Specifically, we prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Besides, we give an easy-to-verified sufficient and necessary condition to determine whether a state can be probabilistically enhanced via a stochastic strictly incoherent operation (sSIO). Our findings provide two feasibility criteria for the deterministic purification and the probabilistic enhancement of coherence, respectively. These results have repercussions on the understanding of quantum coherence in real quantum systems.