Arbitrarily many independent observers can share the nonlocality of a single maximally entangled qubit pair

Abstract

Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. This scenario was introduced in [Phys. Rev. Lett. 114, 250401 (2015)] where the authors mentioned evidence that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH inequality with Alice. Here we show that, contrary to this evidence, arbitrarily many independent Bobs can have an expected CHSH violation with the single Alice. Our proof is constructive and our measurement strategies can be generalized to work with a larger class of two-qubit states that includes all pure entangled two-qubit states. Since violation of a Bell inequality is necessary for device-independent tasks, our work represents a step towards an eventual understanding of the limitations on how much device-independent randomness can be robustly generated from a single pair of qubits.

arXiv comment4+7 pages, 2 figures, v2: minor updates to match published version

References in corpus (21)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• No Signalling and Quantum Key Distribution
• General properties of Nonsignaling Theories
• Free randomness can be amplified
• Private Randomness Expansion With Untrusted Devices
• Randomness vs Non Locality and Entanglement
• Multiple Observers Can Share the Nonlocality of Half of an Entangled Pair by Using Optimal Weak Measurements
• Device-independent randomness expansion against quantum side information
• Unbounded randomness certification using sequences of measurements
• Device-independent Randomness Expansion with Entangled Photons
• Steering a single system sequentially by multiple observers
• Witnessing entanglement sequentially: Maximally entangled states are not special
• Experimental Realization of Device-Independent Quantum Randomness Expansion
• Unbounded sequence of observers exhibiting Einstein-Podolsky-Rosen steering
• Facets of bipartite nonlocality sharing by multiple observers via sequential measurements
• Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions
• Experimental Certification of Sustained Entanglement and Nonlocality after Sequential Measurements
• Detection of genuine tripartite entanglement by multiple sequential observers
• Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side

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