Coherence non-generating channels

TL;DR

This paper investigates the properties of coherence non-generating quantum channels, showing how they affect quantum coherence measures and revealing superadditivity effects in quantum coherence.

Contribution

It introduces the concept of coherence non-generating channels, analyzes their impact on coherence measures, and derives their general form for qubit channels, advancing the resource theory of quantum coherence.

Findings

Relative entropy of coherence decreases under these channels.

Coherence of formation can increase, but is bounded for single qubits.

Superadditivity of coherence increase power in combined channels.

Abstract

We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the coherence non-generating channels. We prove that the relative entropy of coherence is monotonically decreasing under the coherence non-generating channels, while the coherence of formation may increase under such channels. Interestingly, by combining mathematically the coherence of formation to the entanglement of formation, we show that the coherence of formation of a single-qubit is never increased by a coherence non-generating channel. This leads to the superadditivity property for the coherence increasing power of quantum channels, namely, while two channels can not increase coherence individually, they may increase the quantum coherence of a composed system. Further, we derive the general form of the rank-2 coherence non-generating qubit channels. Our results contribute to the resource theory of quantum coherence.