Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses

Lu, He; Zhao, Qi; Li, Zheng Da; Yin, Xu Fei; Yuan, Xiao; Hung, Jui Chen; Chen, Luo Kan; Li, Li; Liu, Nai Le; Peng, Cheng; Liang, Yeong-Cherng; Ma, Xiongfeng; Chen, Yu Ao; Pan, Jian-Wei

doi:10.1103/physrevx.8.021072

Cited by 43 publications

(57 citation statements)

References 27 publications

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“…Fourth, it is also intriguing to study the entanglement detection under other types of coherent noises, which appear in certain experimental systems. In addition, the detection of more detailed multipartite entanglement structures [36][37][38] under coherent noises is significant to investigate.…”

Section: Discussionmentioning

confidence: 99%

Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states

Zhou

2020

Phys. Rev. A

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Entanglement is an essential resource in many quantum information tasks and entanglement witness is a widely used tool for its detection. In experiments the prepared state generally deviates from the target state due to some noise. Normally the white noise model is applied to quantifying such derivation and in the same time reveals the robustness of the witness. However, there may exist other kind of noise, in which the coherent noise can dramatically "rotate" the prepared state. In this way, the coherent noise is likely to lead to a failure of the detection, even though the underlying state is actually entangled. In this work, we propose an efficient entanglement detection protocol for N -partite Greenberger-Horne-Zeilinger (GHZ)-like states. The protocol can eliminate the effect of the coherent noise and in the same time feedback the corresponding noise parameters, which are beneficial to further improvements on the experiment system. In particular, we consider two experiment-relevant coherent noise models, one is from the unconscious phase accumulation on N qubits, the other is from the rotation on the control qubit. The protocol effectively realizes a family of entanglement witnesses by postprocessing the measurement results from N + 2 local measurement settings, which only adds one more setting than the original witness specialized for the GHZ state. Our protocol can enhance the entanglement detection under coherent noises and acts as a benchmark and calibration for the state-of-the-art quantum devices. *

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Section: Discussionmentioning

confidence: 99%

Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states

Zhou

2020

Phys. Rev. A

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“…Nonetheless, even without global genuine entanglement as the target state possesses, the experimental prepared state might still have fewer-body entanglement within a subsystem and/or among distinct subsystems [23][24][25]. The study of lower-order entanglement, which can be characterized by the detailed entanglement structures [26][27][28], is important for quantum hardware development, because it might reveal the information on unwanted couplings to the environment and acts as a benchmark of the underlying system. Moreover, the certified lower-order entanglement among several subsystems could be still useful for some quantum information tasks.…”

Section: Introductionmentioning

confidence: 99%

“…In other cases, one might not need to specify the partition in the beginning. By going through all possible partitions, one can investigate higher level entanglement structures, such as entanglement intactness (non-separability) [25,28], which quantifies how many pieces in the N -partite state are separated.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with genuine entanglement, multipartite entanglement structure still lacks a systematic exploration, due to the rich and complex structures of N -partite system. Recently, positive results have been achieved for detecting entanglement structures of GHZ-like states with two measurement settings [28] and the entanglement of a specific 1-D cluster state of the 16-qubit superconducting quantum processor ibmqx5 machine from the IBM cloud [38]. Unfortunately, it remains an open problem of efficient entanglement structure detection of general multipartite quantum states.…”

Section: Introductionmentioning

confidence: 99%

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Detecting multipartite entanglement structure with minimal resources

et al. 2019

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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]

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“…These examples involve only entanglement between two parties but the concept of entanglement goes beyond this. With more complicated entanglement structures [4], such as that endowed by the two-dimensional graph states [5], one can perform universal quantum computation [6] through a one-way quantum computer [7]. Entanglement can thus be seen as useful resources for a variety of different tasks.…”

Section: Introductionmentioning

confidence: 99%

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

et al. 2019

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Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the employment of device-independent witnesses catered for the particular property of interest. In this work, we consider a one-parameter family of multipartite, two-setting, two-outcome Bell inequalities and demonstrate the extent to which they are suited for the device-independent certification of genuine many-body entanglement (and hence the entanglement depth) present in certain well-known multipartite quantum states, including the generalized Greenberger-Horne-Zeilinger (GHZ) states with unbalanced weights, the higher-dimensional generalizations of balanced GHZ states, and the W states. As a by-product of our investigations, we have found that, in contrast with well-established results, provided trivial qubit measurements are allowed, full-correlation Bell inequalities can also be used to demonstrate the nonlocality of weakly entangled unbalanced-weight GHZ states. Besides, we also demonstrate how two-setting, two-outcome Bell inequalities can be constructed, based on the so-called GHZ paradox, to witness the entanglement depth of various graph states, including the ring graph states, the fully connected graph states, and some linear graph states, etc.

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Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses

Cited by 43 publications

References 27 publications

Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states

Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states

Detecting multipartite entanglement structure with minimal resources

Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

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