Detecting entanglement of quantum channels

Abstract

Entanglement is the crucial resource for different quantum information processing tasks. While conventional studies focus on the entanglement of bipartite or multipartite quantum states, recent works have extended the scenario to the entanglement of quantum channels, an operational quantification of the channel entanglement manipulation capability. Based on the recently proposed channel entanglement resource framework, here we study a further task of resource detection—witnessing entanglement of quantum channels. We first introduce the general framework and show how channel entanglement detection is related to the Choi state of the channel, enabling channel entanglement detection via conventional state entanglement detection methods. We also consider entanglement of multipartite quantum channels and use the stabilizer formalism to construct entanglement witnesses for circuits consisting of controlled-Z gates. We study the effectiveness of the proposed detection methods and compare their performance for several typical channels. Our work paves the way for systematic theoretical studies of channel entanglement and practical benchmarking of noisy intermediate scaled quantum devices.

Convolution algebra of superoperators and nonseparability witnesses for quantum operations

“…This fact and the channel-state duality can be used to study the problem of nonseparability witnesses for a bipartite quantum operation [20]. Nonseparability of quantum operation or 'entanglement' of quantum operation was studied in a recent work [21] using the nonseparability of the corresponding CJKS state. They have also considered 'entanglement' of multipartite quantum channels and constructed entanglement witnesses for circuits consisting of controlled-Z gates using the stabilizer formalism.…”

Thermodynamic optimization of quantum algorithms: on-the-go erasure of qubit registers

“…Within this setting, one could attempt to generalize the no-go result and the trade-off found in this paper for the HSP algorithm. In that general setting it would also be interesting to explore automatization of the search for optimized erasure (or algorithm simplification) points, for example using entanglement detection [36,37], without affecting the state of the main register.…”