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arXiv:2302.06522 · Optica

Experimental post-selection loophole-free time-bin and energy-time nonlocality with integrated photonics

Francesco B. L. Santagiustina, Costantino Agnesi, Alvaro Alarcón, Adán Cabello, GUILHERME BARRETO XAVIER, Paolo Villoresi, Giuseppe Vallone

Published Feb 5, 2024• 21 citations

Abstract

Time-bin (TB) and energy-time (ET) entanglements are crucial resources for long-distance quantum information processing. However, their standard implementations suffer from the so-called post-selection loophole that allows for classical simulation and thus prevents quantum advantage. The post-selection loophole has been addressed in proof-of-principle experiments. An open problem though is to close it in real-life applications based on integrated technologies. This is especially important since, so far, all integrated sources of TB and ET entanglements suffer from the post-selection loophole. Here, we report post-selection loophole-free certification of TB or ET entanglement in integrated technologies, by implementing in a silicon nitride chip the “hug” scheme [ Phys. Rev. Lett. 102 , 040401 ( 2009 ) PRLTAO 0031-9007 10.1103/PhysRevLett.102.040401 ] and certifying genuine TB entanglement through the violation of a Bell inequality.

DOI: 10.1364/optica.499247

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Time-bin (TB) and energy-time (ET) entanglements are crucial resources for long-distance quantum information processing. However, their standard implementations suffer from the so-called post-selection loophole that allows for classical simulation and thus prevents quantum advantage. The post-selection loophole has been addressed in proof-of-principle experiments. An open problem though is to close it in real-life applications based on integrated technologies. This is especially important since, so far, all integrated sources of TB and ET entanglements suffer from the post-selection loophole. Here, we report post-selection loophole-free certification of TB or ET entanglement in integrated technologies, by implementing in a silicon nitride chip the “hug” scheme [ Phys. Rev. Lett. 102 , 040401 ( 2009 ) PRLTAO 0031-9007 10.1103/PhysRevLett.102.040401 ] and certifying genuine TB entanglement through the violation of a Bell inequality.

The distribution of entangled photons between remote parties is fundamental for quantum communication protocols such as quantum teleportation and quantum key distribution (QKD). Among the various encoding schemes, time-bin entanglement is particularly promising as it ensures reliable long-distance communication for both optical fibre and free-space channels. However, the practical utility of time bin entanglement is constrained by the post-selection loophole (PSL), which allows for the possibility of local hidden variable models [1]. Temporal post-selection also opens the door to attack schemes and demands high temporal resolution. Initial efforts to close the PSL employed hyperentangled states combining polarization and time-bin degrees of freedom [2]. Later, Vedovato et al. used active switching to remove the need for post-selection [3], and an integrated “hug” scheme was used to demonstrate PSL-free certification through a phase-stabilized optical link [4].

Entanglement gives rise to correlations between distant quantum systems that cannot be explained by local realistic theories. Bell inequality violations provide a direct way to reveal these correlations and certify nonlocality, especially when the relevant experimental loopholes are closed. Time-bin encoding, in which quantum information is encoded into well-defined temporal modes, is a commonly used platform for distributing photonic entanglement in optical fibers. Yet loophole-free Bell tests with time-bin entanglement have received comparatively little attention, owing in part to the postselection loophole introduced by conventional interferometric measurements. Here, we demonstrate a fiber-based platform for Bell tests with time-bin entanglement that simultaneously closes the locality, freedom-of-choice, and postselection loopholes. We observe a CHSH violation of

S=2.583 \pm 0.002

, exceeding the local-realistic bound by over 265 standard deviations. Notably, this rigorous certification of nonlocality is achieved at a separation distance of

49.0 \pm 0.7

m, substantially shorter than previous photonic Bell tests addressing comparable space-time constraints. Beyond its foundational significance, our results demonstrate time-bin entanglement as a viable route towards practical device-independent quantum communication and a future quantum internet.

Entanglement is an invaluable resource for fundamental tests of physics and the implementation of quantum information protocols such as device-independent secure communications. In particular, time-bin entanglement is widely exploited to reach these purposes both in free space and optical fiber propagation, due to the robustness and simplicity of its implementation. However, all existing realizations of time-bin entanglement suffer from an intrinsic postselection loophole, which undermines their usefulness. Here, we report the first experimental violation of Bell's inequality with "genuine" time-bin entanglement, free of the postselection loophole. We introduced a novel function of the interferometers at the two measurement stations, that operate as fast synchronized optical switches. This scheme allowed us to obtain a postselection-loophole-free Bell violation of more than 9 standard deviations. Since our scheme is fully implementable using standard fiber-based components and is compatible with modern integrated photonics, our results pave the way for the distribution of genuine time-bin entanglement over long distances.

Entanglement is a unique resource for quantum information processing, which allows for device-independent (DI) quantum communication protocols, such as Quantum Key Distribution and Quantum Random Number Generation. Loophole-free violation of Bell inequalities is a necessary condition for DI protocols. While timebin entanglement is promising for long-distance distribution over fiber optics, its most common implementation suffers from a post-selection loophole (PSL) which invalidates Bell non-locality tests. We present an implementation of a postselection-free “genuine” time-bin entanglement scheme working with 1550 nm biphotons with an estimated Bell violation of S = 2.56.