Detecting multipartite entanglement structure with minimal resources

Abstract

Recently, there are tremendous developments on the number of controllable qubits in several quantum computing systems. For these implementations, it is crucial to determine the entanglement structure of the prepared multipartite quantum state as a basis for further information processing tasks. In reality, evaluation of a multipartite state is in general a very challenging task owing to the exponential increase of the Hilbert space with respect to the number of system components. In this work, we propose a systematic method using very few local measurements to detect multipartite entanglement structures based on the graph state -one of the most important classes of quantum states for quantum information processing. Thanks to the close connection between the Schmidt coefficient and quantum entropy in graph states, we develop a family of efficient witness operators to detect the entanglement between subsystems under any partitions and hence the entanglement intactness. We show that the number of local measurements equals to the chromatic number of the underlying graph, which is a constant number, independent of the number of qubits. In reality, the optimization problem involved in the witnesses can be challenging with large system size. For several widely-used graph states, such as 1-D and 2-D cluster states and the Greenberger-Horne-Zeilinger state, by taking advantage of the area law of entanglement entropy, we derive analytical solutions for the witnesses, which only employ two local measurements. Our method offers a standard tool for entanglement structure detection to benchmark multipartite quantum systems. arXiv:1904.05001v2 [quant-ph]

Multipartite uncertainty relation with quantum memory

“…This generalized entropic uncertainty depends on the conditional von-Neumann entropies, Holevo quantities, and the mutual information. We expect that the inequality will bring on more potential applications in quantum information and communication, e.g., entanglement detection 64 , multipartite entanglement-structure detection 65 , witnessing multipartite entanglement 66 , detection of genuine multipartite entanglement in multipartite systems 67 , exploring the efficient multipartite entanglement criteria 68 – 70 , analyzing the monogamy and polygamy relations of multipartite quantum states 71 , 72 , and so on. It means that our multipartite uncertainty relation will have significant applications in entanglement detection and precision measurements.…”

Characterizing correlation within multipartite quantum systems via local randomized measurements

“…However, Rényi entropy can violate the subadditivity [2,17], which makes it nonideal for quantifying total correlation. Alternative approaches include uses of witnesses [18,19] to detect the presence of certain correlations [20][21][22][23]. These witnesses are typically tailored for specific classes of states (e.g.…”

“…These witnesses are typically tailored for specific classes of states (e.g. [23,24]) and are generally ineffective when applied to states without the preparation information [25][26][27].…”

High efficient multipartite entanglement purification using hyperentanglement

“…The GHZ state also have been realized with superconducting system [22,23], trapped ions [24], and photonic system [25]. The detection of the multipartite entanglement structure has also been reported [26].…”