Coherence of quantum channels

Yajing Fan, Lulu Li

Jianwei Xu

We investigate the coherence of quantum channels and establish a resource theory for quantifying the coherence of quantum channels. To this aim, we define the incoherent channels and incoherent superchannels. This theory recovers the case of quantum states when we view quantum states as a special case of quantum channels and also allows some analytical expressions for coherence measures.

Yu Luo, Mingfei Ye, Yongming Li

Tong Liu

In quantum information theory, in order for two (or more) parties to communicate, there must be a communication channel. The two central quantities that must be considered are quantum channel capacity and the quantum coherent information. The first describes the capability for a given channel to communicate the required quantum information and the latter describes the amount of information that has been successfully transmitted through the corresponding quantum channel. The capacity of a quantum channel is actually a function of the coherent information, and so the basic step for getting the channel capacity is to calculate its coherent information which serves as a lower bound on the capacity. Generally speaking, it is hard to find the capacity of a given quantum channel, this is because of regularization which is to introduce additional process to solve an ill-conditioned problem. Comparing to general quantum channels, the capacity is easily achieved for the two fundamental classes of quantum channels, degradable and antidegradable, in such a way that degradable channels have capacity given exactly by the coherent information and antidegradable channels have zero coherent information. However, this is not true for general quantum channels, by all means that, under certain restrictions, it is possible to find a non-Pauli quantum channel such that its coherent information is zero but its capacity is non-zero.

Jianwei Xu

Masaya Takahashi, Swapan Rana, Alexander Streltsov

The emerging quantum technologies rely on our ability to establish and control quantum systems in nonclassical states, exhibiting entanglement and quantum coherence. It is thus crucial to understand how entanglement and coherence can be created in the most efficient way. In this Letter we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on a multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of the coherence generating capacity of quantum channels, which we also discuss.