Observing High-Dimensional Nonlocality using Multi-Outcome Spectral Measurements

Jonathan Leach, Kiki Dekkers, Laura Serino, Nicola d'Alessandro, Abhinandan Bhattacharjee, Benjamin Brecht, Armin Tavakoli, Christine Silberhorn

Published Aug 19, 2025• 0 citations

Publisher

Abstract

Abstract Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements, since the emulation of these with separate dichotomic projections opens a binarisation loophole that local hidden variable theories can exploit. Here we show that the joint spectral intensity of a two-photon entangled state contains access to the necessary multi-outcome measurements to overcome this obstacle and certify nonlocality for high-dimensional states. This result is contrary to the belief that the joint spectral intensity is a phase-insensitive quantity and does not have sufficient information to certify entanglement or nonlocality. Using this approach, we violate the CGLMP Bell inequality up to dimension d = 8, all with negligible p-values, and for the first time close the binarisation loophole in high-dimensional Bell experiments. Guaranteeing nonlocal correlations using frequency-only measurements removes the technological hurdle of measurements in the temporal domain, thus greatly simplifying any practical implementation of future high-dimensional quantum information protocols.

DOI: 10.21203/rs.3.rs-6976482/v1

Related papers

Observing High-dimensional Bell Inequality Violations using Multi-Outcome Spectral Measurements

Kiki Dekkers, Laura Serino, Nicola d'Alessandro +5 more

Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements, since the emulation of these with separate dichotomic projections opens a binarisation loophole that local hidden variable theories can exploit. Here we show that the joint spectral intensity of a two-photon entangled state contains access to the necessary multi-outcome measurements to overcome this obstacle and certify and violate a Bell inequality for high-dimensional states. This result is contrary to the belief that the joint spectral intensity is a phase-insensitive quantity and does not have sufficient information to certify entanglement or Bell-nonlocality. Using this approach, we violate the CGLMP Bell inequality up to dimension d = 8, all with negligible p-values, and for the first time close the binarisation loophole in high-dimensional Bell experiments. Guaranteeing Bell-nonlocal correlations using frequency-only measurements removes the technological hurdle of measurements in the temporal domain, thus greatly simplifying any practical implementation of future high-dimensional quantum information protocols.

arXiv:2506.20796Jun 25, 20250 citations

Binarisation-loophole-free observation of high-dimensional quantum nonlocality

Jia-le Miao, Elna Svegborn, Zhuo Chen +7 more

Bell inequality tests based on high-dimensional entanglement usually require measurements that can resolve multiple possible outcomes. However, the implementation of high-dimensional multi-outcome measurements is often only emulated via a collection of ``click or no-click'' measurements. This reduction of multi-outcome measurements to binary-outcome measurements opens a loophole in high-dimensional tests Bell inequalities which can be exploited by local hidden variable models [Tavakoli et al., Phys. Rev. A 111, 042433 (2025)]. Here, we close this loophole by using four-dimensional photonic path-mode entanglement and multi-outcome detection. We test both the well-known Collins-Gisin-Linden-Massar-Popescu inequality and a related Bell inequality tailored for maximally entangled states in high-dimension. We observe violations that are large enough to also rule out any quantum model based on entanglement of lower dimension, thereby demonstrating genuinely high-dimensional nonlocality free of the binarisation loophole.

quant-pharXiv:2601.02350Physical Review LettersJan 6, 20260 citations

Optimal Strategy to Certify Quantum Nonlocality

Santiago Gómez, Daniel Uzcátegui Contreras, I. Machuca +4 more

Abstract Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is only weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represent an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

Jul 15, 20210 citations

Optimal strategy to certify quantum nonlocality

Santiago Gómez, Daniel Uzcátegui Contreras, I. Machuca +4 more

Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is only weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represents an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

Scientific ReportsOct 14, 20211 citation

Bell-Inequality Violation for Continuous, Non-Projective Measurements

Shalender Singh, Santosh Kumar

Many solid-state quantum platforms do not permit sharp, projective measurements but instead yield continuous voltage or field traces under weak, non-demolition readout. In such systems, standard Bell tests based on dichotomic projective measurements are not directly applicable, raising the question of how quantum nonlocality can be certified from continuous time-series data. Here we develop a general theoretical framework showing that Bell-CHSH inequality violation can be extracted from continuous, non-projective measurements without assuming any specific collapse model or phase distribution. We show that sufficiently long continuous measurements of a single entangled pair sample its internal phase-probability structure, enabling effective dichotomic observables to be constructed through phase-sensitive projections and coarse-graining. The resulting Bell correlator is governed by two experimentally accessible resources: intrinsic single-qubit phase spread and nonlocal phase locking between qubits. We benchmark the resulting estimator against conventional projective-measurement CHSH tests implemented via quantum-circuit simulations using Qiskit, finding quantitative agreement in the Bell-violating regime without parameter fitting. Classical deterministic correlations cannot violate the CHSH bound, whereas quantum phase-locked systems recover the nonlinear angular dependence characteristic of entanglement. Our results provide a practical route to demonstrating Bell nonlocality in platforms where measurements are inherently continuous and weak.

quant-pharXiv:2512.22229Scientific ReportsDec 24, 20250 citations

Optimal strategy to certify quantum nonlocality

S. Gómez, Daniel Uzcátegui Contreras, I. Machuca +4 more

Certification of quantum nonlocality plays a central role in practical applications like device-independent quantum cryptography and random number generation protocols. These applications entail the challenging problem of certifying quantum nonlocality, something that is hard to achieve when the target quantum state is weakly entangled, or when the source of errors is high, e.g. when photons propagate through the atmosphere or a long optical fiber. Here, we introduce a technique to find a Bell inequality with the largest possible gap between the quantum prediction and the classical local hidden variable limit for a given set of measurement frequencies. Our method represents an efficient strategy to certify quantum nonlocal correlations from experimental data without requiring extra measurements, in the sense that there is no Bell inequality with a larger gap than the one provided. Furthermore, we also reduce the photodetector efficiency required to close the detection loophole. We illustrate our technique by improving the detection of quantum nonlocality from experimental data obtained with weakly entangled photons.

arXiv:2107.09120Jul 19, 20210 citations