Maneuvering measurement-coherence into measurement-entanglement

TL;DR

This paper extends the understanding of quantum resource transformation by showing that a channel's measurement-cohering power can be converted into measurement-entangling power, linking coherence and entanglement at the measurement level.

Contribution

It introduces a resource-theoretic framework for measurement-coherence and measurement-entanglement, completing the coherence-to-entanglement paradigm for quantum channels.

Findings

Measurement-cohering power can be converted into measurement-entangling power.

The state-cohering power equals the measurement-cohering power of the adjoint map.

The state-entangling power equals the measurement-entangling power.

Abstract

Quantum dynamics governs the transformation of static quantum resources, such as coherence and entanglement, in both quantum states and measurements. Prior studies have established that a quantum channel's state-cohering power can be converted into the state-entangling power without additional coherence. Here, we complete this coherence-to-entanglement paradigm by demonstrating that a channel's measurement-cohering power can likewise be converted into the measurement-entangling power. This result reinforces, on the dynamical level, the intuition that entanglement emerges as a manifestation of coherence. To formalize this picture, we develop resource theories for measurement-cohering and measurement-entangling powers and characterize the structure of incoherent measurements to analyze measurement-coherence generation. Furthermore, we show that the state-cohering power of a quantum channel is equivalent to the measurement-cohering power of its adjoint map, and a corresponding equivalence also exists between the state-entangling power and the measurement-entangling power.