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Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of Riemannian geometry to perform optimization on the manifolds of unitary and isometric matrices as well as the cone of positive-definite matrices. Combining this approach with the up-to-date computational methods of automatic differentiation, we demonstrate the efficacy of the Riemannian optimization in the study of the low-energy spectrum and eigenstates of multipartite Hamiltonians, variational search of a tensor network in the form of the multiscale entanglement-renormalization ansatz, preparation of arbitrary states (including highly entangled ones) in the circuit implementation of quantum computation, decomposition of quantum gates, and tomography of quantum states. Universality of the developed approach together with the provided open source software enable one to apply the Riemannian optimization to complex quantum architectures well beyond the listed problems, for instance, to the optimal control of noisy quantum systems.

We analyse the properties and dynamics of generalized squeezed states. We find that, in stark contrast to displacement and two-photon squeezing, higher-order squeezing leads to oscillatory dynamics. The state is squeezed in the initial stages of the dynamics but the squeezing reverses at later stages, and the state reverts almost completely back to the initial state. We analyse various quantities to verify that the oscillatory dynamics is physical and not a mathematical artefact. We also show that the maximum squeezing diminishes with increasing squeezing order, rendering the squeezing mechanism increasingly ineffective. Our results provide important rules that can help guide the development of more effective higher-order squeezing techniques.

In our paper (Ashhab and Ayyash 2025 New J. Phys. 27 054104), our numerical simulations showed that, unlike displacement and conventional squeezing, higher-order squeezing exhibits oscillatory dynamics. Subsequently, Gordillo and Puebla pointed out that simulation results depend on whether the size of the state space in the simulations is even or odd (Gordillo and Puebla 2026 arXiv:2507.12250). Using additional derivations, they argued that the oscillatory dynamics is unphysical and that the photon number must increase monotonically as a function of the squeezing parameter r . We agree with the observation of an even–odd parity dependence in the simulations. We independently noticed the same feature in our simulations after the publication of Ashhab and Ayyash (2025 New J. Phys. 27 054104). This observation led us to perform a more detailed investigation of the numerical simulation and mathematical aspects of the generalized squeezing problem. Our new findings were reported in Ashhab et al (2026 Phys. Rev. A 113 013703). Further analysis was reported in Fischer et al (2025 arXiv:2508.09044). Our conclusion is that the generalized squeezing operator is physically not well defined but can be made well defined when combined with additional information about the physical system under study. We demonstrated this point in the case where we include an additional nonlinear interaction term in the Hamiltonian. We disagree with the claim that the photon number must be a monotonically increasing function of r . This claim contradicts the mathematically rigorous results of Fischer et al (2025 arXiv:2508.09044). Furthermore, we show that the oscillatory behaviour persists in two closely related, well-behaved models.

The generation and manipulation of hybrid entanglement of light involving discrete- and continuous-variable states have recently appeared as essential resources towards the realization of heterogeneous quantum networks. Here we investigate a scheme for the remote generation of hybrid entanglement between particle-like and wave-like optical qubits based on a non-local heralding photon detection. We also extend this scheme with additional local or non-local detections. An additional local heralding allows the resulting state to exhibit a higher fidelity with the targeted entangled qubits while a two-photon non-local heralding detection gives access to a higher dimensionality in the discrete-variable subspace, resulting thereby in the generation of hybrid entangled qutrits. The implementation of the presented schemes, in combination with ongoing works on high-fidelity quantum state engineering, will provide novel non-classical light sources for the development of optical hybrid architectures.

The interaction of a three-level atom with the electromagnetic field of a quantum cavity in the presence of a laser field presents a rich behavior in the dispersive regime that we exploit to discuss two quantum batteries. In the first setup, we consider a single three-level atom interacting sequentially with many cavities, each in a thermal state. We show that under this process, the atom converges towards an equilibrium state that displays population inversion. In the second setup, a stream of atoms in a thermal state interacts sequentially with a single cavity initially in a thermal state at the same temperature as the atoms. We show that the cavity’s energy increases continuously as the stream of atoms continues to cross, and the cavity does not reach an equilibrium state. After many atoms have traveled, the cavity’s state becomes active, storing extractable energy that increases in proportion to the work done by the laser. However, the same dynamics may involve only two cavity levels in an interesting limit called the highly selective regime. In that regime, the cavity reaches an equilibrium state similar to the one of the atom in the first scenario. The charging process we propose is robust. We discuss its thermodynamics and evaluate the energy supplied by the laser, the energy stored in the battery, and, thus, the device’s efficiency. We also analyze the role of damping.

A recent article (Ashhab and Ayyash 2025 New J. Phys. 27 , 054104) has reported unexpected oscillatory dynamics in generalized squeezed states of order higher than two as their squeezing parameter increases. This behaviour, observed through numerical simulations using truncated bosonic annihilation and creation operators, appeared in several properties of these states, including their average photon number. The authors argued that these oscillations reflect a genuine physical effect. Here, however, we demonstrate that the observed oscillatory behaviour is a consequence of numerical artefacts. A numerical analysis reveals that the oscillations are highly sensitive to the truncation of the Fock basis, indicating a lack of convergence. This is further supported by a theoretical analysis of the Taylor series of the average photon number, suggesting that these generalized squeezed states contain infinite energy after a finite value of the squeezing parameter. Finally, we provide an analytical proof that the average photon number of any generalized squeezed state is a non-decreasing function, thereby ruling out the possibility of intrinsic oscillatory dynamics. We hope these results help clarify the origin of the reported oscillations and highlight the special care required when dealing with high-order squeezing states.

In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a phase shift to a high precision. Our algorithm efficiently produces a number of novel solutions: we find experimentally ready schemes to produce states that show significant improvements over the state-of-the-art, and can measure with a precision that beats the shot noise limit by over a factor of 4. Furthermore, these states demonstrate a robustness to moderate/high photon losses, and we present a conceptually simple measurement scheme that saturates the Cramér-Rao bound.

The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.

We explore a recently demonstrated deterministic photon subtraction scheme, based on single-photon Raman interaction with a Λ-type three-level atom, as a tool for manipulating quantum state of few-photon light pulses. We establish a comprehensive theoretical framework using input–output formalism and quantum regression theorem, enabling calculation of the first order autocorrelation matrices of the output light and identification of the temporal modes present in the generated light via their eigendecomposition. By modeling the entire system as a quantum network consisting multiple virtual cavities and a lambda-type emitter cascaded in two parallel guided modes of opposite propagation directions, we extract the quantum state occupying the modes of interest. For both squeezed vacuum and coherent light input pulses, the Wigner function of the output light after photon subtraction clearly reveals its non-Gaussian character. Furthermore, we propose a measurement-based scheme on the subtracted photon which can lead to conditional generation of quantum states resembling Schrodinger’s kitten state directly from coherent input light with fidelities above 99%. This result is particularly nothworthy, as coherent pulses, unlike the squeezed vacuum inputs commonly used in previous studies, are readily available in most experimental setups.

Cavity magnomechanics has become an ideal platform to explore macroscopic quantum effects. Bringing together magnons, phonons, and photons in a system, it opens many opportunities for quantum technologies. It was conventionally realized by an yttrium iron garnet, which exhibits a parametric magnon–phonon coupling m ˆ † m ˆ ( b ˆ † + b ˆ ) , with m ˆ and b ˆ being the magnon and phonon modes. Inspired by the recent realization of two-dimensional (2D) magnets, we propose a cavity magnomechanical system using a 2D magnetic material with both optical and magnetic drivings. It features the coexisting photon–phonon radiation-pressure coupling and quadratic magnon–phonon coupling m ˆ † m ˆ ( b ˆ † + b ˆ ) 2 induced by the magnetostrictive interaction. A stable squeezing of the phonon and bi- and tri-partite entanglements among the three modes are generated in the regimes with a suppressed phonon number. Compared with previous schemes, ours does not require any extra nonlinear interaction and reservoir engineering and is robust against the thermal fluctuation. Enriching the realization of cavity magnomechanics, our system exhibits its superiority in quantum-state engineering due to the versatile interactions enabled by its 2D feature.