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Certification of high-dimensional quantum steering via experimentally-friendly energy-time measurements

Kai-Chi Chang, Murat Can Sarihan, Xiang Cheng, Paul Erker, Andrew Mueller, Matthew D. Shaw, Boris A. Korzh, M. Spiropulu, Marcus Huber, Chee Wei Wong

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Here we develop a scheme and experimentally demonstrate the first multi-dimensional quantum steering using discretized time-frequency bases. At the qudit source, we extract a lower bound of steering robustness of 8.9 ± 0.1 that demonstrates a 9-dimensional quantum steering, after the transportation, a 7-dimensional quantum steering is preserved.

DOI
10.1364/cleo_fs.2025.ff105_5

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Optica•Apr 5, 2022•22 citations
Here we develop a scheme and experimentally demonstrate the first multi-dimensional quantum steering using discretized time-frequency bases. At the qudit source, we extract a lower bound of steering robustness of 8.9 ± 0.1 that demonstrates a 9-dimensional quantum steering, after the transportation, a 7-dimensional quantum steering is preserved.
High-dimensional entanglement provides unique ways of transcending the limitations of current approaches in quantum information processing, quantum communications based on qubits. The generation of time-frequency qudit states offer significantly increased quantum capacities while keeping the number of photons constant, but pose significant challenges regarding the possible measurements for certification of entanglement. Here, we develop a new scheme and experimentally demonstrate the certification of 24-dimensional entanglement and a 9-dimensional quantum steering. We then subject our photon-pairs to dispersion conditions equivalent to the transmission through 600-km of fiber and still certify 21-dimensional entanglement. Furthermore, we use a steering inequality to prove 7-dimensional entanglement in a semi-device independent manner, proving that large chromatic dispersion is not an obstacle in distributing and certifying high-dimensional entanglement and quantum steering. Our approach, leveraging intrinsic large-alphabet nature of telecom-band photons, enables scalable, commercially viable, and field-deployable entangled and steerable quantum sources, providing a pathway towards fully scalable quantum information processer and high-dimensional quantum communication networks.
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.
A primary requirement for a robust and unconditionally secure quantum network is the establishment of quantum nonlocal correlations over a realistic channel.While loophole-free tests of Bell nonlocality allow for entanglement certification in such a device-independent setting, they are extremely sensitive to loss and noise, which naturally arise in any practical communication scenario.Quantum steering relaxes the strict technological constraints of Bell nonlocality by reframing it in an asymmetric manner, with a trusted party only on one side.However, tests of quantum steering still require either extremely high-quality entanglement or very low loss.Here we introduce a test of quantum steering that harnesses the advantages of high-dimensional entanglement to be simultaneously noise robust and loss tolerant.Despite being constructed for qudits, our steering test is designed for single-detector measurements and is able to close the fair-sampling loophole in a time-efficient manner.We showcase the improvements over qubit-based systems by experimentally demonstrating quantum steering in up to 53 dimensions, free of the fairsampling loophole, through simultaneous loss and noise conditions corresponding to 14.2-dB loss equivalent to 79 km of telecommunication fiber, and 36% of white noise.We go on to show how the use of high dimensions counterintuitively leads to a dramatic reduction in total measurement time, enabling a quantum steering violation almost 2 orders of magnitude faster obtained by simply doubling the Hilbert space dimension.Our work conclusively demonstrates the significant resource advantages that highdimensional entanglement provides for quantum steering in terms of loss, noise, and measurement time, and opens the door toward practical quantum networks with the ultimate form of security.
Quantum systems of high dimensions are attracting a lot of attention because they feature interesting properties when it comes to observing entanglement or other forms of correlations. In particular, their improved resistance to noise is favorable for experiments in quantum communication or quantum cryptography. However, witnessing this high-dimensional nature remains challenging, especially when the assumptions on the parties involved are weak, typically when one of them is considered as a black box. In this context, the concept of genuine high-dimensional steering has been recently introduced and experimentally demonstrated [Phys. Rev. Lett. 126, 200404 (2021)]; it allows for a one-sided device-independent certification of the dimension of a bipartite shared state by only using two measurements. Here I overcome this limitation by developing, for more than two measurements, universal bounds on the incompatibility robustness, turned into meaningful dimension certificates. Interestingly, even though the resulting bounds are quite loose, they still often offer an increased resistance to noise and could then be advantageously employed in experiments.
Genuine high-dimensional (HD) quantum steering was recently proposed for certifying HD entanglement in the one-sided device-independent setting, as quantified by the Schmidt number [ Phys. Rev. Lett. 126 , 200404 ( 2021 ) PRLTAO 0031-9007 10.1103/PhysRevLett.126.200404 ]. As one of the central challenges in the steering test is the tolerated noise threshold, here we develop a more robust method for certifying genuine HD steering in noisy environments. We derive genuine HD steering criteria using multiple mutually unbiased bases, surpassing the previous restriction of only two measurement settings. Although the present multisetting criteria are not tight, we theoretically show that they are more robust to noise than the tight two-setting criteria. To test the practicality of our method under realistic conditions, we report an experimental demonstration using photonic orbital angular momentum entangled states in dimensions d = 3 , 4 , 5 . Our work offers a more robust way to witness the entanglement dimension in practical one-sided device-independent quantum information processing.