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Communications in Theoretical Physics

Detecting entanglement of quantum channels

Chaojian Li, Bang-Hai Wang, Bujiao Wu, Xiao Yuan

Published Aug 16, 2021• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1572-9494/ac1da1

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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.
Quantum entanglement and quantum coherence are important physical resources in the field of quantum information. It is an essential task to detect whether the prepared quantum states have these quantum resources in quantum information processing. Based on witness operator, a unified method of detecting quantum resources is provided. The lower bounds of multipartite entanglement and quantum coherence can be estimated by measuring the multipartite entanglement witness and coherence witness, respectively. In the process of the optimal conversion between single-qubit coherence and three-qubit entanglement, this method is applied to resource detection via constructing the fidelity witness operators, and the obtained lower bounds of coherence, tripartite entanglement and genuine tripartite entanglement are all the same. This conclusion can be extended to the case of any n-qubit. In addition, under the influence of white noise, the estimated coherence and multipartite entanglement are still equal, which indicates that the resource detection method is robust to noise.
The design of detection strategies for multipartite entanglement stands as a central importance on our understanding of fundamental quantum mechanics and has had a substantial impact on quantum information applications. However, accurate and robust detection approaches are severely hindered, particularly when the number of nodes grows rapidly like in a quantum network. Here we present a general and operational framework that generates alternative entanglement witness for an arbitrary targeted state. The framework enjoys a systematic and high-efficient character and allows to substantiate genuine multipartite entanglement for a variety of states that arise naturally in practical situations and to dramatically outperform currently standard methods. With excellent noise tolerance, our framework should be broadly applicable to witness genuine multipartite entanglement in various practically scenarios and to facilitate the best use of entangled resources in the emerging area of quantum network.
For any $N\ensuremath{\bigotimes}N$-type bipartite system with even N>2N>2N>2, two-parameter continuous families of unital block-dephasing quantum channels and of weakly optimal entanglement witnesses are constructed from special forms of a parametrized positive map. The parameter domains of the families are complementary subsets of a convex set and this fact reveals unusual combination rules of quantum channels and entanglement witnesses. These rules make it possible to develop many physically implementable direct entanglement-detection methods that provide a unified framework to accomplish both information-processing and entanglement-detection tasks by means of smooth quantum channels, without any reference to entanglement witnesses.
We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite density matrices based on witness operators. We first illustrate the method in the case of entanglement-breaking channels and nonseparable random unitary channels and show how it can be implemented experimentally by means of local measurements. We then study the detection of nonseparable maps and show that for pairs of systems of dimension higher than two the detection operators are not the same as in the random unitary case, highlighting a richer separability structure of quantum channels with respect to quantum states. Finally we consider the set of PPT maps, developing a technique to reveal NPT maps.
Quantum entanglement is a critical physical process in quantum mechanics and quantum information theory. It is a required process in quantum computing, quantum teleportation, and quantum cryptography. Entanglement detection affects the performance of quantum information processing tasks. Entanglement detection has grown in popularity over the years, and various entanglement detection methods are available, though some have application and system scale limitations. This scoping review sought to identify various measurement methods for entanglement detection in both bipartite and multipartite entanglement systems. Secondary resource indexed literatures were selected based on specific keywords from literatures published between 2017 and 2021. The goal of this study is to present a proposed conceptual framework of entanglement detection based on previous work as a guidance and reference founded on one’s specific requirements.
Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but also the entanglement structure in both fundamental theories and the applications of quantum information technologies. However, it is proved to be challenging to detect the entanglement structures, including entanglement depth, entanglement intactness and entanglement stretchability, especially for general states and large-scale quantum systems. By using the partitions of the tensor product space we propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Besides, an efficient algorithm using semi-definite programming and a gradient descent algorithm are designed to detect entanglement structure from the inner polytope of the convex set containing all the states with the same entanglement structure. We demonstrate by detailed examples that our criteria perform better than other known ones. Our results may be applied to many quantum information processing tasks.