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arXiv:2602.12269

Certification of linear optical quantum state preparation

Riko Schadow, Naomi Spier, Stefan N. van den Hoven, Malaquias Correa Anguita, Redlef B. G. Braamhaar, Sara Marzban, Jens Eisert, Jelmer J. Renema, Nathan Walk

quant-phSubmitted Feb 12, 2026• Announced Feb 13, 2026• 0 citations
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Abstract

Certification is important to guarantee the correct functioning of quantum devices. A key certification task is verifying that a device has produced a desired output state. In this work, we study this task in the context of photonic platforms, where single photons are propagated through linear optical interferometers to create large, entangled resource states for metrology, communication, quantum advantage demonstrations and for so-called linear optical quantum computing (LOQC). This setting derives its computational power from the indistinguishability of the photons, i.e., their relative overlap. Therefore, standard fidelity witnesses developed for distinguishable particles (including qubits) do not apply directly, because they merely certify the closeness to some fixed target state. We introduce a measure of fidelity suitable for this setting and show several different ways to witness it, based on earlier proposals for measuring genuine multi-photon indistinguishability. We argue that a witness based upon the discrete Fourier transform is an optimal choice. We experimentally implement this witness and certify the fidelity of several multi-photon states.

Comments
32 pages, 6 figures

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Certification is important to guarantee the correct functioning of quantum devices. A key certification task is verifying that a device has produced a desired output state. In this work, we study this task in the context of photonic platforms, where single photons are propagated through linear optical interferometers to create large, entangled resource states for metrology, communication, quantum advantage demonstrations and for so-called linear optical quantum computing (LOQC). This setting derives its computational power from the indistinguishability of the photons, i.e., their relative overlap. Therefore, standard fidelity witnesses developed for distinguishable particles (including qubits) do not apply directly, because they merely certify the closeness to some fixed target state. We introduce a measure of fidelity suitable for this setting and show several different ways to witness it, based on earlier proposals for measuring genuine multi-photon indistinguishability. We argue that a witness based upon the discrete Fourier transform is an optimal choice. We experimentally implement this witness and certify the fidelity of several multi-photon states.
Multiphoton indistinguishability is a key resource for photonic quantum technologies, yet its characterization typically relies on resource-intensive methods. In this work, we develop two efficient and experimentally friendly protocols to estimate or bound the fidelity FindF_{\mathrm{ind}}Find​ of an NNN-photon state to the closest perfectly indistinguishable state. The first protocol applies to sources preparing separable states, uses a single Fourier interferometer together with photon-number-resolving detection, and yields tight two-sided bounds on FindF_{\mathrm{ind}}Find​. The second protocol combines randomized implementations of linear-optical interferometers with photon counting, enabling direct estimation of FindF_{\mathrm{ind}}Find​ for arbitrary NNN-photon states. Both protocols can certify Find=1−O(ε)F_{\mathrm{ind}} = 1 - \mathcal{O}(ε)Find​=1−O(ε) using provably optimal O(1/ε)\mathcal{O}(1/ε)O(1/ε) samples, in contrast to previous approaches which required prior assumptions on the model of partial distinguishability. Our methods, based on a multiphoton generalization of the Hong-Ou-Mandel test, bring the rigorous and operationally meaningful certification of multiphoton indistinguishability within reach of current photonic technologies.
Entangled quantum states are essential ingredients for many quantum technologies, but they must be validated before they are used. As a full characterization is prohibitively resource intensive, recent work has focused on developing methods to efficiently extract a few parameters of interest, in a so-called verification framework. Most existing approaches are based on preparing an ensemble of nominally identical and independently distributed (IID) quantum states and then measuring each copy of the ensemble. However, this leaves no states left for the intended quantum tasks and the IID assumptions do not always hold experimentally. To overcome these challenges, we experimentally implement quantum state certification (QSC), which measures only a subset of the ensemble, certifying the fidelity of multiple copies of the remaining states. We use active optical switches to randomly sample from sources of two-photon Bell states and three-photon GHZ (Greenberger-Horn-Zeilinger) states, reporting statistically sound fidelities in real time without destroying the entire ensemble. In addition, our QSC protocol removes the assumption that the states are identically distributed (but still assumes independent copies); can achieve close N −1 scaling, in the number of states measured N ; and can be implemented in a device-independent manner. Together, these benefits make our QSC protocol suitable for benchmarking large-scale quantum computing devices and deployed quantum communication setups relying on entanglement in both standard and adversarial situations.
Proposals for linear optical quantum computation (LOQC) rely on quantum interference between single photons which, when coupled with photon detection, provides a mechanism to generate photonic entanglement. However, ideal quantum interference between photons only occurs if the photons are completely indistinguishable in all degrees of freedom except the one being interfered. In practice, no photons will be perfectly indistinguishable and therefore it is important to understand how using partially-distinguishable photons will affect the quantum information within the linear optical quantum computer. Here we describe how states of partially-distinguishable photons are transformed by linear-optical networks and measured by photon-counting detectors. In addition we show how to calculate the logical content of a given photonic state containing partially-distinguishable photons. Using a realistic model of single photon sources, we then apply these tools to calculate the resulting logical error rates on recent proposals for universal LOQC. Understanding the connection between physical imperfections and logical errors is crucial in assessing the fault-tolerance prospects of a quantum computation platform. Our results will help inform error correction strategies and allow one to specify the necessary fabrication and operational tolerances required for scalability.
Quantum photonic technologies have many exciting applications including secure commu- nication, quantum enhanced measurement and quantum computing. Linear optical quantum computing (LOQC) is a technology of particular interest - especially given that recent progress in on-chip waveguide technology removes the requirement for complex and costly bulk optics setups and state-of-the-art detectors have detection efficiencies of over 90%. Arguably the largest remaining technological hurdle for LOQC is the development of a suitable photon source. A suitable source would produce single, indistinguishable photons deterministically. Additionally, it would be beneficial if the generated photons were entangled, as this can significantly reduce the degree of multiplexing needed to implement LOQC. Quantum dots are a suitable candidate system for these photon sources as they exhibit bright single photon emission and can act as the interface between light and a trapped spin qubit. These properties have resulted in proposals to generate multi-photon entangled states suitable for use in LOQC. This thesis presents some of the progress we have made towards the creation of a suitable photon source. After introducing the background material, we demonstrate pulsed resonant excitation using a single-electron-charged quantum dot. Deterministic excitation is demonstrated by performing Rabi oscillations and Ramsey interference in the excitonic population. We also investigate Ramsey interference in a Faraday geometry magnetic field and observe a variety of beats and oscillations in the interferograms. We develop a model to explain our results and conclude that controlling the phase between the two Ramsey interference pulses allows a degree of control over the state of the trapped spin. We then also demonstrate the coherent optical manipulation of a trapped spin in a Voigt geometry magnetic field. Once we have presented the manipulation of the excitonic state and the state of the trapped spin, we proceed to investigate the properties of the light produced by the resonant excitation of a quantum dot. Hong Ou Mandel interference experiments allow us to probe the indistinguishability of the photons resulting from the resonant excitation of the negative trion transition. Repeating the measurement using light generated from a similar system (this time with a trapped hole rather than a trapped electron) that is embedded in a micropillar cavity, we find that the cavity enhancement of the transition results is higher indistinguishabilities. We make use of this bright source of indistinguishable photons to perform an on-chip quantum enhanced measurement and observe the phase superresolution associated with N00N states. In the final experimental chapter, we propose and implement a scheme to generate multi- qubit single photon states. We show that by repeatedly driving a micropillar-cavity-enhanced Raman transition of a single-hole-charged quantum dot in a Voigt geometry magnetic field it is possible to coherently superpose a photon across multiple time bins. The scheme is conceptually similar to proposed schemes for producing multi-photon entangled states. Lastly, we propose a scheme that makes use of the capabilities shown in the three experimental chapters to overcome several of the experimental difficulties associated with generating multi-photon entangled states.
Bosonic interference is a fundamental physical phenomenon, and it is believed to lie at the heart of quantum computational advantage. It is thus necessary to develop practical tools to witness its presence, both for a reliable assessment of a quantum source and for fundamental investigations. Here we describe how linear interferometers can be used to unambiguously witness genuine n-boson indistinguishability. The amount of violation of the proposed witnesses bounds the degree of multiboson indistinguishability, for which we also provide a novel intuitive model using set theory. We experimentally implement this test to bound the degree of three-photon indistinguishability in states we prepare using parametric down-conversion. Our approach results in a convenient tool for practical photonic applications, and may inspire further fundamental advances based on the operational framework we adopt.
Abstract Demonstrating quantum superiority for some computational task will be a milestone for quantum technologies and would show that computational advantages are possible not only with a universal quantum computer but with simpler physical devices. Linear optics is such a simpler but powerful platform where classically-hard information processing tasks, such as Boson Sampling, can be in principle implemented. In this work, we study a fundamentally different type of computational task to achieve quantum superiority using linear optics, namely the task of verifying NP-complete problems. We focus on a protocol by Aaronson et al. (2008) that uses quantum proofs for verification. We show that the proof states can be implemented in terms of a single photon in an equal superposition over many optical modes. Similarly, the tests can be performed using linear-optical transformations consisting of a few operations: a global permutation of all modes, simple interferometers acting on at most four modes, and measurement using single-photon detectors. We also show that the protocol can tolerate experimental imperfections.