Multimode States Research Articles

Realistic photon-number resolution in Gaussian boson sampling

Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024

Reduction in Optical Feedback Noise of Atomic Force Microscopy by High-Frequency Current Modulation

Introduction: With the advancement of technology, nanotechnology has emerged as a prominent research field. The Atomic Force Microscope (AFM) serves as a vital tool in nanoscience and technology, playing an indispensable role across various domains. Method: However, in the AFM photoelectric sensing system, the optical feedback noise from the beam deflection method can lead to inaccuracies in signal identification and analysis, impacting the accuracy and reliability of AFM measurements. To mitigate this interference, this study proposes a highfrequency current superposition system aimed at reducing optical feedback noise. By superimposing high-frequency currents, the semiconductor laser transitions from a single-mode to a multi-mode operational state, thereby altering its mode of operation and consequently reducing optical feedback noise during sensing. Initially, mathematical modeling and simulation analysis were conducted on the high-frequency current superposition noise reduction system to examine the impact of high-frequency current on the intensity noise of the semiconductor laser. Subsequently, the design of the high-frequency current superposition noise reduction system was outlined, encompassing the development of a constant current drive circuit, a voltage-controlled oscillator circuit, and a biasing circuit. Finally, the high-frequency current superposition noise reduction system underwent testing. Results: During the high-frequency current superposition noise reduction test, the system's Signal-to-Noise Ratio (SNR) increased from 15.57 dB to 17.81 dB, and the system's noise peak-to-peak value decreased from 8 mV to 6 mV. Analysis of the superposition frequency and noise reduction effect determined the optimal superposition frequency of the AFM photoelectric sensor system to be 400 MHz. Characterization experiments of the high-frequency superposition noise reduction system compared the clarity of Escherichia coli images before and after noise reduction. Conclusion: The aforementioned experimental results demonstrated that high-frequency current superposition is an effective noise reduction method capable of mitigating optical noise in the AFM photoelectric sensing system.

Remote implementation of hidden or partially unknown quantum operators using optimal resources: a generalized view

Two protocols are proposed for two closely linked but different variants of remote implementation of quantum operators of specific forms The first protocol is designed for the remote implementation of the single qubit hidden quantum operator, whereas the second one is designed for the remote implementation of the partially unknown single qubit quantum operator. In both cases two-qubit maximally entangled state, which is entangled in the spatial degree of freedom is used. The quantum resources used here are optimal and easy to realize and maintain in comparison to the multi-partite or multi-mode entangled states used in earlier works. The impact of photon loss due to interaction with the environment is analyzed for both the schemes. The proposed protocols are also generalized to their controlled, bidirectional, cyclic, controlled cyclic, and controlled bidirectional versions and it is shown that either Bell state alone or products of Bell states will be sufficient to perform these tasks with some additional classical communications in the controlled cases only. This is in sharp contrast to the earlier proposals that require large entangled states. In addition, it’s noted that remote implementation of hidden or partially unknown operators involving multiple controllers and/or multiple players who jointly apply the desired operator(s) would require quantum channels more complex than the Bell states and their products. Explicit forms of such quantum channels are also provided.

Efficient learning of continuous-variable quantum states

The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation, and computing. However, a full characterization of multimode quantum states requires a number of experiments that grows exponentially with the number of modes. Here we propose an alternative approach where the goal is not to reconstruct the full quantum state, but rather to estimate its characteristic function at a given set of points. For multimode states with reflection symmetry, we show that the characteristic function at M points can be estimated using only O(logM) copies of the state, independently of the number of modes. When the characteristic function is known to be positive, as in the case of squeezed vacuum states, the estimation is achieved by an experimentally friendly setup using only beamsplitters and homodyne measurements. Published by the American Physical Society 2024

Polygon relations and subadditivity of entropic measures for discrete and continuous multipartite entanglement

In a recent work by us Ge et al [Phys. Rev. A 110, L010402 (2024)], we have derived a series of polygon relations of bipartite entanglement measures that is useful to reveal entanglement properties of discrete, continuous, and even hybrid multipartite quantum systems. In this work, with the information-theoretical measures of Rényi and Tsallis entropies, we study the relationship between the polygon relation and the subadditivity of entropy. In particular, the entropy-polygon relations are derived for pure multi-qubit states and then generalized to multi-mode Gaussian states, by utilizing the known results from the quantum marginal problem. Then the equivalence between the polygon relation and subadditivity is established, in the sense that for all discrete or continuous multipartite states, the polygon relation holds if and only if the underlying entropy is subadditive. As a byproduct, the subadditivity of Rényi and Tsallis entropies is proven for all bipartite Gaussian states. Finally, the difference between polygon relations and monogamy relations is clarified, and generalizations of our results are discussed. Our work provides a better understanding of the rich structure of multipartite states, and hence is expected to be helpful for the study of multipartite entanglement.

Holographic Gaussian Boson Sampling with Matrix Product States on 3D cQED Processors.

We introduce quantum circuits for simulations of multimode state vectors on 3D circuit quantum electrodynamics (cQED) processors using matrix product state representations. The circuits are demonstrated as applied to simulations of molecular docking based on holographic Gaussian boson sampling (GBS), as illustrated for the binding of a thiol-containing aryl sulfonamide ligand to the tumor necrosis factor-α converting enzyme receptor. We show that cQED devices with a modest number of modes could be employed to simulate multimode systems by repurposing working modes through measurement and reinitialization. We anticipate that a wide range of GBS applications could be implemented on compact 3D cQED processors analogously using the holographic approach. Simulations on qubit-based quantum computers could be implemented analogously using circuits that represent continuous variables in terms of truncated expansions of Fock states.

Variable hyperparameterized Gaussian kernel using displaced squeezed vacuum state

There are machine learning schemes for realizing different types of kernels by quantum states of light. It is particularly interesting to realize a Gaussian kernel due to its wider applicability. A multimode coherent state can generate the Gaussian kernel with a constant value of hyperparameter. However, this constancy has limited the application of the Gaussian kernel when it is applied to complex learning problems. We improve it by introducing a variable hyperparameterized Gaussian kernel with a multimode-displaced squeezed vacuum state. The learning capacity of this kernel is tested with the support vector machines over some synthesized data sets, as well as public benchmark data sets. We establish that the proposed variable hyperparameterized Gaussian kernel offers better accuracy over the constant Gaussian kernel.

Performance optimization of continuous-variable quantum teleportation with generalized photon-varying non-Gaussian operations

Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the protocol. However, for a given type of non-Gaussian operation, the achievable fidelity varies with the parameters associated with the operation. Previous work only focused on particular settings of the parameters, over which an optimization was missing. The potential of such operations is not fully uncovered. Given a fixed non-Gaussian operation, the achievable fidelity also varies with input states. An operation that increases the fidelity for teleporting one class of states might do the contrary for other classes of states. A performance metric, upon which an operation is optimized, suitable for different input states, is also missing. In this work, we build a framework for photon-varying non-Gaussian operations for multimode states, upon which we propose a performance metric suitable for arbitrary teleportation input states. We then apply the new metric to evaluate different types of non-Gaussian operations. Starting from simple multiphoton photon subtraction and photon addition, we find that increasing the number of ancillary photons involved in the operation does not guarantee performance improvement. We then investigate a generalization of the operations mentioned above, finding that operations that approximate a particular form provide the best improvement. The results provided here will be valuable for real-world implementations of quantum teleportation networks and applications that harness the non-Gaussianity of quantum states. Published by the American Physical Society 2024

Quench dynamics of interacting bosons: generalized coherent states versus multi-mode Glauber states

Multi-mode Glauber coherent states (MMGS) as well as Bloch states with zero quasi-momentum, which are a special case of generalized coherent states (GCS), are frequently used to describe condensed phases of bosonic many-body systems. The difference of two-point correlators of MMGS and GCS vanishes in the thermodynamic limit. Using the established expansion of MMGS in terms of GCS, we derive a Fourier-type relation between the (auto-)correlation functions of the two different time-evolved states. This relation reveals that the (auto-)correlation and thus the dynamical free-energy density for the two cases are still different, even in the thermodynamic limit, due to the lack of the U(1) symmetry of the MMGS. Analytic results for the deep lattice model of interacting bosons for increasing filling factors show multiple sharp structures in the dynamical free energy-density of increasing complexity. These are explained using the evolution of Husimi functions in phase space.

Optimal multiple-phase estimation with multi-mode NOON states against photon loss

Multi-mode NOON states can quantum-enhance multiple-phase estimation in the absence of photon loss. However, a multi-mode NOON state is known to be vulnerable to photon loss, and its quantum-enhancement can be dissipated by lossy environment. In this work, we demonstrate that a quantum advantage in estimate precision can still be achieved in the presence of photon loss. This is accomplished by optimizing the weights of the multi-mode NOON states according to photon loss rates in the multiple modes, including the reference mode which defines the other phases. For practical relevance, we also show that photon-number counting via a multi-mode beam-splitter achieves the useful, albeit sub-optimal, quantum advantage. We expect this work to provide valuable guidance for developing quantum-enhanced multiple-phase estimation techniques in lossy environments.

Pretty good measurement for bosonic Gaussian ensembles

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory 66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.

Multipartite continuous-variable optical quantum entanglement: Generation and application

Quantum entanglement is a fundamental resource for various quantum applications and generation of large-scale entanglement is a key quantum technology. In recent years, continuous-variable optical systems have shown promising results in this direction, thanks to deterministic generation and multiplexing via rich degrees of freedom naturally occurring in the optical system. In this paper, we review the generation and applications of multipartite optical quantum entanglement. We begin with a theoretical overview of how to represent and verify multimode continuous-variable quantum states and entanglement. Then, we discuss the multiplexing technique in time, frequency, and spatial domains, and their applications in generation of large-scale entangled states. Afterward, we review the current status and development of the basic technology used in the generation of multipartite quantum entanglement. Finally, we discuss the applications of large-scale quantum entanglement and possible future perspectives. Published by the American Physical Society 2024

Optimal parameter estimation of shaped phase objects

We show a general method to estimate with optimum precision, i.e., the best precision determined by the light-matter interaction process, a set of parameters that characterize a phase object. The method is derived from ideas presented by Pezze []. Our goal is to illuminate the main characteristics of this method as well as its applications to the physics community probably not familiar with the quantum language usually employed in works related to quantum estimation theory. First, we derive precision bounds for the estimation of the set of parameters characterizing the phase object. We compute the Crámer-Rao lower bound for two experimentally relevant types of illumination: a multimode coherent state with mean photon number N and N copies of a multimode single-photon quantum state. We show under which conditions these two models are equivalent. Second, we show that the optimum precision can be achieved by projecting the light reflected or transmitted from the object onto a set of modes with engineered spatial shape. We describe how to construct these modes and demonstrate explicitly that the precision of the estimation using these measurements is optimum. As an example, we apply these results to the estimation of the height and sidewall angle of a cliff-like nanostructure, an object relevant in the semiconductor industry for the evaluation of nanofabrication techniques. Published by the American Physical Society 2024

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Network mechanism for generating genuinely correlative Gaussian states* *The paper is dedicated to Prof. Jinchuan Hou on the occasion of his 70th birthday.

Generating a long-distance quantum state with genuine quantum correlation (GQC) is one of the most essential functions of quantum networks to support quantum communication. Here, we provide a deterministic scheme for generating multimode Gaussian states with certain GQC (including genuine entanglement). Efficient algorithms of generating multimode states are also proposed. Our scheme is useful for resolving the bottleneck in generating some multimode Gaussian states and may pave the way towards real world applications of preparing multipartite quantum states in current quantum technologies.

Multimodal and multi-omics-based deep learning model for screening of optic neuropathy

PurposeTo examine the use of multimodal data and multi-omics strategies for optic nerve disease screening. MethodsThis was a single-center retrospective study. A deep learning model was created from fundus photography and infrared reflectance (IR) images of patients with diabetic optic neuropathy, glaucomatous optic neuropathy, and optic neuritis. Patients who were seen at the Ophthalmology Department of First Affiliated Hospital of Nanchang University in Jiangxi Province from November 2019 to April 2023 were included in this study. The data were analyzed in single and multimodal modes following the traditional omics, Resnet101, and fusion models. The accuracy and area-under-the-curve (AUC) of each model were compared. ResultsA total of 312 images fundus and infrared fundus photographs were collected from 156 patients. When multi-modal data was used, the accuracy of the traditional omics mode, Resnet101, and fusion models with the training set were 0.97, 0.98, and 0.99, respectively. The accuracy of the same models with the test sets were 0.72, 0.87, and 0.88, respectively. We compared single- and multi-mode states by applying the data to the different groups in the learning model. In the traditional omics model, the macro-average AUCs of the features extracted from fundus photography, IR images, and multimodal data were 0.94, 0.90, and 0.96, respectively. When the same data were processed in the Resnet101 model, the scores were 0.97 equally. However, when multimodal data was utilized, the macro-average AUCs in the traditional omics, Resnet101, and fusion modesl were 0.96, 0.97, and 0.99, respectively. ConclusionThe deep learning model based on multimodal data and multi-omics strategies can improve the accuracy of screening and diagnosing diabetic optic neuropathy, glaucomatous optic neuropathy, and optic neuritis.

Experimental demonstration of phase-sensitive multimode continuous variable quantum key distribution with improved secure key rate

We develop and experimentally demonstrate a phase-sensitive continuous variable quantum key distribution system with improved secure key rate. This is achieved using multimode coherent states with phase-conjugated subcarrier modulation and phase-sensitive detection. The local oscillator for phase-sensitive detection is regenerated from a polarization-multiplexed carrier wave via optical injection locking. The proposed scheme has a higher classical information capacity at a given number of received photons and exhibits a higher secure key rate when applying the security analysis of the GG02 protocol. Experimental results confirm the higher secret key rate and better excess noise tolerance of the new scheme compared to the typical implementation of GG02.

Quantum repeaters and teleportation via entangled phase-modulated multimode coherent states

Quantum repeaters and teleportation via entangled phase-modulated multimode coherent states

Quantum roughness as sensitivity to diffusion noise: Quantifying non-classicality of multi-mode systems

The quantumness of a physical system is context-sensitive, contingent on the particular quantum behavior selected for quantification. One such measure, roughness, recently introduced to assess nonclassicality, gauges the waviness of the Wigner function of a quantum state. This work explores some properties of roughness, generalizes its definition to include multimode systems, and presents a new geometric interpretation of this measure of nonclassicality. Furthermore, the roughness of several families of multimode states is reported, shedding light on their nonclassical features.

Label-free quantum super-resolution imaging using entangled multi-mode squeezed light

In this study, we explore the theoretical application of entangled multi-mode squeezed light for label-free optical super-resolution imaging. By generating massively entangled multi-mode squeezed light through an array of balanced beam splitters, using a single-mode squeezed light input, we create a multi-mode quantum light state with exceptional entanglement and noise suppression below the shot noise level. This significantly reduces imaging measurement errors compared to classical coherent state light imaging when the same number of photons are used on the imaging sample. We demonstrate how to optimize the imaging system’s parameters to achieve the Heisenberg imaging error limit, taking into account the number of entangled modes and photons used. We also examine the effects of optical losses in the imaging system, necessitating adjustments to the optimized parameters based on the degree of optical loss. In practical applications, this new quantum imaging approach reduces the number of photons needed to achieve the same image quality by two orders of magnitude compared to classical imaging methods that use non-entangled, non-squeezed coherent state light.