Universal Quantum Filter

Measurement-based local quantum filters and their ability to transform quantum entanglement

We introduce local filters as a means to detect the entanglement of bound entangled states which do not yield to detection by witnesses based on positive (P) maps which are not completely positive (CP). We demonstrate how such non-detectable bound entangled states can be locally filtered into detectable bound entangled states. Specifically, we show that a bound entangled state in the orthogonal complement of the unextendible product bases (UPB), can be locally filtered into a another bound entangled state that is detectable by the Choi map. We reinterpret these filters as local measurements on…

Interferometric Phase Estimation Though Quantum Filtering in Coherent States

We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.

An efficient quantum filter for multiphoton states

We propose a scheme for implementing a multipartite quantum filter that uses entangled photons as a resource. It is shown that the success probability for the 2-photon parity filter can be as high as 1/2, which is the highest that has so far been predicted without the help of universal two-qubit quantum gates. Furthermore, the required number of ancilla photons is the least of all current parity filter proposals. Remarkably, the quantum filter operates with probability 1/2 even in the N-photon case, irregardless of the number of photons in the input state.

Diagnosis, prescription and prognosis of a Bell-state filter by quantum process tomography

Using a Hong-Ou-Mandel interferometer, we apply the techniques of quantum process tomography to characterize errors and decoherence in a prototypical two-photon operation, a singlet-state filter. The quantum process tomography results indicate a large asymmetry in the process and also the required operation to correct for this asymmetry. Finally, we quantify errors and decoherence of the filtering operation after this modification.

Assessment of Quantum Annealing for the Construction of Satisfiability Filters

Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard random $k$-SAT problems. This paper compares simulated annealing, simulated quantum annealing and walkSAT, an open-source SAT solver, in terms of their ability to find such solutions. The results indicate that solutions found by simulated quantum annealing are generally less disparate than solutions found by the other solvers and therefore less useful for th…

Universal nonclassicality witnesses for harmonic oscillators

It is shown that a nonclassicality witness, whose expectation value can be measured for all quantum states, can be constructed from every nonclassicality filter. This finding leads to a set of universal witnesses, parameterized by only three real numbers, for the detection of nonclassicality of any quantum state of a harmonic oscillator. An explicit operator expression is given for such a universal witness. The application of the witnesses is demonstrated for a nontrivial example, and its experimental measurement is briefly considered.

Quantum filter for non-local polarization properties of photonic qubits

We present an optical filter that transmits photon pairs only if they share the same horizontal or vertical polarization, without decreasing the quantum coherence between these two possibilities. Various applications for entanglement manipulations and multi-photon qubits are discussed.

Experimental demonstration of optimal probabilistic enhancement of quantum coherence

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 im…

Generating Nonclassical Quantum Input Field States with Modulating Filters

The behaviour of quantum open systems, and their output response, when driven by quantum input noise in a nonclassical state is of key importance to quantum technology. Here we give explicit constructions of quantum modulating filters which generate desired nonclassical states (coherent states, cat states, shaped single and multi-photon states) of quantum optical fields from vacuum noise input. The nonclassical state features (coherence, entanglement, Fock state, etc.) of the modulating filter, itself a linear passive open system, are transferred to the continuous variable output field state. …

Linear optical implementation of a single mode quantum filter and generation of multi-photon polarization entangled state

We propose a scheme to implement a single-mode quantum filter, which selectively eliminates the one-photon state in a quantum state $α|0>+β|1>+γ|2>$. The vacuum state and the two photon state are transmitted without any change. This scheme requires single-photon sources, linear optical elements and photon detectors. Furthermore we demonstrate, how this filter can be used to realize a two-qubit projective measurement and to generate multi-photon polarization entangled states.

Quantum Filtering of Optical Coherent States

We propose and experimentally demonstrate non-destructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors i.e. vacuum states in the quantum information are diagnosed through a weak measurement, and on that basis, probabilistically filtered out. We consider three different filters based on on/off detection phase stabilized and phase randomized homodyne detection. We find that on/off etection, optimal in the ideal theoretical setting, is superior to the homodyne strategy in a practical setting.

Feasible quantum engineering of quantum multiphoton superpositions

We examine an experimental setup implementing a family of quantum non-Gaussian filters. The filters can be applied to an arbitrary two-mode input state. We assume realistic photodetection in the filtering process and explore two different models of inefficient detection: a beam splitter of a small reflectivity located in front of a perfect detector and a Weierstrass transform applied to the unperturbed measurement outcomes. We explicitly give an operator which describes the coherent action of the filters in the realistic experimental conditions. The filtered states may find applications in qua…

Generalized Hofmann quantum process fidelity bounds for quantum filters

We propose and investigate bounds on quantum process fidelity of quantum filters, i.e. probabilistic quantum operations represented by a single Kraus operator K. These bounds generalize the Hofmann bounds on quantum process fidelity of unitary operations [H.F. Hofmann, Phys. Rev. Lett. 94, 160504 (2005)], and are based on probing the quantum filter by pure states forming two mutually unbiased bases. Determination of these bounds therefore requires much less measurements than full quantum process tomography. We find that it is particularly suitable to construct one of the probe basis from the r…

光通过偏振滤光片的经典与量子分析

Classical and Quantum Analysis of Light Transmission Through Polarizing Filters

本文分别从经典光学和量子力学角度分析了光通过偏振滤光片系统的行为，利用 Malus 定律计算透射强度，并用量子态投影概率解释该现象。

A Simple and Efficient Absorption Filter for Single Photons from a Cold Atom Quantum Memory

The ability to filter unwanted light signals is critical to the operation of quantum memories based on neutral atom ensembles. Here we demonstrate an efficient frequency filter which uses a vapor cell filled with $^{85}$Rb and a buffer gas to attenuate both residual laser light and noise photons by nearly two orders of magnitude with little loss to the single photons associated with our cold $^{87}$Rb quantum memory. This simple, passive filter provides an additional 18 dB attenuation of our pump laser and erroneous spontaneous emissions for every 1 dB loss of the single photon signal. We show…

An Entanglement Filter

The ability to filter quantum states is a key capability in quantum information science and technology, in which one-qubit filters, or polarizers, have found wide application. Filtering on the basis of entanglement requires extension to multi-qubit filters with qubit-qubit interactions. We demonstrated an optical entanglement filter that passes a pair of photons if they have the desired correlations of their polarization. Such devices have many important applications to quantum technologies.

Quantum filter for a class of non-Markovian quantum systems

In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtai…

A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control

We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-functions set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency…

用于超导量子电路的3D集成嵌入式滤波器

3D Integrated Embedded Filters for Superconducting Quantum Circuits

本文提出了一种用于超导量子电路的3D集成嵌入式滤波器，通过多层PCB实现高效多路复用读出，并验证了其在高相干性量子比特中的应用。

Revealing of hidden quantum steerability using local filtering operations

Nonlocal quantum correlation is at the heart of bizarre nature of quantum physics. While there are various classes of nonlocal quantum correlation, steerability of a quantum state by local measurements provides unique operational features. Here, we theoretically and experimentally investigate the hidden quantum steerability. In particular, we find that there are initially unsteerable states which can reveal the steerability by using local filters on individual quantum systems. It is remarkable that a certain set of local filters are more effective on revealing steerability than Bell nonlocalit…

Quantum projection filter for a highly nonlinear model in cavity QED

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection…

Broadband Filters for Abatement of Spontaneous Emission in Circuit Quantum Electrodynamics

The ability to perform fast, high-fidelity readout of quantum bits (qubits) is essential to the goal of building a quantum computer. However, coupling a fast measurement channel to a superconducting qubit typically also speeds up its relaxation via spontaneous emission. Here we use impedance engineering to design a filter by which photons may easily leave the resonator at the cavity frequency but not at the qubit frequency. We implement this broadband filter in both an on-chip and off-chip configuration.

Mechanical Purcell Filters for Microwave Quantum Machines

In circuit quantum electrodynamics, measuring the state of a superconducting qubit introduces a loss channel which can enhance spontaneous emission through the Purcell effect, thus decreasing qubit lifetime. This decay can be mitigated by performing the measurement through a Purcell filter which forbids signal propagation at the qubit transition frequency. If the filter is also well-matched at the readout cavity frequency, it will protect the qubit from decoherence channels without sacrificing measurement speed. We propose and analyze design for a mechanical Purcell filter, which we also fabri…

变分量子本征求解器与量子高斯滤波器用于解决量子多体系统中的基态问题

Variational Quantum Eigensolvers with Quantum Gaussian Filters for solving ground-state problems in quantum many-body systems

提出一种结合变分量子本征求解器与量子高斯滤波器的量子算法，用于在NISQ设备上高效求解多体系统基态，在横场伊辛模型上展现出更快的收敛和更高的精度。

Erasing Quantum Distinguishability via Single-Mode Filtering

Erasing quantum-mechanical distinguishability is of fundamental interest and also of practical importance, particularly in subject areas related to quantum information processing. We demonstrate a method applicable to optical systems in which single-mode filtering is used with only linear optical instruments to achieve quantum indistinguishability. Through "heralded" Hong-Ou-Mandel interference experiments we measure and quantify the improvement of indistinguishability between single photons generated via spontaneous four-wave mixing in optical fibers. The experimental results are in excellent…

最优滤波与纠缠光子生成用于量子应用中的噪声环境

Optimal filtering and generation of entangled photons for quantum applications in the presence of noise

本文研究了在噪声环境下通过滤波优化多光子应用中的纠缠光子生成，利用可调带宽滤波器和低抖动探测器实现高纯度单光子源，提升量子通信效率。

Teleportation scheme implementing the Universal Optimal Quantum Cloning Machine and the Universal NOT gate

The universal quantum cloning machine and the universal NOT gate acting on a single qubit can be implemented very generally by slightly modifying the protocol of quantum state teleportation. The experimental demonstration of the 1 to 2 cloning process according to the above scheme has been realized for a qubit encoded in photon polarization.

Direct approach to realising quantum filters for high-precision measurements

Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using non-classical states and quantum filters, which modify both the noise and signal response. We find a novel approach to realising quantum filters directly from their frequency-domain transfer functions, utilising techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show a new optic…

An Exponential Quantum Projection Filter for Open Quantum Systems

An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden associated with online calculation of the quantum filter. By using a differential geometric approach, the quantum trajectory is constrained in a finite-dimensional differentiable manifold consisting of an unnormalized exponential family of quantum density operators, and an exponential quantum projection filter is then formulated as a number of stochastic differentia…

通过量子投影滤波器实现反馈镇定

Feedback stabilization via a quantum projection filter

针对开放量子系统中的非理想QND测量，本文利用基于指数族结构的量子投影滤波器设计反馈，证明其可保证原始滤波器方程指数收敛至测量算子的目标本征态。

开放量子系统在非完美测量下的精确解与投影滤波器

Exact solution and projection filters for open quantum systems subject to imperfect measurements

本文研究了非完美间接测量下的开放量子系统，针对QND测量推导了量子滤波器方程的精确解，并提出低维流形投影滤波器，误差分析与仿真表明其在稳定反馈控制下依然有效。

Fidelity is a sub-martingale for discrete-time quantum filters

Fidelity is known to increase through any Kraus map: the fidelity between two density matrices is less than the fidelity between their images via a Kraus map. We prove here that, in average, fidelity is also increasing for any discrete-time quantum filter: fidelity between the density matrix of the underlying Markov chain and the density matrix of its associated quantum filter is a sub-martingale. This result is not restricted to pure states. It also holds true for mixed states.

An Improved Quantum Projection Filter

This work extends the previous quantum projection filtering scheme in [Gao Q., Zhang G., & Petersen I. R. (2019). An exponential quantum projection filter for open quantum systems. \emph{Automatica}, 99, 59-68.], by adding an optimality analysis result. A reformulation of the quantum projection filter is derived by minimizing the truncated Stratonovich stochastic Taylor expansion of the difference between the true quantum trajectory and its approximation on a lower-dimensional submanifold through quantum information geometric techniques. Simulation results for a qubit example demonstrate bette…

用于全天候最优自由空间量子通信的可调空间滤波器

Adjustable spatial filter for optimal free-space quantum communication round the clock

针对日间自由空间量子通信需适配动态链路条件的需求，研发可调空间滤波器实现实时视场调整，经1.7公里链路实验及与多模光纤耦合滤波对比，验证其可大幅提升系统安全密钥输出。

A Quantum Extended Kalman Filter

A stochastic filter uses a series of measurements over time to produce estimates of unknown variables based on a dynamic model. For a quantum system, such an algorithm is provided by a quantum filter, which is also known as a stochastic master equation (SME). For a linear quantum system subject to linear measurements and Gaussian noise, the quantum filter reduces to a quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to non-commutative quantum stochastic differential eq…

Quantum Enhanced Filter: QFilter

Convolutional Neural Networks (CNN) are used mainly to treat problems with many images characteristic of Deep Learning. In this work, we propose a hybrid image classification model to take advantage of quantum and classical computing. The method will use the potential that convolutional networks have shown in artificial intelligence by replacing classical filters with variational quantum filters. Similarly, this work will compare with other classification methods and the system's execution on different servers. The algorithm's quantum feasibility is modelled and tested on Amazon Braket Noteboo…

Design and Stability of Discrete-Time Quantum Filters with Measurement Imperfections

This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement perform…

滤波量子相位估计

Filtered Quantum Phase Estimation

针对量子相位估计中初始重叠不足的问题，提出滤波态制备框架，通过谱滤波增强重叠，并引入改进的Krylov子空间滤波，在Fermi-Hubbard模型上实现两个数量级的加速。

Quantum Error Mitigation Relying on Permutation Filtering

Quantum error mitigation (QEM) is a class of promising techniques capable of reducing the computational error of variational quantum algorithms tailored for current noisy intermediate-scale quantum computers. The recently proposed permutation-based methods are practically attractive, since they do not rely on any a priori information concerning the quantum channels. In this treatise, we propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. In particular, we show that the proposed filter design algorithm always converg…

连续时间量子滤波器的稳定性

On stability of continuous-time quantum-filters

本文证明由维纳过程驱动的连续时间随机主方程所描述的量子态与其关联的量子滤波器态之间的保真度是一个下鞅，从而推广到非纯量子态情况，并表明滤波过程的稳定性但不保证渐近收敛。

On-chip nanomechanical filtering of quantum-dot single-photon sources

Semiconductor quantum dots in photonic integrated circuits enable scaling quantum-information processing to many single photons and quantum-optical gates. On-chip spectral filters are essential to achieve high-purity and coherent photon emission from quantum dots embedded in waveguides, without resorting to free-space optics. Such spectral filters should be tunable, to compensate for the inhomogeneous spectral distribution of the quantum dots transitions. Here, we report an on-chip filter monolithically integrated with quantum dots, that uses nanomechanical motion for tuning its resonant wavel…

Eigenvalue decomposition method for photon statistics of frequency filtered fields and its applications to quantum dot emitters

A simple calculation method for photon statistics of frequency-filtered fields is proposed. This method, based on eigenvalue decompositions of superoperators, allows us to study effects on the photon statistics of spectral filtering by various types of filters, such as Gaussian and rectangular filters as well as Lorentzian filters, which is not possible by conventional approaches. As an example, this method is applied to a simulation of quantum dot single-photon emitters, where we found the efficient choice of the filter types to have pure single photons depends on the excitation conditions i.…

Fault Tolerant Quantum Filtering and Fault Detection for Quantum Systems

This paper aims to determine the fault tolerant quantum filter and fault detection equation for a class of open quantum systems coupled to a laser field that is subject to stochastic faults. In order to analyze this class of open quantum systems, we propose a quantum-classical Bayesian inference method based on the definition of a so-called quantum-classical conditional expectation. It is shown that the proposed Bayesian inference approach provides a convenient tool to simultaneously derive the fault tolerant quantum filter and the fault detection equation for this class of open quantum system…

A silicon photonic add-drop filter for quantum emitters

Integration of single-photon sources and detectors to silicon-based photonics opens the possibility of complex circuits for quantum information processing. In this work, we demonstrate integration of quantum dots with a silicon photonic add-drop filter for on-chip filtering and routing of telecom single photons. A silicon microdisk resonator acts as a narrow filter that transfers the quantum dot emission and filters the background over a wide wavelength range. Moreover, by tuning the quantum dot emission wavelength over the resonance of the microdisk we can control the transmission of the emit…

Faraday Filtering on the Cs-D$_1$-Line for Quantum Hybrid Systems

Narrow-band filtering of light is widely used in optical spectroscopy. Atomic filters, which rely on the Faraday effect, allow for GHz-wide transmission spectra, which are intrinsically matched to an atomic transition. We present an experimental realization and a theoretical study of a Faraday anomalous dispersion optical filter (FADOF) based on cesium and its D$_1$-line-transition ($6^2S_{1/2}\rightarrow6^2P_{1/2}$) around 894nm. We also present the prospects and visions for combining this filter with the single photon emission of a single quantum dot (QD), which matches with the atomic trans…

Universal classical-quantum superposition coding and universal classical-quantum multiple access channel coding

We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. The former universally achieves corner points of the capacity region and the latter u…

Quantum filtering for multiple diffusive and Poissonian measurements

We provide a rigorous derivation of a quantum filter for the case of multiple measurements being made on a quantum system. We consider a class of measurement processes which are functions of bosonic field operators, including combinations of diffusive and Poissonian processes. This covers the standard cases from quantum optics, where homodyne detection may be described as a diffusive process and photon counting may be described as a Poissonian process. We obtain a necessary and sufficient condition for any pair of such measurements taken at different output channels to satisfy a commutation re…

The Estimation Lie Algebra Associated with Quantum Filters

We introduce the Lie algebra of super-operators associated with a quantum filter, specifically emerging from the Stratonovich calculus. In classical filtering, the analogue algebra leads to a geometric theory of nonlinear filtering which leads to well-known results by Brockett and by Mitter characterizing potential models where the curse-of-dimensionality may be avoided, and finite dimensional filters obtained. We discuss the quantum analogue to these results. In particular, we see that, in the case where all outputs are subjected to homodyne measurement, the Lie algebra of super-operators is …

Quantum Reality Filters

An anhomomorphic logic $\ascript ^*$ is the set of all possible realities for a quantum system. Our main goal is to find the "actual reality" $ϕ_a\in\ascript ^*$ for the system. Reality filters are employed to eliminate unwanted potential realities until only $ϕ_a$ remains. In this paper, we consider three reality filters that are constructed by means of quantum integrals. A quantum measure $μ$ can generate or actualize a $ϕ\in\ascript ^*$ if $μ(A)$ is a quantum integral with respect to $ϕ$ for a density function $f$ over events $A$. In this sense, $μ$ is an "average" of the truth values of $ϕ…

squeezed噪声输入的量子滤波

Quantum Filtering for Squeezed Noise Inputs

本文研究了在四度测量下，输入场为一般准自由态的量子开放系统，提出了一种新的量子滤波方法，适用于压缩噪声输入，并利用Tomita-Takesaki理论构建了输入C*-代数的对易量。

在量子计算机上实现有限脉冲响应滤波器

Implementing Finite Impulse Response Filters on Quantum Computers

本文研究如何用量子系统实现经典离散时间信号处理，通过将输入信号编码为量子态并设计酉算子实现FIR滤波器，并提出级联低阶滤波器构造高阶滤波器的方法。

Mismatched Quantum Filtering and Entropic Information

Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum metrology, and quantum control. If the filter assumes a nominal model that differs from reality, however, the estimation accuracy is bound to suffer. Here I derive identities that relate the excess error caused by quantum filter mismatch to the relative entropy between the true and nominal observation probability measures, with one identity…

基于状态空间的量子计算机有限脉冲响应滤波

State-Space-Based FIR Filtering on a Quantum Computer

本文提出一种基于状态空间框架的量子FIR滤波器实现，利用酉量子电路和量子延迟门，支持并行与组合，并通过模拟投影算子实现低通等有界滤波，在量子电路模拟器上验证。

Stability of continuous-time quantum filters with measurement imperfections

The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic Master Equation (SME), driven simultaneously by Wiener and Poisson processes and that takes into account incompleteness and errors in measurements. This stability result is the continuous-time counterpart of a similar stability result already established for discrete-time quantum systems and where the measurement imperfections are modeled by a left stochastic …