@article{65575,
  abstract     = {{<jats:p>For the ever-growing field of quantum information processing, large-scale, efficient multiport interferometers serving as photonic processors are required. In this context, the suitability of quantum walks as the interferometric base for universal computation has been theoretically proven. In this work, we bridge the gap between theoretical proposals and state-of-the-art experimental capabilities by providing the recipe for the implementation of a universal photonic processor in discrete-time quantum walks. Specifically, we present the protocol for translating arbitrary linear transformations into the coin and step operator of a quantum walk and map these to the experimental parameters of the established time-multiplexed platform [A. Schreiber , Phys. Rev. Lett. , 050502 (2010)]. We show that our interface is highly scalable and resource efficient due to the hybrid encoding consisting of multiple degrees of freedom. Finally, we prove that our system is highly resilient against experimental imperfections and show that it compares favorably against existing architectures.</jats:p>}},
  author       = {{Lammers, Jonas and Ares, Laura and Pegoraro, Federico and Held, Philip and Brecht, Benjamin and Sperling, Jan and Silberhorn, Christine}},
  issn         = {{2331-7019}},
  journal      = {{Physical Review Applied}},
  number       = {{5}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Resource-efficient universal photonic processors based on time-multiplexed hybrid architectures}}},
  doi          = {{10.1103/x99y-2sms}},
  volume       = {{25}},
  year         = {{2026}},
}

@article{65574,
  author       = {{Pinske, Julien and Sperling, Jan and Mølmer, Klaus}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{5}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Entangling power of nonentangling channels}}},
  doi          = {{10.1103/vy93-dnc8}},
  volume       = {{113}},
  year         = {{2026}},
}

@article{65777,
  abstract     = {{<jats:title>Abstract</jats:title>
                  <jats:p>In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states, together with the discretization of the space of variables for numerical computations. As a first approach, we apply linear splitting methods to the restricted, continuous equations of motion derived from variational principles. We utilize an exchange interaction Hamiltonian to confirm that the numerical and analytical solutions coincide in the limit of small time steps. The application to different Hamiltonians shows the wide applicability of the method to detect dynamical entanglement. To avoid the derivation of analytical solutions for complex dynamics, we consider variational, numerical integration schemes, introducing a variational discretization for Lagrangians linear in velocities. Here, we examine and compare two approaches: one in which the system is discretized before the restriction is applied, and another in which the restriction precedes the discretization. We find that the ‘first-discretize-then-restrict’ method becomes numerically unstable, already for the example of an exchange-interaction Hamiltonian, which can be an important consideration for the numerical analysis of constrained quantum dynamics. Thereby, broadly applicable numerical tools, including their limitations, for studying entanglement over time are established for assessing the entangling power of processes that are used in quantum information theory.</jats:p>}},
  author       = {{Offen, Christian and Wembe Moafo, Boris Edgar and Ares, Laura and Sperling, Jan and Ober-Blöbaum, Sina}},
  issn         = {{1751-8113}},
  journal      = {{Journal of Physics A: Mathematical and Theoretical}},
  number       = {{22}},
  publisher    = {{IOP Publishing}},
  title        = {{{Numerical approaches to entangling dynamics from variational principles}}},
  doi          = {{10.1088/1751-8121/ae6d51}},
  volume       = {{59}},
  year         = {{2026}},
}

@article{66640,
  abstract     = {{<jats:p>
                    We develop a framework for identifying nonclassical speedups in systems with polarization, likewise spin degrees of freedom. By confining the dynamics to the manifold of angular momentum coherent states, which act as the classical reference in this case, we compute the speed limit that bounds the rate of change of the state achievable without generating quantum coherence. A comparison with the unrestricted quantum speed limit enables the quantitative identification of speedups arising from polarization nonclassicality. We apply this framework to the cross-Kerr interaction, demonstrating a persistent speedup scaling as
                    <a:math xmlns:a="http://www.w3.org/1998/Math/MathML">
                      <a:mrow>
                        <a:mi mathvariant="script">O</a:mi>
                        <a:mo>(</a:mo>
                        <a:msqrt>
                          <a:mi>N</a:mi>
                        </a:msqrt>
                        <a:mo>)</a:mo>
                      </a:mrow>
                    </a:math>
                    with the photon number
                    <c:math xmlns:c="http://www.w3.org/1998/Math/MathML">
                      <c:mi>N</c:mi>
                    </c:math>
                    , with a parity effect in favor of even photon numbers. The results establish polarization nonclassicality as a genuine dynamical resource, linking quantum coherence to quantum-enhanced evolution speeds in nonlinear photonic systems.
                  </jats:p>}},
  author       = {{Aßbrock, Tim and Sperling, Jan and Ares, Laura}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Quantum speedup from nonclassical polarization}}},
  doi          = {{10.1103/mflc-2mzq}},
  volume       = {{8}},
  year         = {{2026}},
}

@article{61245,
  author       = {{Barkhausen, Franziska and Ares Santos, Laura and Schumacher, Stefan and Sperling, Jan}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Entanglement between dependent degrees of freedom: Quasiparticle correlations}}},
  doi          = {{10.1103/physreva.111.032404}},
  volume       = {{111}},
  year         = {{2025}},
}

@article{60992,
  abstract     = {{Non-Hermitian systems hosting exceptional points (EPs) exhibit enhanced sensitivity and unconventional mode dynamics. Going beyond isolated EPs, here we report on the existence of exceptional rings (ERs) in planar optical resonators with specific form of circular dichroism and TE-TM splitting. Such exceptional rings possess intriguing topologies as discussed earlier for condensed matter systems, but they remain virtually unexplored in presence of nonlinearity, for which our photonic platform is ideal. We find that when Kerr-type nonlinearity (or saturable gain) is introduced, the linear ER splits into two concentric ERs, with the larger-radius ring being a ring of third-order EPs. Transitioning from linear to nonlinear regime, we present a rigorous analysis of spectral topology and report enhanced and adjustable perturbation response in the nonlinear regime. Whereas certain features are specific to our system, the results on non-Hermitian spectral topology and nonlinearity-enhanced perturbation response are generic and equally relevant to a broad class of other nonlinear non-Hermitian systems, providing a universal framework for engineering ERs and EPs in nonlinear non-Hermitian systems.}},
  author       = {{Wingenbach, Jan and Ares Santos, Laura  and Ma, Xuekai and Sperling, Jan and Schumacher, Stefan}},
  journal      = {{Arxiv}},
  publisher    = {{Arxiv}},
  title        = {{{Sensitivity and Topology of Exceptional Rings in Nonlinear Non-Hermitian Planar Optical Microcavities}}},
  doi          = {{10.48550/ARXIV.2507.07099}},
  year         = {{2025}},
}

@article{62980,
  abstract     = {{<jats:p>We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which is in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.</jats:p>}},
  author       = {{Kopylov, Denis A. and Offen, Christian and Ares, Laura and Wembe Moafo, Boris Edgar and Ober-Blöbaum, Sina and Meier, Torsten and Sharapova, Polina R. and Sperling, Jan}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{3}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Multiphoton, multimode state classification for nonlinear optical circuits}}},
  doi          = {{10.1103/sv6z-v1gk}},
  volume       = {{7}},
  year         = {{2025}},
}

@article{63021,
  abstract     = {{<jats:p>Bell measurements, entailing the projection onto one of the Bell states, play a key role in quantum information and communication, where the outcome of a variety of protocols crucially depends on the success probability of such measurements. Although in the case of qubit systems, Bell measurements can be implemented using only linear optical components, the same result is no longer true for qudits, where at least the use of ancillary photons is required. In order to circumvent this limitation, one possibility is to introduce nonlinear effects. In this work, we adopt the latter approach and propose a scalable Bell measurement scheme for high-dimensional states, exploiting multiple squeezer devices applied to a linear optical circuit for discriminating the different Bell states. Our approach does not require ancillary photons, is not limited by the dimension of the quantum states, and is experimentally scalable, thus paving the way toward the realization of an effective high-dimensional Bell measurement.</jats:p>}},
  author       = {{Bianchi, Luca and Marconi, Carlo and Sperling, Jan and Bacco, Davide}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Predetection squeezing as a resource for high-dimensional Bell-state measurements}}},
  doi          = {{10.1103/physrevresearch.7.023038}},
  volume       = {{7}},
  year         = {{2025}},
}

@article{63534,
  abstract     = {{<jats:p>Boson sampling is a key candidate for demonstrating quantum advantage and has already yielded significant advances in quantum simulation, machine learning, and graph theory. In this work, a unification and extension of distinct forms of boson sampling is developed. The devised protocol merges discrete-variable scattershot boson sampling with continuous-variable Gaussian boson sampling. Therefore, it is rendered possible to harness the complexity of more interesting states, such as squeezed photons, in advanced sampling protocols. A generating function formalism is developed for the joint description of multiphoton and multimode light undergoing Gaussian transformations. The resulting analytical tools enable one to explore interfaces of different photonic quantum-information-processing platforms. A numerical simulation of unified sampling is carried out, benchmarking its performance, complexity, and scalability. Entanglement is characterized to exemplify the generation of quantum correlations from the nonlinear interactions of a unified sampler.</jats:p>}},
  author       = {{Bianchi, Luca and Marconi, Carlo and Ares, Laura and Bacco, Davide and Sperling, Jan}},
  issn         = {{2643-1564}},
  journal      = {{Physical Review Research}},
  number       = {{4}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Unified boson sampling}}},
  doi          = {{10.1103/8hy1-m5gg}},
  volume       = {{7}},
  year         = {{2025}},
}

@article{54093,
  author       = {{Pinske, Julien and Sperling, Jan}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{5}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Unbreakable and breakable quantum censorship}}},
  doi          = {{10.1103/physreva.109.052408}},
  volume       = {{109}},
  year         = {{2024}},
}

@article{55140,
  author       = {{Yasmin, Farha and Sperling, Jan}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Entanglement-assisted quantum speedup: Beating local quantum speed limits}}},
  doi          = {{10.1103/physreva.110.012424}},
  volume       = {{110}},
  year         = {{2024}},
}

@article{55173,
  author       = {{Di Fidio, Christian and Ares, Laura and Sperling, Jan}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Quantum walks and entanglement in cavity networks}}},
  doi          = {{10.1103/physreva.110.013705}},
  volume       = {{110}},
  year         = {{2024}},
}

@article{57743,
  author       = {{Krishnaswamy, Suchitra and Schlue, Fabian and Ares, L. and Dyachuk, V. and Stefszky, Michael and Brecht, Benjamin and Silberhorn, Christine and Sperling, Jan}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{2}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Experimental retrieval of photon statistics from click detection}}},
  doi          = {{10.1103/physreva.110.023717}},
  volume       = {{110}},
  year         = {{2024}},
}

@article{44050,
  author       = {{Sperling, Jan and Agudelo, Elizabeth}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{4}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Entanglement of particles versus entanglement of fields: Independent quantum resources}}},
  doi          = {{10.1103/physreva.107.042420}},
  volume       = {{107}},
  year         = {{2023}},
}

@article{40477,
  author       = {{Sperling, Jan and Gianani, Ilaria and Barbieri, Marco and Agudelo, Elizabeth}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{1}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Detector entanglement: Quasidistributions for Bell-state measurements}}},
  doi          = {{10.1103/physreva.107.012426}},
  volume       = {{107}},
  year         = {{2023}},
}

@article{42973,
  author       = {{Lüders, Carolin and Pukrop, Matthias and Barkhausen, Franziska and Rozas, Elena and Schneider, Christian and Höfling, Sven and Sperling, Jan and Schumacher, Stefan and Aßmann, Marc}},
  issn         = {{0031-9007}},
  journal      = {{Physical Review Letters}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{11}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Tracking Quantum Coherence in Polariton Condensates with Time-Resolved Tomography}}},
  doi          = {{10.1103/physrevlett.130.113601}},
  volume       = {{130}},
  year         = {{2023}},
}

@article{61266,
  abstract     = {{<jats:p>This review examines the use of continuous-variable spectroscopy techniques for investigating quantum coherence and light-matter interactions in semiconductor systems with ultrafast dynamics. Special emphasis is placed on multichannel homodyne detection as a powerful tool to measure the quantum coherence and the full density matrix of a polariton system. Observations, such as coherence times that exceed the nanosecond scale obtained by monitoring the temporal decay of quantum coherence in a polariton condensate, are discussed. Proof-of-concept experiments and numerical simulations that demonstrate the enhanced resourcefulness of the produced system states for modern quantum protocols are assessed. The combination of tailored resource quantifiers and ultrafast spectroscopy techniques that have recently been demonstrated paves the way for future applications of quantum information technologies.</jats:p>}},
  author       = {{Lüders, Carolin and Barkhausen, Franziska and Pukrop, Matthias and Rozas, Elena and Sperling, Jan and Schumacher, Stefan and Aßmann, Marc}},
  issn         = {{2159-3930}},
  journal      = {{Optical Materials Express}},
  number       = {{11}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Continuous-variable quantum optics and resource theory for ultrafast semiconductor spectroscopy [Invited]}}},
  doi          = {{10.1364/ome.497006}},
  volume       = {{13}},
  year         = {{2023}},
}

@inproceedings{43744,
  abstract     = {{We demonstrate theoretically and experimentally complex correlations in the photon numbers of two-mode quantum states using measurement-induced nonlinearity. For this, we combine the interference of coherent states and single photons with photon sub-traction.}},
  author       = {{Meier, Torsten and Hoepker, Jan Philipp and Protte, Maximilian and Eigner, Christof and Silberhorn, Christine and Sharapova, Polina R. and Sperling, Jan and Bartley, Tim}},
  booktitle    = {{Conference on Lasers and Electro-Optics: Applications and Technology}},
  isbn         = {{978-1-957171-05-0}},
  location     = {{San Jose, California United States}},
  pages        = {{JTu3A. 17}},
  publisher    = {{Optica Publishing Group}},
  title        = {{{Two-Mode Photon-Number Correlations Created by Measurement-Induced Nonlinearity}}},
  doi          = {{10.1364/CLEO_AT.2022.JTu3A.17}},
  year         = {{2022}},
}

@article{34884,
  author       = {{Prasannan, Nidhin and Sperling, Jan and Brecht, Benjamin and Silberhorn, Christine}},
  issn         = {{0031-9007}},
  journal      = {{Physical Review Letters}},
  keywords     = {{General Physics and Astronomy}},
  number       = {{26}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Direct Measurement of Higher-Order Nonlinear Polarization Squeezing}}},
  doi          = {{10.1103/physrevlett.129.263601}},
  volume       = {{129}},
  year         = {{2022}},
}

@article{30921,
  abstract     = {{Quantum walks function as essential means to implement quantum simulators, allowing one to study complex and often directly inaccessible quantum processes in controllable systems. In this contribution, the notion of a driven Gaussian quantum walk is introduced. In contrast to typically considered quantum walks in optical settings, we describe the operation of the walk in terms of a nonlinear map rather than a unitary operation, e.g., by replacing a beam-splitter-type coin with a two-mode squeezer, being a process that is controlled and driven by a pump field. This opens previously unattainable possibilities for quantum walks that include nonlinear elements as core components of their operation, vastly extending their range of applications. A full framework for driven Gaussian quantum walks is developed, including methods to dynamically characterize nonlinear, quantum, and quantum-nonlinear effects. Moreover, driven Gaussian quantum walks are compared with their classically interfering and linear counterparts, which are based on classical coherence of light rather than quantum superpositions. In particular, the generation and boost of highly multimode entanglement, squeezing, and other quantum effects are studied over the duration of the nonlinear walk. Importantly, we prove the quantumness of the evolution itself, regardless of the input state. A scheme for an experimental realization is proposed. Furthermore, nonlinear properties of driven Gaussian quantum walks are explored, such as amplification that leads to an ever increasing number of correlated quantum particles, constituting a source of new walkers during the walk. Therefore, a concept for quantum walks is proposed that leads to—and even produces—directly accessible quantum phenomena, and that renders the quantum simulation of nonlinear processes possible.}},
  author       = {{Held, Philip and Engelkemeier, Melanie and De, Syamsundar and Barkhofen, Sonja and Sperling, Jan and Silberhorn, Christine}},
  issn         = {{2469-9926}},
  journal      = {{Physical Review A}},
  number       = {{4}},
  publisher    = {{American Physical Society (APS)}},
  title        = {{{Driven Gaussian quantum walks}}},
  doi          = {{10.1103/physreva.105.042210}},
  volume       = {{105}},
  year         = {{2022}},
}