Cohering power of quantum operations

Zhengjun Xi, Ming‐Liang Hu, Yongming Li +1 more

Carlos Navarrete–Benlloch

Kaifeng Bu, Lin Zhang, Junde Wu

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.

Ingemar Bengtsson, Karol Życzkowski

Kaifeng Bu, Chunhe Xiong

Cohering power and de-cohering power have recently been proposed to quantify the ability of a quantum operation to produce and erase coherence respectively. In this paper, we investigate the properties of cohering power and de-cohering power. First, we prove the equivalence between two different kinds of cohering power for any quantum operation on single qubit systems, which implies that l1 norm of coherence is monotone under Maximally incoherent operation (MIO) and Dephasing-covariant operation (DIO) in 2-dimensional space. In higher dimensions, however, we show that the monotonicity under MIO or DIO does not hold. Besides, we compare the set of quantum operations with zero cohering power with Maximally incoherent operation (MIO) and Incoherent operation (IO). Moreover, two different types of de-cohering power are defined and we find that they are not equal in single qubit systems. Finally, we make a comparison between cohering power and de-cohering power for single qubit unitary operations and show that cohering power is always larger than de-cohering power.

Ingemar Bengtsson, Karol Zyczkowski