Detecting nonlocality of noisy multipartite states with the CHSH inequality

Abstract

The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of multipartite quantum states. We apply this to study the nonlocality of multipartite Greenberger-Horne-Zeilinger, W and graph states under local decoherence processes. We derive lower bounds on the critical local-noise strength tolerated by GHZ states before becoming local. In addition, for the whole noisy dynamics, we derive lower bounds on the corresponding nonlocal content for the three classes of states. All the bounds presented can be calculated efficiently and, in some cases, provide significantly tighter estimates than with any other known method. For example, they reveal that $N$-qubit GHZ states undergoing local dephasing are, for all $N$, nonlocal throughout all the dephasing dynamics.

8 pages, 3 figures

References in corpus (11)

• Device-independent security of quantum cryptography against collective attacks
• Multi-party entanglement in graph states
• Private Randomness Expansion With Untrusted Devices
• Scaling laws for the decay of multiqubit entanglement
• Noisy metrology beyond the standard quantum limit
• Full randomness from arbitrarily deterministic events
• Open-system dynamics of graph-state entanglement
• Quantifying the nonlocality of GHZ quantum correlations by a bounded communication simulation protocol
• Noisy entanglement evolution for graph states
• Scalability of GHZ and random-state entanglement in the presence of decoherence
• Nonlocality activation in entanglement swapping chains

Cited by in corpus (9)

• Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing
• Decoherence Effects on the Non-locality of Symmetric States
• Bounding the persistency of the nonlocality of W states
• Nonlocality Distillation and Quantum Voids
• Characterizing nonlocality of pure symmetric three-qubit states
• Genuine three qubit Einstein-Podolsky-Rosen steering under decoherence: Revealing hidden genuine steerability via pre-processing
• Experimental Approach to Demonstrating Contextuality for Qudits
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?
• Quantifying tolerance of a nonlocal multi-qudit state to any local noise