Cohering power of quantum operations

TL;DR

This paper investigates the ability of quantum operations to generate quantum coherence, providing an operational interpretation, decomposition into basic operations, and bounds on cohering power, which is crucial for quantum information processing.

Contribution

It introduces the concept of cohering power of quantum operations, offers an operational interpretation, and establishes bounds and comparisons for different measures of coherence.

Findings

Cohering power is upper bounded by the unitary component of quantum operations.

Decomposition of quantum operations into unitary, appending, and dismissal operations.

Comparison of cohering power and generalized cohering power across measures.

Abstract

Quantum coherence is a basic feature of quantum physics. Combined with tensor product structure of state space, it gives rise to the novel concepts such as entanglement and quantum correlations, which play a crucial role in quantum information processing tasks. However, quantum correlations, especially entanglement, are fragile under decoherence. In this context, very few investigations have touched on the production of quantum coherence by quantum operations. In this paper, we study cohering power -- the ability of quantum operations to produce coherence. First, we provide an operational interpretation of cohering power. Then, we decompose a generic quantum operation into three basic operations, namely, unitary, appending and dismissal operations, and show that the cohering power of any quantum operation is upper bounded by the corresponding unitary operation. Furthermore, we compare cohering power and generalized cohering power of quantum operations for different measures of coherence.