Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation

TL;DR

This paper demonstrates that quantum coherence can be arbitrarily amplified in various operational settings, revealing fundamental limits and capabilities in coherence transformation and resource manipulation.

Contribution

It introduces the concept that low coherent states can be transformed into high coherent states arbitrarily well, including unbounded rates with catalysts, highlighting novel properties of quantum coherence.

Findings

Any low coherent state can be converted to any high coherent state in asymptotic and catalytic settings.

Catalysts can significantly increase coherence distillation rates from zero to infinite.

A small but non-zero coherence is necessary for anomalous transformations to occur.

Abstract

Quantum coherence is one of the fundamental aspects distinguishing classical and quantum theories. Coherence between different energy eigenstates is particularly important, as it serves as a valuable resource under the law of energy conservation. A fundamental question in this setting is how well one can prepare good coherent states from low coherent states and whether a given coherent state is convertible to another one. Here, we show that any low coherent state is convertible to any high coherent state arbitrarily well in two operational settings: asymptotic and catalytic transformations. For a variant of asymptotic coherence manipulation where one aims to prepare desired states in local subsystems, the rate of transformation becomes unbounded regardless of how weak the initial coherence is. In a non-asymptotic transformation with a catalyst, a helper state that locally remains in the original form after the transformation, we show that an arbitrary state can be obtained from any low coherent state. Applying this to the standard asymptotic setting, we find that a catalyst can increase the coherence distillation rate significantly -- from zero to infinite rate. We also prove that such anomalous transformation requires small but non-zero coherence in relevant modes, establishing the condition under which a sharp transition of the operational capability occurs. Our results provide a general characterization of the coherence transformability in these operational settings and showcase their peculiar properties compared to other common resource theories such as entanglement and quantum thermodynamics.