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Quantum non-Gaussian states of light have fundamental properties that are essential for a multitude of applications in quantum technology. However, many of these features are difficult to detect using standard criteria due to optical losses and detector inefficiency. As the statistics of light are unknown, the loss correction on the data is unreliable, despite the fact that the losses can be precisely measured. To address this issue, we employ a loss-mitigated verification technique utilising quantum non-Gaussian witnesses, which incorporate the known optical losses and detector inefficiency into their derivation. This approach allows us to address the considerable challenge of experimentally demonstrating unheralded quantum non-Gaussian states of single photons and photon pairs., Comment: 5 pages, 3 figures and supplemental material (2 pages)

Emitters of single-photons are essential resources for emerging quantum technologies and developed within different platforms including nonlinear optics, atomic and solid-state systems. The energy level structures of emission processes are critical for reaching and controlling high-quality sources. The most commonly applied test uses a Hanbury-Brown and Twiss (HBT) setup to determine the emitter energy level structure based on fitting temporal correlations of photon detection events. However, only partial information about the emission process is extracted from such detection, that might be followed by an inconclusive fitting of the data. This process predetermines our limited ability to quantify and understand the dynamics in the photon emission process that are of importance for the applications in communication, sensing and computing. In this work, we present a complete analysis based on all normalized coincidences between detection and no-detection events recorded in the same HBT setup to certify expected properties of an emitted photonic state. As a proof of concept we apply our methodology to single nitrogen-vacancy centers in diamond, in which case the certification conclusively rejects a model based on a two-level emitter that radiates a photonic states mixed with any classical noise background., Comment: 15 pages, 8 figures

We analyze dynamics of the Rabi model describing interactions of a qubit with a single soft-mode oscillator. We show that the model with a slightly violated parity generates symmetric Schr{\"o}dinger cat states of the oscillator, which suddenly perish in a spontaneous unitary process similar to the measurement-induced wave-function collapse. The effect is sufficiently robust to be tested experimentally, e.g., with trapped ions, macroscopic mechanical oscillators or superconducting circuits., Comment: 8 pages, 7 figures

Quantum non-Gaussian states of phononic systems coupled to light are essential for fundamental studies of single-phonon mechanics and direct applications in quantum technology. Although nonclassical mechanical states have already been demonstrated, more challenging quantum non-Gaussianity of such states remains limited. Using photon counting detection, we propose the quantum non-Gaussian generation of few-phonon states of low-temperature vibrating superfluid Helium. We predict the quantum non-Gaussian depth of such phononic states and investigate their robustness under relevant mechanical heating. As the quality of such phononic states is very high, we confirm a single-phonon bunching capability to further classify such states for future mechanical experiments. Moreover, we predict increasing capability for force sensing and thermometry for increasing heralded phonon numbers., Comment: 7+8 pages, 5+2 figures

Quantum non-Gaussian states are crucial for the fundamental understanding of non-linear bosonic systems and simultaneously advanced applications in quantum technologies. In many bosonic experiments the important quantum non-Gaussian feature is the negativity of the Wigner function, a cornerstone for quantum computation with bosons. Unfortunately, the negativities present in complex quantum states are extremely vulnerable to the effects of decoherence, such as energy loss, noise and dephasing, caused by the coupling to the environment, which is an unavoidable part of any experimental implementation. An efficient way to mitigate its effects is by adapting quantum states into more resilient forms. We propose an optimal protection of superpositions of coherent states against a sequence of asymmetric thermal lossy channels by suitable squeezing operations.

Nonlinear processes with individual quanta beyond bilinear interactions are essential for quantum technology with bosonic systems. Diverse coherent splitting and merging of quanta in them already manifest in the estimation of their nonlinear coupling from observed statistics. We derive non-trivial, but optimal strategies for sensing the basic and experimentally available trilinear interactions using non-classical particle-like Fock states as a probe and feasible measurement strategies. Remarkably, the optimal probing of nonlinear coupling reaches estimation errors scaled down with $N^{-1/3}$ for overall $N$ of quanta in specific but available high-quality Fock states in all interacting modes. It can reveal unexplored aspects of nonlinear dynamics relevant to using such nonlinear processes in bosonic experiments with trapped ions and superconducting circuits and opens further developments of quantum technology with them.

Measurement-induced quantum computation with continuous-variable cluster states utilizes teleportation propagating the states through the cluster accompanied by non-Gaussian measurements and feedforward control. We analyze such propagation of a quantum non-Gaussian state with nonlinear squeezing through a small cluster state and show that when a nonlinear feedforward is involved in the teleportation protocol, higher nonlinear squeezing can be transferred. In a probabilistic regime, the improvement can be manifested even with current experimental resources. Better processing of non-Gaussian states can bring us closer to the necessary interplay between cluster states and non-Gaussianity required by quantum computing., Comment: references added

Quantum metrology offers superior measurement precision compared to classical counterparts. Traditionally, achieving this enhancement involves employing multi-particle entangled quantum states, necessitating state preparation and detection schemes that are practically challenging. In this article, we present a versatile and on-demand protocol for deterministic parameter estimation that leverages two state-transfer operations on a single bosonic mode. Specifically, we demonstrate this protocol in the context of phase and amplitude estimation using the superposition of coherent states in the bosonic circuit quantum electrodynamics (cQED) platform. With low photon numbers of up to 1.76, we achieve quantum-enhanced precision approaching the Heisenberg scaling, reaching a metrological gain of 7.5(6) dB and 9.3(5) dB respectively for phase and amplitude estimation. We show that the gain or sensitivity range can be further enhanced on the fly by tailoring the input states based on specific system constraints. Our protocol can be adapted to further optimize the desired figures of merit using tailored quantum states or operations, not only for bosonic cQED hardware but also readily extensible to other continuous-variable platforms. The realisation of this versatile and effective scheme affords a promising path towards practical quantum-enhanced sensing., Comment: Main text (4 figures, 5 pages without references) and Supplementary text (6 figures, 5 pages)

Bosonic systems with negative Wigner function superposition states are fundamentally witnessing nonlinear quantum dynamics beyond linearized systems and, recently, have become essential resources of quantum technology with many applications. Typically, they appear due to sophisticated combination of external drives, nonlinear control, measurements or strong nonlinear dissipation of subsystems to an environment. Here, we propose a conceptually different and more autonomous way to obtain such states, avoiding these ingredients, using purely sudden interaction decay in the paradigmatic interacting qubit-oscillator system weakly coupled to bath at thermal equilibrium in a low-temperature limit. We demonstrate simultaneously detectable unconditional negative Wigner function and quantum coherence and their qualitative enhancement employing more qubits.

A contactless control of fluctuations of phase space variables of a nanoobject belongs among the key methods needed for ultra-precise nanotechnology and the upcoming quantum technology of macroscopic systems. Here we utilize the experimental platform of a single levitating nanoparticle (NP) to demonstrate essential protocols providing linear amplification of the mechanical phase space variables together with squeezing of phase space probability distribution. The protocol combines a controlled fast switching between the parabolic trapping potential and either weak parabolic or inverted parabolic amplifying potential leading to amplification of mean value and variance (fluctuations) along an arbitrary phase space variable and squeezing along the complementary one. The protocol is completed with cold damping scheme to control the initial fluctuations of the NP phase space variables. We reached the amplification gain $|G|>2$, the squeezing coefficient above 4 dB, and the second-order energy correlation function approaching 3 which corresponds to a maximum for a stochastic non-equilibrium classical state. These experimental results will already allow pre-amplification and manipulation of nanomechanical NP motion for all quantum protocols if the NP cooling towards the ground state is applied.

Three-dimensional microwave cavity resonators have been shown to reach lifetimes of the order of a second by maximizing the cavity volume relative to its surface, using better materials, and improving surface treatments. Such cavities represent an ideal platform for quantum computing with bosonic qubits, but their efficient control remains an outstanding problem since the large mode volume results in inefficient coupling to nonlinear elements used for their control. Moreover, this coupling induces additional cavity decay via the inverse Purcell effect which can easily destroy the advantage of a long intrinsic lifetime. Here, we discuss conditions on, and protocols for, efficient utilization of these ultra-high-quality microwave cavities as memories for conventional superconducting qubits. We show that, surprisingly, efficient write and read operations with ultra-high-quality cavities does not require similar quality factors for the qubits and other nonlinear elements used to control them. Through a combination of analytical and numerical calculations, we demonstrate that efficient coupling to cavities with second-scale lifetime is possible with state-of-the-art transmon and SNAIL devices and outline a route towards controlling cavities with even higher quality factors. Our work explores a potentially viable roadmap towards using ultra-high-quality microwave cavity resonators for storing and processing information encoded in bosonic qubits., Comment: 23 pages (incl. appendices), 8 figures, 2 tables

Building scalable and secure quantum networks with many users has a high application potential but also holds many practical challenges. A significant stride in this pursuit involves extending quantum key distribution, an information-theoretically secure method for establishing cryptographic keys between two distant users, from a point-to-point protocol implemented on direct optical connections to a quantum access network. Yet, realizations of quantum access networks have, so far, relied on probabilistic or time-sharing strategies. Here, we show theoretically and experimentally that a solution without these constraints can come from the exclusive features of continuous-variable systems. Based on coherent states, we propose continuous-variable quantum passive-optical-network (CV-QPON) protocols, enabling deterministic and simultaneous secret key generation among all network users. We achieve this by leveraging the inherent wave-like property of coherent states split at a beam splitter and electric-field quadrature measurements. We show two protocols with different trust levels assigned to the network users and experimentally demonstrate key generation in a quantum access network with 8 users, each with an 11 km span of access link. Depending on the trust assumptions about users, we reach 1.5 Mbits/s and 2.1 Mbits/s of total network key generation. Demonstrating the potential to expand the network's capacity to accommodate tens of users at a high rate, our CV-QPON protocols offer a pathway toward establishing low-cost, high-rate, and scalable quantum access networks using standard telecom technologies and directly exploiting the existing access network infrastructure.

Quantum simulations provide means to probe challenging problems within controllable quantum systems. However, implementing or simulating deep-strong nonlinear couplings between bosonic oscillators on physical platforms remains a challenge. We present a deterministic simulation technique that efficiently and accurately models nonlinear bosonic dynamics. This technique alternates between tunable Rabi and SNAP gates, both of which are available on experimental platforms such as trapped ions and superconducting circuits. Our proposed simulation method facilitates high-fidelity modeling of phenomena that emerge from higher-order bosonic interactions, with an exponential reduction in resource usage compared to other techniques. We demonstrate the potential of our technique by accurately reproducing key phenomena and other distinctive characteristics of ideal nonlinear optomechanical systems. Our technique serves as a valuable tool for simulating complex quantum interactions, simultaneously paving the way for new capabilities in quantum computing through the use of hybrid qubit-oscillator systems.

We show that the methods for quantification of system-environment entanglement that were recently developed for interactions that lead to pure decoherence of the system can be straightforwardly generalized to time-dependent Hamiltonians of the same type. This includes the if-and-only-if criteria of separability, as well as the entanglement measure applicable to qubit systems, and methods of detection of entanglement by operations and measurements performed solely on the system without accessing the environment. We use these methods to study the nature of the decoherence of a qubit-oscillator system. Qubit-oscillator entanglement is essential for developing bosonic quantum technology with quantum non-Gaussian states and its applications in quantum sensing and computing. The dominating bosonic platforms, trapped ions, electromechanics, and superconducting circuits, are based on the time-dependent gates that use such entanglement to achieve new quantum sensors and quantum error correction. The step-like time-dependence of the Hamiltonian that is taken into account allows us to capture complex interplay between the build-up of classical and quantum correlations, which could not be replicated in time-independent scenarios., Comment: 9 pages, 3 figures

Current advances in nonlinear optics have made it possible to perform a homodyne-like tomography of an unknown state without highly efficient detectors or a strong local oscillator. Thereby, a new experimental direction has been opened into multimode and large-bandwidth quantum optics. An optical parametric amplifier (OPA) allows us to reconstruct the quadrature distribution of an unknown state directly from the measured intensity distribution with high precision. We propose adding a controllable displacement to the standard scheme, obtaining an improved method applicable even to asymmetric and non-Gaussian states while significantly increasing estimation accuracy and lowering the OPA amplification requirement. To demonstrate the power of our method, we accurately detect the sub-Planck phase-space structure by a distillable squeezing from the OPA estimates of various non-Gaussian states. With the improvements, OPA tomography became a generally applicable loss-tolerant and efficient alternative to OPA-assisted homodyne detection., Comment: 14 pages, 15 figures

A quantum computer with low-error, high-speed quantum operations and capability for interconnections is required for useful quantum computations. A logical qubit called Gottesman-Kitaev-Preskill (GKP) qubit in a single Bosonic harmonic oscillator is efficient for mitigating errors in a quantum computer. The particularly intriguing prospect of GKP qubits is that entangling gates as well as syndrome measurements for quantum error correction only require efficient, noise-robust linear operations. To date, however, GKP qubits have been only demonstrated at mechanical and microwave frequency in a highly nonlinear physical system. The physical platform that naturally provides the scalable linear toolbox is optics, including near-ideal loss-free beam splitters and near-unit efficiency homodyne detectors that allow to obtain the complete analog syndrome for optimized quantum error correction. Additional optical linear amplifiers and specifically designed GKP qubit states are then all that is needed for universal quantum computing. In this work, we realize a GKP state in propagating light at the telecommunication wavelength and demonstrate homodyne meausurements on the GKP states for the first time without any loss corrections. Our GKP states do not only show non-classicality and non-Gaussianity at room temperature and atmospheric pressure, but unlike the existing schemes with stationary qubits, they are realizable in a propagating wave system. This property permits large-scale quantum computation and interconnections, with strong compatibility to optical fibers and 5G telecommunication technology., Comment: 11 pages, 5 figures

Quantum non-Gaussianity, a more potent and highly useful form of nonclassicality, excludes all convex mixtures of Gaussian states and Gaussian parametric processes generating them. Here, for the first time, we conclusively test quantum non-Gaussian coincidences of entangled photon pairs with the CHSH-Bell factor $S=2.328\pm0.004$ from a single quantum dot with a depth up to $0.94\pm 0.02$ dB. Such deterministically generated photon pairs fundamentally overcome parametric processes by reducing crucial multiphoton errors. For the quantum non-Gaussian depth of the unheralded (heralded) single-photon state, we achieve the value of $8.08\pm0.05$ dB ($19.06\pm0.29$ dB). Our work experimentally certifies the exclusive quantum non-Gaussianity properties highly relevant for optical sensing, communication and computation.

Quantum coherence is a crucial prerequisite for quantum technologies. Therefore, the robust generation, as autonomous as possible, of quantum coherence remains the essential problem for developing this field. We consider a method of synthesizing and multiplexing quantum coherence from spin systems without any direct drives only coupled to bosonic baths. The previous studies in this field have demonstrated that a back-action of the bath to the spin subsystem is important to generate it, however, it simultaneously gives significant limits to the generated coherence. We propose a viable approach with the bosonic bath that allows overcoming these limits by avoiding the destructive effect of the back-action processes. Using this approach, we suggest an advanced synthesis of the quantum coherence non-perturbatively in the spin-boson coupling parameters of multiple bosonic baths to increase and multiplex it for upcoming proof-of-principle experiments., Comment: 28 pages, 6 figures

This work presents two distinct approaches to estimating the exponent related to the distribution of optical rogue waves observed in supercontinuum generated in a single-mode fiber, that is, to quantifying the rogueness. The first is a generalization of the well-known Hill estimator, and the second relies on estimating all parameters of a multi-parameter model. We show that the model shows a good correspondence with experimental data, and that the two estimating approaches provide consistent results, which are significantly more accurate than those obtained with earlier methods of estimation. Furthermore, alternative visualization through the tail function revealed the presence of pump depletion as well as detector saturation leading to the breakdown of power-law behavior for the largest observations. We characterized this breakdown via a combination of an exponential and a generalized Pareto distribution. Additionally, we have uncovered a weak memory effect in the data, which can be attributed to changes of the refractive index in the single-mode fiber., Comment: 12 pages, 5 figures

Maxwell's demon principle of extracting valuable resources through measuring fluctuations in the system already stimulated modern quantum physics. In contrast to classical physics, a free coupling to a probe and its free measurement fundamentally shape the system state. This becomes a new dimension of the Maxwell demon effect, as in addition to the gained information, the back action on the system can be exploited and essential for further applications. We investigate quantum bosonic Maxwell's demon coupled to a two-level system to address this issue straightforwardly. The deterministic multiple subtractions of energy quanta by an energetically conservative Jaynes-Cummings interaction leads to an out-of-equilibrium state. Although still super-Poissonian, it can resonantly excite another two-level system better than any thermal state. To further reduce the super-Poissonian statistics close to a Poissonian by a Maxwell's demon operation and increase the excitation rate, we suggest subsequent use of still energetically conservative multiphonon subtractions performed by an available nonlinear Jaynes-Cummings interaction. The optimal combination of both deterministic subtractions leads to statistics that approaches a Poissonian distribution otherwise produced by shot-noise-limited sources as an ideal laser requiring extreme bosonic nonlinear saturations., Comment: 19 pages, 8 figures

In the field of continuous-variable quantum information processing, non-Gaussian states with negative values of the Wigner function are crucial for the development of a fault-tolerant universal quantum computer. While several non-Gaussian states have been generated experimentally, none have been created using ultrashort optical wave packets, which are necessary for high-speed quantum computation, in the telecommunication wavelength band where mature optical communication technology is available. In this paper, we present the generation of non-Gaussian states on wave packets with a short 8-ps duration in the 1545.32 nm telecommunication wavelength band using photon subtraction up to three photons. We used a low-loss, quasi-single spatial mode waveguide optical parametric amplifier, a superconducting transition edge sensor, and a phase-locked pulsed homodyne measurement system to observe negative values of the Wigner function without loss correction up to three-photon subtraction. These results can be extended to the generation of more complicated non-Gaussian states and are a key technology in the pursuit of high-speed optical quantum computation., Comment: 14 pages, 5 figures

Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly susceptible to photon loss, which inevitably diminishes their quantum non-Gaussian features. Here, we protect these non-Gaussian features against photon loss by compressing the phase-space distribution of a cat state. We achieve this compression with a deterministic technique based on the echo conditional displacement operation in a circuit QED device. We present a versatile technique for creating robust non-Gaussian continuous-variable resource states in a highly linear bosonic mode and manipulating their phase-space distribution to achieve enhanced resilience against photon loss. Compressed cat states offer an attractive avenue for obtaining new insights into quantum foundations and quantum metrology, and for developing inherently more protected bosonic codewords for quantum error correction., Comment: 12 pages, 9 figures

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of $N$ independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Quantum coherent superpositions of states with different energies, i.e., states with coherence with respect to energy basis, are important resource for modern quantum technologies. States with small coherence can be obtained either autonomously, due to the effect of a weak coherent drive or, potentially, due to the presence of an environment. In this paper, we propose a measurement-based protocol for quantum coherence synthesis from individual systems (with low initial coherence) into a global (and higher) coherence of the joint system. As an input, it uses $N$ non-interacting copies of two-level systems (TLS), with low initial energy and coherence. These can be supplied by, e.g., a weak external drive or can result from an interaction with a bath. This protocol conditionally synthesizes an output state with higher energy and coherence than the initial state had, representing an universal process whose rules have not been well studied, yet. In addition to energy and coherence, we study the quantity called mutual coherence, showing increase after the protocol application, as well. This approach is based on application of sequential pairwise projective measurements on TLS pairs (conditionally removing their ground states), that are diagonal in the TLS energy basis. The functionality of the coherence synthesis is robust with respect to dephasing effects of the TLS environment on the system. Our approach may show its benefits in quantum sensing, quantum batteries charging, or other applications where synthesis of a larger coherent system from smaller (weaker) resources is useful., Comment: 13 pages, 8 figures

Quantum superposition of energy eigenstates can appear autonomously in a single quantum two-level system coupled to a low-temperature thermal bath, if such coupling has a proper composite nature. We propose here a principally different and more feasible approach employing engineered interactions between two-level systems being thermalized into a global Gibbs state by weakly coupled thermal bath at temperature $T$. Therefore, in such case quantum coherence appears by a different mechanism, whereas the system-bath coupling does not have to be engineered. We demonstrate such autonomous coherence generation reaching maximum values of coherence. Moreover, it can be alternatively built up by using weaker but collective interaction with several two-level systems. This approach surpasses the coherence generated by the engineered system-bath coupling for comparable interaction strengths and directly reduces phase estimation error in quantum sensing. This represents a necessary step towards the autonomous quantum sensing., Comment: 10 pages, 4 figures

Measurement-based quantum computation with optical time-domain multiplexing is a promising method to realize a quantum computer from the viewpoint of scalability. Fault tolerance and universality are also realizable by preparing appropriate resource quantum states and electro-optical feedforward that is altered based on measurement results. While a linear feedforward has been realized and become a common experimental technique, nonlinear feedforward was unrealized until now. In this paper, we demonstrate that a fast and flexible nonlinear feedforward realizes the essential measurement required for fault-tolerant and universal quantum computation. Using non-Gaussian ancillary states we observed 10$\%$ reduction of the measurement excess noise relative to classical vacuum ancilla., Comment: 35 pages, 11 figures

The nonclassicality of quantum states is a fundamental resource for quantum technologies and quantum information tasks in general. In particular, a pivotal aspect of quantum states lies in their coherence properties, encoded in the nondiagonal terms of their density matrix in the Fock-state bosonic basis. We present operational criteria to detect the nonclassicality of individual quantum coherences that only use data obtainable in experimentally realistic scenarios. We analyze and compare the robustness of the nonclassical coherence aspects when the states pass through lossy and noisy channels. The criteria can be immediately applied to experiments with light, atoms, solid-state systems, and mechanical oscillators, thus providing a toolbox allowing practical experiments to more easily detect the nonclassicality of generated states.

Quanta splitting is an essential generator of Gaussian entanglement, exemplified by Einstein-Podolsky-Rosen states and apparently the most commonly occurring form of entanglement. In general, it results from the strong pumping of a nonlinear process with a highly coherent and low-noise external drive. In contrast, recent experiments involving efficient trilinear processes in trapped ions and superconducting circuits have opened the complementary possibility to test the splitting of a few thermal quanta. Stimulated by such small thermal energy, a strong degenerate trilinear coupling generates large amounts of nonclassicality, detectable by more than 3 dB of distillable quadrature squeezing. Substantial entanglement can be generated via frequent passive linear coupling to a third mode present in parallel with the trilinear coupling. This new form of entanglement, outside any Gaussian approximation, surprisingly grows with the mean number of split thermal quanta; a quality absent from Gaussian entanglement. Using distillable squeezing we shed light on this new entanglement mechanism for nonlinear bosonic systems.

Nanoparticles trapped in optical tweezers emerged as an interesting platform for investigating fundamental effects in quantum physics. The ability to shape the optical trapping potential using spatial light modulation and quantum control of their motion using coherent scattering to an optical cavity mode predispose them for emulating a range of physical systems and studying quantum phenomena with massive objects. To extend these capabilities of levitated nanoparticles to quantum many-body systems, it is crucial to develop feasible strategies to couple and entangle multiple particles either directly or via a common optical bus. Here, we propose a variable and deterministic scheme to generate Gaussian entanglement in the motional steady state of multiple levitated nanoparticles using coherent scattering to multiple cavity modes. Coupling multiple nanoparticles to a common optical cavity mode allows cooling of a collective Bogoliubov mode to its quantum ground state; cooling multiple Bogoliubov modes (enabled by trapping each particle in multiple tweezers such that each tweezer scatters photons into a separate cavity mode) removes most thermal noise, leading to strong entanglement between nanoparticles. We present numerical simulations for three nanoparticles showing great tuneability of the generated entanglement with realistic experimental parameters. Our proposal thus paves the way towards creating complex quantum states of multiple levitated nanoparticles for advanced quantum sensing protocols and many-body quantum simulations., Comment: 11 pages, 5 figures

Quantum coherence, the ability of a quantum system to be in a superposition of orthogonal quantum states, is a distinct feature of the quantum mechanics, thus marking a deviation from classical physics. Coherence finds its applications in quantum sensing and metrology, quantum thermodynamics and computation. A particularly interesting is the possibility to observe coherence arising in counter-intuitive way from thermal energy that is without implementation of intricate protocols involving coherent driving sequences. In this manuscript, we investigate quantum coherence emerging in a hybrid system composed of a two-level system (qubit) and a thermal quantum harmonic oscillator (a material mechanical oscillator), inspired by recent experimental progress in fabrication of such systems. We show that quantum coherence is created in such a composite system solely from the interaction of the parts and persists under relevant damping. Implementation of such scheme will demonstrate previously unobserved mechanisms of coherence generation and can be beneficial for hybrid quantum technologies with mechanical oscillators and qubits., Comment: 14 pages, 5 + 2 figures

Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and error correction with diverse continuous-variable systems. This review introduces theoretical analyses of nonclassical and quantum non-Gaussian states of photons and phonons. It recapitulates approaches used to derive operational criteria for photons tolerant to optical losses, their application in experiments and their nowadays extension to quantum non-Gaussian photon coincidences. It extends to a recent comparison of quantum non-Gaussianity, including robustness to thermal noise, and sensing capability for high-quality phononic Fock states of single trapped cooled ions. The review can stimulate further development in the criteria of quantum non-Gaussian states and experimental effort to prepare and detect such useful features, navigating the community to advanced quantum physics and technology.

The precise determination of a displacement of a mechanical oscillator or a microwave field in a predetermined direction in phase space can be carried out with trapped ions or superconducting circuits, respectively, by coupling the oscillator with ancilla qubits. Through that coupling, the displacement information is transferred to the qubits which are then subsequently read out. However, unambiguous estimation of displacement in an unknown direction in the phase space has not been attempted in such oscillator-qubit systems. Here, we propose a hybrid oscillator-qubit interferometric setup for the unambiguous estimation of phase space displacements in an arbitrary direction, based on feasible Rabi interactions beyond the rotating-wave approximation. Using such a hybrid Rabi interferometer for quantum sensing, we show that the performance is superior to the ones attained by single-mode estimation schemes and a conventional interferometer based on Jaynes-Cummings interactions. Moreover, we find that the sensitivity of the Rabi interferometer is independent of the thermal occupation of the oscillator mode, and thus cooling it to the ground state before sensing is not required. We also perform a thorough investigation of the effect of qubit dephasing and oscillator thermalization. We find the interferometer to be fairly robust, outperforming different benchmark estimation schemes even for large dephasing and thermalization.

Multi-parameter estimation is necessary for force sensing due to simultaneous and nontrivial small changes of position and momentum. Designing quantum probes that allow simultaneous estimation of all parameters is therefore an important task. The optimal methods for estimation of the conjugate changes of position and momentum of quantum harmonic oscillator employ probes in entangled or quantum non-Gaussian states. We show that the same results can be obtained in a significantly more feasible fashion by employing independent sets of differently squeezed Gaussian states classically correlated to position or momentum measurements. This result demonstrates an unexplored power of a classical correlation between the probe states and measurements directly applicable to force sensing, Comment: 8 pages, 4 figures, journal reference added

Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.

The distributed quantum information processing and hybridization of quantum platforms raises increasing demands on the quality of light-matter interaction and realization of efficient quantum interfaces. This becomes particularly challenging for needed states possessing fundamental quantum non-Gaussian (QNG) aspects. They correspond to paramount resources in most potent applications of quantum technologies. We demonstrate the generation of light with provably QNG features from a tunable warm atomic ensemble in a single-mode regime. The light is generated in a spontaneous four-wave mixing process in the presence of decoherence effects caused by a large atomic thermal motion. Despite its high sensitivity to any excess noise, a direct observability of heralded QNG light could be achieved due to a combination of a fast resonant excitation, large spectral bandwidth, and a low absorption loss of resonant photons guaranteed by the source geometry., Comment: 10 pages, 5 figures

In hybrid circuit QED architectures containing both ancilla qubits and bosonic modes, a controlled beam splitter gate is a powerful resource. It can be used to create (up to a controlled-parity operation) an ancilla-controlled SWAP gate acting on two bosonic modes. This is the essential element required to execute the `swap test' for purity, prepare quantum non-Gaussian entanglement and directly measure nonlinear functionals of quantum states. It also constitutes an important gate for hybrid discrete/continuous-variable quantum computation. We propose a new realization of a hybrid cSWAP utilizing `Kerr-cat' qubits -- anharmonic oscillators subject to strong two-photon driving. The Kerr-cat is used to generate a controlled-phase beam splitter (cPBS) operation. When combined with an ordinary beam splitter one obtains a controlled beam-splitter (cBS) and from this a cSWAP. The strongly biased error channel for the Kerr-cat has phase flips which dominate over bit flips. This yields important benefits for the cSWAP gate which becomes non-destructive and transparent to the dominate error. Our proposal is straightforward to implement and, based on currently existing experimental parameters, should achieve controlled beam-splitter gates with high fidelities comparable to current ordinary beam-splitter operations available in circuit QED.

The Mach--Zehnder interferometer is a powerful device for detecting small phase shifts between two light beams. Simple input states -- such as coherent states or single photons -- can reach the standard quantum limit of phase estimation while more complicated states can be used to reach Heisenberg scaling; the latter, however, require complex states at the input of the interferometer which are difficult to prepare. The quest for highly sensitive phase estimation therefore calls for interferometers with nonlinear devices which would make the preparation of these complex states more efficient. Here, we show that the Heisenberg scaling can be recovered with simple input states (including Fock and coherent states) when the linear mirrors in the interferometer are replaced with controlled-swap gates and measurements on ancilla qubits. These swap tests project the input Fock and coherent states onto NOON and entangled coherent states, respectively, leading to improved sensitivity to small phase shifts in one of the interferometer arms. We perform detailed analysis of ancilla errors, showing that biasing the ancilla towards phase flips offers a great advantage, and perform thorough numerical simulations of a possible implementation in circuit quantum electrodynamics. Our results thus present a viable approach to phase estimation approaching Heisenberg-limited sensitivity.

Quantum non-Gaussian mechanical states from inherently nonlinear quantum processes are already required in a range of applications spanning from quantum sensing up to quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates - Fock states. Despite the progress in their preparation, the remaining imperfections can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant in the applications. We derive the most challenging hierarchy of quantum non-Gaussian criteria for the individual mechanical Fock states and demonstrate its implementation on the characterization of single trapped-ion oscillator states up to 10~phonons. We analyze the depth of quantum non-Gaussian features under mechanical heating and predict their application in quantum sensing. These results uncover that the crucial quantum non-Gaussian features are demanded to reach quantum advantage in the applications.

Two-mode squeezed states are scalable and robust entanglement resources for continuous-variable and hybrid quantum information protocols at a distance. We consider the effect of a linear cross talk in the multimode distribution of two-mode squeezed states propagating through parallel similar channels. First, to reduce degradation of the distributed Gaussian entanglement, we show that the initial two-mode squeezing entering the channel should be optimized already in the presence of a small cross talk. Second, we suggest simultaneous optimization of relative phase between the modes and their linear coupling on a receiver side prior to the use of entanglement, which can fully compensate the cross talk once the channel transmittance is the same for all the modes. For the realistic channels with similar transmittance values for either of the modes, the cross talk can be still largely compensated. This method relying on the mode interference overcomes an alternative method of entanglement localization in one pair of modes using measurement on another pair and feed-forward control. Our theoretical results pave the way to more efficient use of multimode continuous-variable photonic entanglement in scalable quantum networks with cross talk., Comment: $\copyright$ 2021 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved. 18 pages, 8 figures

Quantum key distribution with continuous variables already uses advantageous high-speed single-mode homodyne detection with low electronic noise at room temperature. Together with continuous-variable information encoding to nonclassical states, the distance for secure key transmission through lossy channels can approach 300 km in current optical fibers. Such protocols tolerate higher channel noise and also limited data processing efficiency compared to coherent-state protocols. The secret key rate can be further increased by increasing the system clock rates, and, further, by a suitable frequency-mode-multiplexing of optical transmission channels. However, the multiplexed modes couple together in the source or any other part of the protocol. Therefore, multiplexed communication will experience crosstalk and the gain can be minuscule. Advantageously, homodyne detectors allow solving this crosstalk problem by proper data processing. It is a potential advantage over protocols with single-photon detectors, which do not enable similar data processing techniques. We demonstrate the positive outcome of this methodology on the experimentally characterized frequency-multiplexed entangled source of femtosecond optical pulses with natural crosstalk between eight entangled pairs of modes. As the main result, we predict almost 15-fold higher secret key rate. This experimental test and analysis of frequency-multiplexed entanglement source opens the way for the field implementation of high-capacity quantum key distribution with continuous variables., Comment: 14 pages, 5 figures; to be published in Photonics Research

Quantum coupling between mechanical oscillators and atomic gases generating entanglement has been recently experimentally demonstrated using their subsequent interaction with light. The next step is to build a hybrid atom-mechanical quantum gate showing bosonic interference effects of single quanta in the atoms and oscillators. We propose an experimental test of Hong-Ou-Mandel interference between single phononic excitation and single collective excitation of atoms using the optical connection between them. A single optical pulse is sufficient to build a hybrid quantum-nondemolition gate to observe the bunching of such different quanta. The output atomic-mechanical state exhibits a probability of a hybrid bunching effect that proves its nonclassical aspects. This proposal opens a feasible road to broadly test such advanced quantum bunching phenomena in a hybrid system with different specific couplings., Comment: 34 pages

We study a system of a single qubit (or a few qubits) interacting with a soft-mode bosonic field. Considering an extended version of the Rabi model with both parity-conserving and parity-violating interactions, we disclose a complex arrangement of quantum phase transitions in the ground- and excited-state domains. An experimentally testable signature of some of these transitions is a dynamical stabilization of a fully factorized qubit-field state involving the field vacuum. It happens in the ultrastrong coupling regime where the superradiant field equilibrium is far from the vacuum state. The degree of stabilization varies abruptly with interaction parameters and increases with the softness of the field mode. We analyze semiclassical origins of these effects and show their connection to various forms of excited-state quantum phase transitions., Comment: 16 pages, 9 figures

Many applications in quantum communication, sensing and computation need provably quantum non-Gaussian light. Recently such light, witnessed by a negative Wigner function, has been estimated using homodyne tomography from a single atom dispersively coupled to a high-finesse cavity. This opens an investigation of quantum non-Gaussian light for many experiments with atoms and solid-state emitters. However, at their early stage, an atom or emitter in a cavity system with different channels to the environment and additional noise are insufficient to produce negative Wigner functions. Moreover, homodyne detection is frequently challenging for such experiments. We analyse these issues and prove that such cavities can be used to emit quantum non-Gaussian light employing single-photon detection in the Hanbury Brown and Twiss configuration and quantum non-Gaussianity criteria suitable for this measurement. We investigate in detail cases of considerable cavity leakage when the negativity of the Wigner function disappears completely. Advantageously, quantum non-Gaussian light can be still conclusively proven for a large set of the cavity parameters at the cost of overall measurement time, even if noise is present., Comment: 13 pages, 5 figures

We theoretically and experimentally investigate conditional enhancement of overall coherence of quantum states by probabilistic quantum operations that apply to the input state a quantum filter diagonal in the basis of incoherent states. We identify the optimal filters that for a given probability of successful filtering maximize the output coherence. We verify the performance of the studied quantum filters in a proof-of-principle experiment with linear optics, where a pair of two-level quantum systems is represented by polarization states of two photons. We comprehensively characterize the implemented two-qubit linear optical quantum filters by full quantum process tomography and we experimentally observe the optimal quantum coherence enhancement by quantum filtering., Comment: 10 pages, 7 figures

Quantum non-Gaussian states represent an important class of highly non-classical states whose preparation requires quantum operations or measurements beyond the class of Gaussian operations and statistical mixing. Here we derive criteria for certification of quantum non-Gaussianity based on probability of vacuum in the original quantum state and a state transmitted through a lossy channel with transmittance T. We prove that the criteria hold for arbitrary multimode states, which is important for their applicability in experiments with broadband sources and single-photon detectors. Interestingly, our approach allows to detect quantum non-Gaussianity using only one photodetector instead of complex multiplexed photon detection schemes, at the cost of increased experimental time. We also formulate a quantum non-Gaussianity criterion based on the vacuum probability and mean photon number of the state and we show that this criterion is closely related to the criteria based on pair of vacuum probabilities. We illustrate the performance of the obtained criteria on the example of realistic imperfect single-photon states modeled as a mixture of vacuum and single-photon states with background Poissonian noise., Comment: 22 pages, 5 figures