Aaron Pearlman, Alexander Ling, Elizabeth Goldschmidt, Jingyun Fan, Alan Migdall
We experimentally map the transverse profile of diffraction-limited beams using photon-number-resolving detectors. We observe strong compression of diffracted beam profiles for high detected photon number. This effect leads to higher contrast than a conventional irradiance profile between two Airy disk-beams separated by the Rayleigh criterion.
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The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal inter…
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon number resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, proof to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
Resolving Mutually Coherent Bright Point-Sources
本文研究任意量子统计下相互相干双点源的分辨问题，利用矩方法灵敏度度量证明空间模式解复用优于直接成像，并达到量子Fisher信息极限。
We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non- probabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver i…
There has been much recent interest in quantum optical interferometry for applications to metrology, sub-wavelength imaging, and remote sensing, such as in quantum laser radar (LADAR). For quantum LADAR, atmospheric absorption rapidly degrades any quantum state of light, so that for high-photon loss the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the Beer law for classical optical attenuation, and which provides sensitivity at the shot-noise limit. This approach leaves open the question -- what is the optimal detection scheme for such states in ord…
We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. I…
There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beer's law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupl…
We present a method for the experimental measurement of nonclassicality witnesses and demonstrate its application. Our proposal only requires the coherent displacement of the initial state, which can be achieved by overlapping the latter with a coherent state at a beam splitter, and subsequent photon-number resolved detection. This setup allows a complete test of nonclassicality of an arbitrary quantum state. The role of the quantum efficiency as well as statistical and systematic uncertainties are discussed. Finally, the scheme is demonstrated for a realistic example.
Multiphoton interference effects can be measured with a single detector when two input photons are temporally well separated when compared with the dead time of the single-photon avalanche detector. Here we experimentally demonstrate that the Hong-Ou-Mandel interference effect can be observed with a single non-photon-number resolving detector via a time-delayed coincidence measurement of successive electrical signals from the detector. The two-photon interference experiment is performed by utilizing temporally well-separated pairwise weak coherent pulses and the interference fringes are succes…
The variance of difference of photocounts (VDPs) is an established measure of quantum correlations for quantum states of light. It enables us to discriminate between the classical correlation of a two-mode coherent state and the quantum correlation of a twin-beam state. We study the effect of loss and saturation of the photon-number-resolving detector on the measurement of the VDPs. An analytic function is derived for this variance, both for the coherent and the twin-beam states. It is found that the VDPs is no longer a reliable entanglement measure in the nonlinear regime of the detector resp…
A number of applications in basic science and technology would benefit from high fidelity photon number resolving photodetectors. While some recent experimental progress has been made in this direction, the requirements for true photon number resolution are stringent, and no design currently exists that achieves this goal. Here we employ techniques from fundamental quantum optics to demonstrate that detectors composed of subwavelength elements interacting collectively with the photon field can achieve high-performance photon number resolution. We propose a new design that simultaneously achiev…
We have created heralded coherent state superpositions (CSS), by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This is the first experiment enabled by and utilizing the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean photon number of 2.75 -0.24/+0.06 and a fidelity of 0.59 -0.14/+0.04 with an ideal CSS. This confirms that subtracting more photons result…
We propose novel coherent-state phase concentration by probabilistic measurement-induced ampli- fication. The amplification scheme uses novel architecture, thermal noise addition (instead of single photon addition) followed by feasible multiple photon subtraction using realistic photon-number resolving detector. It allows to substantially amplify weak coherent states and simultaneously reduce their phase uncertainty, contrary to the deterministic amplifier.
We investigate how the entanglement properties of a two-mode state can be improved by performing a coherent superposition operation of photon subtraction and addition, proposed by Lee and Nha [Phys. Rev. A 82, 053812 (2010)], on each mode. We show that the degree of entanglement, the EPR-type correlation, and the performance of quantum teleportation can be all enhanced for the output state when the coherent operation is applied to a two-mode squeezed state. The effects of the coherent operation are more prominent than those of the mere photon subtraction and the addition particularly in the sm…
Number state filtered coherent states are a class of nonclassical states obtained by removing one or more number states from a coherent state. Phase sensitivity of an interferometer is enhanced if these nonclassical states are used as input states. The optimal phase sensitivity, which is related to the quantum Cramer-Rao bound (QCRB) for the input state, improves beyond the standard quantum limit. It is argued that removal of more than one suitable number state leads to better phase sensitivity. As an important limiting case in this context, the even and odd coherent states, where the odd and …
Enhancing One-Way Steering and Non-Classical Correlations in Magnomechanics via Coherent Feedback
提出利用相干反馈增强腔磁力系统中的量子关联层级，通过调节分束器反射参数显著提升量子关联对热噪声的鲁棒性，并实现光子、磁子与声子间增强的真实三部分纠缠。
We propose a near-optimum receiver for the discrimination of binary phase-shift-keyed coherent states employing photon-number-resolving detectors. The receiver exploits a discrimination strategy based on both the so-called homodyne-like and the direct detection, thus resulting in a hybrid scheme. We analyse the performance and the robustness of the proposed scheme under realistic conditions, namely, in the presence of inefficient detection and dark counts. We show that the present hybrid setup is near-optimum and beats both the standard-quantum-limit and the performance of the Kennedy receiver…
Local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) are both two tools used to capture purely quantum correlations in multi-partite quantum systems. In this paper, we study these quantifiers in the case of multipartite Glauber coherent state which include the GHZ (Greenberger-Horne-Zeilinger) and Werner states. We perform a comparative study between LQFI and LQU in an isolated system. Besides, by using the Kraus operator representation, we study the behavior of these quantifiers on the dephasing channel to investigate their performances under the decoherence effect. In …
Developing a photon-number-resolving detection chain for quantum communication protocols involving mesoscopic states of light
本文研究了基于硅光电倍增管和14位1Gs/s数字采集系统的光子数分辨检测链，通过测试三种Hamamatsu制造的SiPM模型，系统研究了像素间距、堆叠效应和光子检测效率对检测性能的影响。
Large dynamic range room temperature photon number resolving (PNR) detectors can be very useful for measuring very low light intensities and for analyzing multiphoton quantum states. In this paper we present a PNR detector based on the up-conversion (UC) of telecom signal into visible wavelength and on its detection by a thermoelectrically cooled multi-pixel silicon avalanche photodiodode (APD), also known as Silicon Photon Multiplier (SiPM). An efficiency of 4% is attained and the poissonian statistics of input coherent states is maintained up to approximately 20 simultaneous detections. The …
Resolving problems with the continuum limit in coherent-state path integrals
针对玻色子热相干态路径积分中的连续极限问题，通过构造精确离散版本并比较不同排序的连续极限，证明Weyl排序适用于所有多项式哈密顿量，并利用重整化方法给出一般性证明。
Sum-frequency-based photon-number-resolving detector for telecom wavelengths
针对量子通信中C波段低强度光的探测需求，提出结合低成本光子数分辨探测器与非线性光学的接收器，实现电信波长灵敏度，验证了1.5μm飞秒光源的泊松特性，为复杂量子方案提供探测支持。
Photon number resolving detection using time-multiplexing
在许多量子信息技术中，需要能够分辨光子数的探测器。为了在量子信息处理中有用，这样的检测器应该简单、易于使用，并且可扩展以分辨任何数量的光子，因为应用可能需要很大的便携性，例如在量子密码学中。在这里，我们描述了一个时间复用检测器，它使用一对标准的雪崩光电二极管在盖革模式下工作的建设。理论分析和实验测试使用脉冲光源的弱相干光的检测技术。
Enhancing qubit readout fidelity with two-mode squeezing of the coherent measurement signal
本文提出通过同时测量双模压缩态和相干组合提升量子比特读取保真度，适用于高频放大器和噪声抑制场景。
We present a method of directly obtaining the parity of a Gaussian state of light without recourse to photon-number counting. The scheme uses only a simple balanced homodyne technique, and intensity correlation. Thus interferometric schemes utilizing coherent or squeezed light, and parity detection may be practically implemented for an arbitrary photon flux. Specifically we investigate a two-mode, squeezed-light, Mach-Zehnder interferometer and show how the parity of the output state may be obtained. We also show that the detection may be described independent of the parity operator, and that …
We propose quantum receivers with optical squeezing and photon-number-resolving detector (PNRD) for the near-optimal discrimination of quaternary phase-shift-keyed coherent state signals. The basic scheme is similar to the previous proposals (e.g. Phys. Rev. A 84, 042328 (2012)) in which displacement operations, on-off detectors, and electrical feedforward operations were used. Here we study two types of receivers where one installs optical squeezings and the other uses PNRDs instead of on-off detectors. We show that both receivers can attain lower error rates than that by the previous scheme …
We present optimal schemes, based on photon number measurements, for Gaussian state tomography and for Gaussian process tomography. An $n$-mode Gaussian state is completely specified by $2 n^2+3n$ parameters. Our scheme requires exactly $2 n^2+3n$ distinct photon number measurements to tomograph the state and is therefore optimal. Further, we describe an optimal scheme to characterize Gaussian processes by using coherent state probes and photon number measurements. With much recent progress in photon number measurement experimental techniques, we hope that our scheme will be useful in various …
Enhancing phase sensitivity in Mach-Zehnder interferometer with various detection schemes using SU(1,1) coherent states
本文研究马赫-曾德尔干涉仪在不同相移场景和探测方案下的相位灵敏度，证明以SU(1,1)相干态为输入态时，各探测方案在最优条件下均可达到量子Cramér-Rao界。
Enhancing the security of coherent one-way quantum key distribution using CHSH correlations
本研究通过极小改动COW协议，利用CHSH关联监测量子关联以检测更多攻击，将其最大安全距离从不足20km延长至约259km，增强了该量子密钥分发协议的安全性。
Optical Gottesman-Kitaev-Preskill qubit generation via approximate squeezed coherent state superposition breeding
本文提出通过广义光子减除培育近似压缩相干态叠加，并用高成功概率零差测量补充光子数分辨测量，将光学 GKP 量子比特生成成功概率提升两个数量级至 $10^{-5}$ 以上，同时保持高达 10 dB 压缩级别的纠错能力。
Enhancing Quantum Machine Learning: The Power of Non-Linear Optical Reproducing Kernels
本研究提出基于Kerr相干态构建的新型量子核特征空间，可通过物理参数调控曲率，在含噪声数据集和硬件上表现出更优性能，为量子机器学习提供了灵活鲁棒的新方案。
Conditional Production of Superpositions of Coherent States with Inefficient Photon Detection
结果表明，利用单光子源和简单的全光操作，可以产生两个宏观上可区分的光学相干态的线性叠加。单光子的弱压缩、与辅助相干态的光束混频以及非理想阈值探测器对光子的探测足以在自由传播光场中产生具有大相干振幅（$α>2$）和高保真度（$F>0.99$）的相干态叠加。与以前的所有方案产生这样的状态，我们的计划不需要光子数分辨测量，也没有克尔型非线性相互作用。此外，它对检测效率低下是鲁棒的，并且对光子产生效率低下表现出一定的弹性。
High-efficiency and fast photon-number resolving parallel superconducting nanowire single-photon detector
本文提出一种无串扰、无闩锁的并联超导纳米线单光子探测器，实现92.5%系统效率，并通过建模重建相干光源光子数统计，为单探测器表征多种光源奠定基础。
Collective excitation modes in solid state systems play a central role in circuit quantum electrodynamics, cavity optomechanics, and quantum magnonics. In the latter, quanta of collective excitation modes in a ferromagnet, called magnons, interact with qubits to provide the nonlinearity necessary to access quantum phenomena in magnonics. A key ingredient for future quantum magnonics systems is the ability to probe magnon states. Here we observe individual magnons in a millimeter-sized ferromagnet coherently coupled to a superconducting qubit. Specifically, we resolve magnon number states in sp…
We review and compare Bell-state measurement and quantum teleportation schemes using linear optics with three different types of resources, i.e., two-photon pairs, entangled coherent states and hybrid entangled states. Remarkably, perfect teleportation with linear optics is possible in principle based on a hybrid approach that combines two-photon pairs and entangled coherent states. It turns out that hybrid approach allows to perform Bell-state measurement and local Pauli operations in a deterministic way, while it requires photon number resolving measurements.
We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid photodetector operated above its photon-resolving regime, we obtained both the statistics at different values of the probe field and the values of the probe phase required to reconstruct the Wigner function.
Enhancing capacity of coherent optical information storage and transfer in a Bose-Einstein condensate
研究了原子玻色-爱因斯坦凝聚体的相干光信息存储能力。通过考虑群速度色散，将原子云中的慢光传输理论推广到短脉冲区域。结果表明，在特定的耦合激光功率，温度和原子间相互作用强度的凝聚体中的存储脉冲的数量可以进行优化。采用有效均匀密度区近似，对半理想模型的凝结体进行了解析计算。还进行了详细的数值模拟。研究发现，凝结体的轴向密度分布可以保护脉冲不受群速度色散的影响。此外，考虑到凝聚体的有限径向尺寸，研究了多模光在原子玻色-爱因斯坦凝聚体中的传输。得到了凝聚体所能支持的模数，并确定了单模条件与实验参数的函数关系，这些参数包括阱尺寸、温度、凝聚体数密度和散射长度。提出了一种增强多模光传输效应的量子相干原子-光相互作用方案。
With the progress of optical detection technology, the classical diffraction limit raised a hundred years ago has been continuously broken through. In previous experiments within fluorescence sources, one of the techniques used is detecting auto-correlation functions. The image is reconstructed by single-photon and multi-photon detecting intensities. By taking the joint intensity of more than one single-photon detectors into consideration, the point spread function of each photon emitter can be resolved even when the distance of their central position is below the classical diffraction limit. …
Entangled coherent states can be prepared remotely by subtracting non-locally a single photon from two quantum superpositions of coherent states, the so-called "Schroedinger's cat" state. Such entanglement can further be distributed over longer distances by successive entanglement swapping operations using linear optics and photon-number resolving detectors. The aim of this paper is to evaluate the performance of this approach to quantum repeaters for long distance quantum communications. Despite many attractive features at first sight, we show that, when using state-of-the-art photon counters…
Enhancing Optomechanical Entanglement and Mechanical Squeezing by the Synergistic Effect of Quadratic Optomechanical Coupling and Coherent Feedback
研究含相干反馈回路的膜嵌入腔光机械系统中，如何通过线性和二次光机械耦合实现强光机械纠缠和机械压缩。利用系统参数可调性及协同效应，给出增强纠缠和压缩的方法。
Enhancing nonclassical properties of quantum states of light using linear optics
本文提出一种仅用线性光学和光电探测器增强光态非经典性质的通用方案，通过调谐相干态振幅滤除福克分量，可增强子泊松统计或正交压缩。
We investigate the coherent energy transfer between two quantum systems mediated by a quantum bus. In particular, we consider the energy transfer process between two qubits, and how it can be influenced by using a third qubit or photons in a resonant cavity as mediators. Inspecting different figures of merit and considering both on and off-resonance configurations, we characterize the energy transfer performances. We show that, while the qubit-mediated transfer shows no advantages with respect to a direct coupling case, the cavity-mediated one is progressively more and more efficient as functi…
Photon-number-revolving (PNR) detection allows the direct measurement of the Wigner quasiprobability distribution of an optical mode without the need for numerically processing an inverse Radon transform [K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996)]. In this work, we reproduced the seminal experiment of Banaszek et al. [Phys. Rev. A 60, 674 (1999)] of quantum tomography of a pure coherent state, and of a statistical mixture thereof, and extended it to the more general case of photon fluxes with much more than one photon per detection time. This was made possible by the use …
We present the generation and characterization of the class of bracket states, namely phase-sensitive mixtures of coherent states exhibiting symmetry properties in the phase-space description. A bracket state can be seen as the statistical ensemble arriving at a receiver in a typical coherent-state-based communication channel. We show that when a bracket state is mixed at a beam splitter with a local oscillator, both the emerging beams exhibit a Fano factor larger than 1 and dependent on the relative phase between the input state and the local oscillator. We discuss the possibility to exploit …
Resolving Photon Numbers Using Ultra-High-Resolution Timing of a Single Low-Jitter Superconducting Nanowire Detector
本文通过对常规超导纳米线单光子探测器产生的电脉冲进行超高分辨率时间标记，实现了光子数分辨能力，该方法兼具高探测效率与高重复率，并在电信C波段通过相干光统计及非经典态相关性验证了其有效性。
Recent evidence suggests that quantum effects may have functional importance in biological light-harvesting systems. Along with delocalized electronic excitations, it is now suspected that quantum coherent interactions with certain near-resonant vibrations may contribute to light-harvesting performance. However, the actual quantum advantage offered by such coherent vibrational interactions has not yet been established. We investigate a quantum design principle, whereby coherent exchange of single energy quanta between electronic and vibrational degrees of freedom can enhance a light-harvesting…
Fiber-assisted detection with photon number resolution
我们报告的光子数分辨探测器的光纤设置和一对标准的雪崩光电二极管的基础上的发展。该探测器能够分辨单个光子数，并根据众所周知的原理进行操作，通过该原理，单模输入状态被分成大量（八个）输出模式。我们重建的光子统计弱相干输入光的实验数据，并表明，有一个很高的概率推断输入光子数从测量的检测事件的数量在一个单一的运行。
Optimized detector tomography for photon-number resolving detectors with hundreds of pixels
针对数百像素光子数可分辨探测器的层析表征计算量大的问题，提出一种减少优化变量的改进探测器层析模型，利用 expectation-maximization-entropy 算法重建光子数分布，在保证保真度超 99% 的同时将求解时间减半。
The Kennedy-like receiver is a quasi-optimal receiver employed in binary phase-shift-keyed communication schemes with coherent states. It is based on the interference of the two signals encoding the message with a reference local oscillator and on/off photodetection. We show both theoretically and experimentally that it is possible to extract useful information about the phase reference by Bayesian processing of the very same data sample used to discriminate the signals shot by shot. We demonstrate that the minimum uncertainty in phase estimation, given by the inverse of the Fisher information…
Enhancing strength and range of atom-atom interaction in a coupled-cavity array via parametric drives
针对原子间相干相互作用随距离指数衰减的问题，本文提出对耦合腔阵列施加双光子参数驱动，以放大单光子束缚态局域化长度和原子-光子耦合，从而增强远距离原子相互作用并促进信息传输与纠缠产生。
It is shown that the maximal phase sensitivity of a two-path interferometer with high-intensity coherent light and squeezed vacuum in the input ports can be achieved by photon-number-resolving detection of only a small number of photons in a dark output port. It is then possible to achieve the quantum Cramér-Rao bound of the two-path interferometer using only the field displacement dependence of the photon number statistics in the single mode output of the dark port represented by a field-displaced squeezed vacuum state. We find that, at small field displacements, it is not sufficient to use t…
Homodyne detection is optimal for quantum interferometry with path-entangled coherent states
针对纠缠相干态和量子比特哪条路径态的差分相位估计，本文证明无需光子数分辨探测器的零差检测可饱和量子Cramér-Rao界，并在光子损失下保持相位无关的稳健性能。
Solid-state quantum coherent devices are quickly progressing. Superconducting circuits, for instance, have already been used to demonstrate prototype quantum processors comprising a few tens of quantum bits. This development also revealed that a major part of decoherence and energy loss in such devices originates from a bath of parasitic material defects. However, neither the microscopic structure of defects nor the mechanisms by which they emerge during sample fabrication are understood. Here, we present a technique to obtain information on locations of defects relative to the thin film edge …
Photon number resolution using a time-multiplexed single-photon detector
光子数分辨探测器是包括线性光学量子计算在内的各种应用所需要的。在这里，我们描述了使用时间复用技术，允许普通的单光子探测器，如硅雪崩光电二极管，被用作光子数分辨探测器。这样的探测器的能力，正确地测量入射数状态的光子数进行了分析。入射相干态的预测结果被发现是在很好的协议与原理验证的实验演示的结果。
Complementarity theory is the essence of the Copenhagen interpretation. Since the Hanbury Brown and Twiss experiments, the particle nature of photons has been intensively studied for various quantum phenomena such as anticorrelation and Bell inequality violation in terms of two-photon correlation. Regarding the fundamental question on these quantum features, however, no clear answer exists for how to generate such an entanglement photon pair and what causes the maximum correlation between them. Here, we experimentally demonstrate the physics of anticorrelation on a beam splitter using sub-Pois…
Hybrid discrimination strategy in quantum communication based on photon-number-resolving detectors and mesoscopic twin-beam states
本文提出一种介观强度下的混合量子通信判别策略，利用光子数分辨探测器读取二元热信号的平均光子数，并以对窃听敏感的孪生光束态提供安全性，兼顾鲁棒性与安全性且可扩展。
Near-optimal discrimination of displaced squeezed binary signals using displacement, inverse-squeezing, and photon-number-resolving detection
本文提出反压缩Kennedy接收器，用于区分二进制相位调制位移压缩真空态，通过反压缩增强光子数对比度，实现超越标准量子限和Helstrom界，且在实际参数下保持鲁棒性。
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting p…
Quantum-Limited Symbol-Blind Channel Estimation for Coherent State Discrimination
研究光子匮乏相干链路中残余色散问题，通过建立量子极限，利用多输出量子脉冲门结合光子数分辨检测，实现群延迟和二阶色散的盲联合估计，支持在湍流衰落时低于标准量子极限接收。
We propose an innovative strategy to discriminate between two coherent states affected by either uniform or gaussian phase noise. The strategy is based on a homodyne-like detection scheme with photon-number-resolving detectors in the regime of low-intensity local oscillator. The experimental implementation of the detection scheme involves two hybrid photodetectors, whose outputs are used in post processing to calculate the shot-by-shot photon-number difference. The performance of this strategy is quantified in terms of the error probability in discriminating the noisy coherent signals as a fun…
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