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arXiv:1906.07412 · Physical Review Applied

Experimental Certification of Sustained Entanglement and Nonlocality after Sequential Measurements

Giulio Foletto, Luca Calderaro, Armin Tavakoli, Matteo Schiavon, Francesco Picciariello, Adán Cabello, Paolo Villoresi, Giuseppe Vallone

Published Apr 3, 2020• 50 citations
arXivHTMLPDF

Abstract

Entanglement is a fundamental resource for quantum information science. However, bipartite entanglement is destroyed when one particle is observed via projective (sharp) measurements, as is typically the case in most experiments. Here, we show experimentally that, if instead of sharp measurements, one performs many sequential unsharp measurements on one particle that are suitably chosen depending on the previous outcomes, then entanglement is preserved and it is possible to reveal quantum correlations through measurements on the second particle at any step of the sequence. Specifically, we observe that pairs of photons entangled in polarization maintain their entanglement when one particle undergoes three sequential measurements and that each of these can be used to violate a Clauser-Horne-Shimony-Holt inequality. This proof-of-principle experiment demonstrates the possibility of repeatedly harnessing two crucial resources, entanglement and Bell nonlocality, that, in most quantum protocols, are destroyed after a single measurement. The protocol we use, which in principle works for an unbounded sequence of measurements, can be useful for randomness extraction.

DOI
10.1103/physrevapplied.13.044008

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Entanglement is a fundamental resource for quantum information science. However, bipartite entanglement is destroyed when one particle is observed via projective (sharp) measurements, as is typically the case in most experiments. Here, we show experimentally that, if instead of sharp measurements, one performs many sequential unsharp measurements on one particle that are suitably chosen depending on the previous outcomes, then entanglement is preserved and it is possible to reveal quantum correlations through measurements on the second particle at any step of the sequence. Specifically, we observe that pairs of photons entangled in polarization maintain their entanglement when one particle undergoes three sequential measurements and that each of these can be used to violate a Clauser-Horne-Shimony-Holt inequality. This proof-of-principle experiment demonstrates the possibility of repeatedly harnessing two crucial resources, entanglement and Bell nonlocality, that, in most quantum protocols, are destroyed after a single measurement. The protocol we use, which in principle works for an unbounded sequence of measurements, can be useful for randomness extraction.
Abstract In the standard Bell experiment, two parties perform local projective measurements on a shared pair of entangled qubits to generate nonlocal correlations. However, these measurements completely destroy the entanglement, rendering the post-measurement state unable for subsequent use. For a long time, it was believed that only unsharp measurements can be used to share quantum correlations. Remarkably, recent research has shown that classical randomness assisted projective measurements are sufficient for sharing nonlocality (Steffinlongo and Tavakoli 2022 Phys. Rev. Lett. 129 230402). Here, by stochastically combining no more than two different projective measurement strategies, we report an experimental observation of double Clauser–Horne–Shimony–Holt inequality violations with two measurements in a sequence made on each pair of maximally and partially entangled polarization photons. Our results reveal that the double violation achieved by partially entangled states can be 11 standard deviations larger than that achieved by maximally entangled ones. Our scheme eliminates the requirement for entanglement assistance in previous unsharp-measurement-based sharing schemes, making it experimentally easier. Our work provides possibilities for sharing other types of quantum correlations in various physical systems with projective measurements.
Sequential sharing of quantum nonlocality enables multiparty collaborative information processing, which is typically realized through unsharp measurements in previous studies. By contrast, we experimentally demonstrate that the sequential sharing of quantum nonlocality can be observed using only projective measurements, with the introduction of classical randomness. We achieve sequential violations of the Clauser-Horne-Shimony-Holt inequality in a bipartite quantum system by sharing classical randomness or using a probabilistic projective measurement. Extending the first protocol to a tripartite quantum system, sequential tripartite nonlocality is observed with the Greenberger-Horne-Zeilinger state, where violations of the Mermin inequality are observed in sequential measurements. We experimentally demonstrate these phenomena through the preparation and measurement of a three-photon entangled state. Our work reveals the key role of projective measurements in the sequential sharing of quantum nonlocality, providing a new experimental complement for measuring quantum nonlocality and opening new technological pathways for distributed utilization nonlocality in quantum networks.
The prevailing consensus is that the sequential sharing of nonlocality in a Bell experiment requires generalized unsharp measurements, given that a sharp measurement inevitably destroys the entanglement of the shared state. In contrast, a recent work [A. Steffinlongo and A. Tavakoli, Projective measurements are sufficient for recycling nonlocality, Phys. Rev. Lett. 129, 230402 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.230402] demonstrated the sharing of nonlocality up to two sequential observers by employing projective measurement aided with local randomness. Here, we introduce a form of local randomness-assisted qubit projective measurement protocol that enables the sharing of nonlocality by an arbitrary number of sequential observers (Bobs) with a single spatially separated observer (Alice). We achieve this by inspecting the diversity involved in implementing generalized measurements that harness nonlocality by preserving a sufficient amount of entanglement of the shared two-qubit entangled state. Furthermore, we highlight the crucial interplay between the degrees of measurement incompatibility of Alice and Bob in demonstrating the unbounded sharing of nonlocality.
Unsharp measurements are widely seen as the key resource for recycling the nonlocality of an entangled state shared between several sequential observers. Contrasting this, we here show that nonlocality can be recycled using only standard, projective, qubit measurements. Focusing on the Clauser-Horne-Shimony-Holt inequality and allowing parties to share classical randomness, we determine the optimal trade-off in the magnitude of Bell violations for a maximally entangled state. We then find that nonmaximally entangled states make possible larger sequential violations, which contrasts the standard Clauser-Horne-Shimony-Holt scenario. Furthermore, we show that nonlocality can be recycled using projective qubit measurements even when no shared classical randomness is available. We discuss the implications of our results for experimental implementations of sequential nonlocality.
Quantum nonlocality offers a secure way to produce random numbers: Their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do this, entangled pairs are generated and measured to violate a Bell inequality with the outcome statistics. However, after a projective quantum measurement, entanglement is entirely destroyed and cannot be used again. This fact poses an upper bound to the amount of randomness that can be produced from each quantum state when projective measurements are employed. Instead, by using weak measurements, some entanglement can be maintained and reutilized, and a sequence of weak measurements can extract an unbounded amount of randomness from a single state as predicted in [Phys. Rev. A 95, 020102(R) (2017)]. We study the feasibility of these weak measurements, analyze the robustness to imperfections in the quantum state they are applied to, and then test them using an optical setup based on polarization-entangled photon pairs. We show that the weak measurements are realizable, but can improve the performance of randomness generation only in close-to-ideal conditions.
As a way of saving quantum resources, recycling of Bell nonlocality has been experimentally studied, but restricted to sequential unsharp measurements. However, it has been theoretically shown recently that projective measurements are sufficient for recycling nonlocality [Phys. Rev. Lett. \textbf{129}, 230402 (2022)]. Here, we go beyond unsharp measurement scenarios and experimentally demonstrate the recycling of nonlocal resources with projective measurements. By verifying the violation of Clauser-Horne-Shimony-Holt (CHSH) inequality, we find that three independent parties can recycle the Bell nonlocality of a two-qubit state, whether it is maximally or partially entangled. Furthermore, in the double violation region, the optimal trade-off for partially entangled states can be 11 standard deviations better than that for maximally entangled states. Our results experimentally eliminate the common misconception that projective measurements are incompatible with the recycling of quantum correlations. In addition, our nonlocality recycling setup does not require entanglement assistance, which is much more experimentally friendly, thus paving the way for the reuse of other kinds of quantum correlations.