Entanglement witnessing by arbitrarily many independent observers recycling a local quantum shared state

Abstract

We investigate the scenario where an observer, Alice, shares a two-qubit state with an arbitrary number of observers, Bobs, via sequentially and independently recycling the qubit in possession of the first Bob. It is known that there exist entangled states which can be used to have an arbitrarily long sequence of Bobs who can violate the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. We show that there exist entangled states that do not violate the Bell inequality and whose entanglement can be detected by an arbitrary number of Bobs by suitably choosing the entanglement witness operator and the unsharp measurement settings by the Bobs. This proves that the set of states that can be used to witness entanglement sequentially is larger than those that can witness sequential violation of local realism. There exist, therefore, two-party quantum correlations that are Bell "classical", but whose entanglement "nonclassicality" can be witnessed sequentially and independently by an arbitrarily large number of observers at one end of the shared state with the single observer at the other end.

Further derivation added

References in corpus (10)

• Entanglement detection
• Device-independent security of quantum cryptography against collective attacks
• Private Randomness Expansion With Untrusted Devices
• Arbitrarily many independent observers can share the nonlocality of a single maximally entangled qubit pair
• Sharing quantum nonlocality and genuine nonlocality with independent observables
• Limitations on sharing Bell nonlocality between sequential pairs of observers
• Einstein-Podolsky-Rosen Steering in Two-sided Sequential Measurements with One Entangled Pair
• Recycling qubits for the generation of Bell nonlocality between independent sequential observers
• Non-locality sharing for a three-qubit system via multilateral sequential measurements
• Bell nonlocality between sequential pairs of observers

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• Sequentially witnessing entanglement by independent observer pairs
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• Recycled detection of genuine multiparty entanglement of unlimitedly stretched array of parties and arbitrarily long series of sequential observers
• Local entanglement transfer to multiple pairs of spatially separated observers
• Unbounded entanglement-sustaining sequential local quantum state discrimination
• Sequential information theoretic protocols in continuous variable systems