Coherence-breaking superchannels

龚洪波 GONG Hong-bo

Danxiang Wu, Kan He

Senrui Chen, Eric Chitambar

In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and superchannels. Unlike its channel counterpart, we find that not every EB superchannel can be implemented as a measure-and-prepare superchannel. We also demonstrate that many EB superchannels can be superactivated, in the sense that they can output non-separable channels when wired in series.We then introduce the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively. This allows us to characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superchannels. Finally, we relax the definition of separable channels to include (p,q) -non-entangling channels, which are bipartite channels that cannot generate entanglement using p - and q -dimensional ancillary systems. By introducing and investigating k -EB maps, we construct examples of (p,q) -EB superchannels that are not fully entanglement breaking. Partial results on the characterization of (p,q) -EB superchannels are also provided.

Yu Luo

A fundamental problem in quantum information is to understand the operational significance of quantum resources. Quantum resource theories (QRTs) provide a powerful theoretical framework that aids in the analysis and comprehension of the operational meaning of these resources. Early resource theories primarily focused on analyzing static quantum resources. Recently, interest in the study of dynamic quantum resources has been growing. In this paper, we utilize superchannel theory to describe the dynamic resource theory of quantum coherence. In this dynamic resource theory, we treat classical channels as free channels and consider two classes of free superchannels that preserve channel incoherence [maximally incoherent superchannels (MISCs) and dephasing-covariant incoherent superchannels (DISCs)] as free resources. We regard the quantum Fourier transform as the golden unit of dynamic coherence resources. We first establish the one-shot theory of dynamic coherence cost and dynamic coherence distillation, which involves converting the quantum Fourier transform into an arbitrary quantum channel using MISCs and DISCs. Next, we introduce a class of free superchannels known as $\ensuremath{\delta}$-MISCs, which asymptotically generate negligible dynamic coherence. Finally, we provide upper and lower bounds for the one-shot catalytic dynamic coherence cost of quantum channels under the action of these $\ensuremath{\delta}$-MISC superchannels.

Ruifen Ma, Yanjing Sun, Xiaofei Qi

Quantum steering is a crucial quantum resource that lies intermediate between entanglement and Bell nonlocality. Gaussian channels, meanwhile, play a foundational role in diverse quantum protocols, secure communication, and related fields. In this paper, we focus on several classes of Gaussian channels associated with quantum steering: Gaussian steering-annihilating channels, Gaussian steering-breaking channels, Gaussian unsteerable channels, and maximal Gaussian unsteerable channels. We give the concepts of these channels, derive the necessary and sufficient conditions for a Gaussian channel to belong to each class, and explore the intrinsic relationships among them. Additionally, since quantifying the steering capability of Gaussian channels in continuous-variable systems requires an understanding of the structure of free superchannels, we also provide a detailed characterization of Gaussian unsteerable superchannels and maximal Gaussian unsteerable superchannels.