Entanglement-breaking superchannels

Abstract

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.

Genuine multipartite entanglement in time

“…For the case of an EB channel on R, within the study of quantum memory, a similar Proposition has been shown in [32]. There, processes on two times that only display classical memory were defined as those that have an EB channel on R. Additionally, related results can be found in [34], where entanglement breaking superchannels and their representations are analysed. Here, we provide direct simple proofs that will also allow us to show the converse for one of the cases and to pinpoint the difficulties with proving the converse of the other two.…”

“…Additionally, we show that in the temporal case -in analogy to its spatial counterpart [33] -there exist processes with entanglement as an emergent quality, i.e., genuinely multipartite entangled states that do not display entanglement in their marginals even when one allows for conditioning. Along the way, we provide explicit circuits for each of the discussed cases, and relate them to existing phenomena discussed in the literature, like entanglement breaking superchannels [34], channel steering [35], as well as the aforementioned concepts of genuine quantum memory and the superposition of direct and common causes. In this way we provide a comprehensive picture of the entanglement properties of temporal processes.…”

Quantum and classical dynamical semigroups of superchannels and semicausal channels

“…Understanding such spectral properties, and potentially how they differ from the properties in the scenario of quantum channels, would in particular lead to a better understanding of the asymptotic behavior of semigroups of superchannels, e.g., w.r.t. entropy production [32,33], the thermodynamics of quantum channels [34] or entanglement-breaking properties [35].…”

Universal construction of decoders from encoding black boxes

“…Universal transformations of quantum states have played an essential role in the fundamental understanding of quantum information theory and its applications [1]. Recently, higher-order quantum transformations, namely, universal transformations of quantum operations given as black boxes, have been studied in the contexts of processing unitary operations , non-Markovian quantum process [24][25][26][27][28][29][30][31][32][33][34][35][36], and dynamical resource theory [37][38][39][40][41][42][43][44][45][46][47][48]. They can also be interpreted as quantum functional programming [49,50].…”