Efficient and robust detection of multipartite Greenberger-Horne-Zeilinger-like states

Abstract

Entanglement is a key resource for quantum information processing. A widely used tool for detecting entanglement is entanglement witness, where the measurement of the witness operator is guaranteed to be positive for all separable states and can be negative for certain entangled states. In reality, due to the exponentially increasing the Hilbert-space dimension with respective to the system size, it is very challenging to construct an efficient entanglement witness for general multipartite entangled states. For $N$-partite Greenberger-Horne-Zeilinger (GHZ)-like states, the most robust witness scheme requires $N+1$ local measurement settings and can tolerate up to $1/2$ white noise. As a comparison, the most efficient witness for GHZ-like states only needs two local measurement settings and can tolerate up to $1/3$ white noise. There is a trade-off between the realization efficiency, the number of measurement settings, and the detection robustness, the maximally tolerable white noise. In this work, we study this trade-off by proposing a family of entanglement witnesses with $k$ ($2\le k\le N+1$) local measurement settings. Considering symmetric local measurements, we calculate the maximal tolerable noise for any given number of measurement settings. Consequently, we design the optimal witness with a minimal number of settings for any given level of white noise. Our theoretical analysis can be applied to other multipartite entangled states with a strong symmetry. Our witnesses can be easily implemented in experiment and applied in practical multipartite entanglement detection under different noise conditions.

arXiv comment8 pages, 1 figure

References in corpus (27)

• Quantum entanglement
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Area laws for the entanglement entropy - a review
• Entanglement detection
• 14-qubit entanglement: creation and coherence
• Multi-party entanglement in graph states
• Experimental ten-photon entanglement
• 18-qubit entanglement with photon's three degrees of freedom
• A complete family of separability criteria
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Further results on the cross norm criterion for separability
• Detecting multiparticle entanglement of Dicke states
• All Entangled Quantum States Are Nonlocal
• Measurement-Device-Independent Entanglement Witnesses for All Entangled Quantum States
• Multipartite Entanglement Witnesses
• Spectral decomposition of Bell's operators for qubits
• Toolbox for entanglement detection and fidelity estimation
• Entanglement Detection by Local Orthogonal Observables
• Observation of Ten-photon Entanglement Using Thin BiB${}_3$O${}_6$ Crystals
• Implementation of a Measurement-Device-Independent Entanglement Witness
• Entanglement Structure: Entanglement Partitioning in Multipartite Systems and Its Experimental Detection Using Optimizable Witnesses
• Multipartite entanglement detection with minimal effort
• Efficient measurement-device-independent detection of multipartite entanglement structure
• Reliable and robust entanglement witness
• Decomposition of symmetric multipartite observable

Cited by in corpus (6)

• Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states
• A scheme to create and verify scalable entanglement in optical lattice
• Efficient entanglement generation and detection of generalized stabilizer states
• Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences
• Multi-linear Monogamy Relations for Three Qubit States
• Witnesses of Genuine Multipartite Entanglement and Nonlocal Measurement Back-action for Raman-scattering Quantum Systems