Defogging computational ghost imaging via eliminating photon number fluctuation and a cycle generative adversarial network

Imaging through fluctuating scattering media such as fog is of challenge since it seriously degrades the image quality.We investigate how the image quality of computational ghost imaging is reduced by fluctuating fog and how to obtain a high-quality defogging ghost image. We show theoretically and experimentally that the photon number fluctuations introduced by fluctuating fog is the reason for ghost image degradation. An algorithm is proposed to process the signals collected by the computational ghost imaging device to eliminate photon number fluctuations of different measurement events. Thus, a high-quality defogging ghost image is reconstructed even though fog is evenly distributed on the optical path. A nearly 100% defogging ghost image is obtained by further using a cycle generative adversarial network to process the reconstructed defogging image.

Single-mode photon number measurement for the squeezed two-mode number state

Based on the fact that a two-mode squeezed number state is a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state, the result of one-mode l-photon measurement for the two-mode squeezed number state S2｜m, n） is discussed. It is found that a remaining field-mode simultaneously collapses into a number state ｜n - m＋l｜ with the coefficient being a Jacobi polynomial of n, m and l, which manifestly exhibits the entanglement between the two modes, i.e. it depends on the number-difference between the two modes. The second mode collapses into an excited coherent state when the first mode is measured as a coherent state.

Photon number cumulant expansion and generating function for photon added-and subtracted-two-mode squeezed states

For the first time, we derive the photon number cumulant for two-mode squeezed state and show that its cumulant expansion leads to normalization of two-mode photon subtracted-squeezed states and photon added- squeezed states. We show that the normalization is related to Jacobi polynomial, so the cumulant expansion in turn represents the new generating function of Jacobi polynomial.

Detecting the possibility of a type of photon number splitting attack in decoy-state quantum key distribution

The existing decoy-state quantum key distribution(QKD)beating photon-number-splitting(PNS)attack provides a more accurate method to estimate the secure key rate,while it still considers that only single-photon pulses can generate secure keys in any case.However,multiphoton pulses can also generate secure keys if we can detect the possibility of PNS attack in the channel.The ultimate goal of this line of research is to confirm the absence of all types of PNS attacks.In particular,the PNS attack mentioned and detected in this paper is only the weaker version of PNS attack which significantly changes the observed values of the legitimate users.In this paper,under the null hypothesis of no weaker version of PNS attack,we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state protocols,extract a Cauchy distribution statistic,and further provide a detection method and the type I error probability.If the result is judged to be an attack,we can use the existing decoy-state method and the GLLP formula to estimate the secure key rate.Otherwise,the pulses with the same basis received including both single-photon pulses and multiphoton pulses,can be used to generate the keys and we give the secure key rate in this case.Finally,the associated experiments we performed(i.e.,the significance level is 5%)show the correctness of our method.

Photon number resolvability of multi-pixel superconducting nanowire single photon detectors using a single flux quantum circuit

Superconducting nanowire single-photon detectors(SNSPDs) are typical switching devices capable of detecting single photons with almost 100% detection efficiency. However, they cannot determine the exact number of incident photons during a detection event. Multi-pixel SNSPDs employing multiple read-out channels can provide photon number resolvability(PNR), but they require increased cooling power and costly multi-channel electronic systems. In this work, a single-flux quantum(SFQ) circuit is employed, and PNR based on multi-pixel SNSPDs is successfully demonstrated. A multi-input magnetically coupled DC/SFQ converter(MMD2 Q) circuit with a mutual inductance M is used to combine and record signals from a multi-pixel SNSPD device. The designed circuit is capable of discriminating the amplitude of the combined signals in accuracy of Φ_(0)/M with Φ_(0) being a single magnetic flux quantum. By employing the MMD2 Q circuit,the discrimination of up to 40 photons can be simulated. A 4-parallel-input MMD2 Q circuit is fabricated, and a PNR of3 is successfully demonstrated for an SNSPD array with one channel reserved for the functional verification. The results confirm that an MMD2 Q circuit is an effective tool for implementing PNR with multi-pixel SNSPDs.

GHz photon-number resolving detection with high detection efficiency and low noise by ultra-narrowband interference circuits

We demonstrate the photon-number resolution(PNR)capability of a 1.25 GHz gated InGaAs single-photon avalanche photodiode(APD)that is equipped with a simple,low-distortion ultra-narrowband interference circuit for the rejection of its background capacitive response.Through discriminating the avalanche current amplitude,we are able to resolve up to four detected photons in a single detection gate with a detection efficiency as high as 45%.The PNR capability is limited by the avalanche current saturation,and can be increased to five photons at a lower detection efficiency of 34%.The PNR capability,combined with high efficiency and low noise,will find applications in quantum information processing technique based on photonic qubits.

The bright and dark photon number states in Young’s interference experiment

In this paper, we derive the bright and dark photon number states for spatial interference of two or more light beams and succeed in the explanation of Young's interference experiment, and also achieve a better comprehension of the well known comment of Dirac 'each photon only interferences with itself'. Prom the fully quantum point of view, the origin of the interference fringes consists in the mode transformation and the detection of double-slit states.

High Photon-Number Squeezing in Strong Field Limit

We show that high photon-number squeezing in bright light can be generated in both lasers and optical bistabilities by the injections of a squeezed vacuum and a classical field, and the high squeezing is maintained for very strong field.

The security of decoy state protocol in the partial photon number splitting attack

The decoy state protocol was proposed to overcome the primitive photon number splitting attack.When using a better strategy,the attacker can ensure that the ratio of the overall gain of the signal state pulse against the decoy state pulse changes very little,even to keep the overall gain of the signal state pulses equal to that obtained without attacker.In this paper we first give a model of the partial photon number splitting attack which contains the original one,and then find that the decoy state protocol still works effectively under the partial photon number splitting attack.

Oscillation behaviour in the photon-number distribution of squeezed coherent states

From the normally ordered form of the density operator of a squeezed coherent state（SCS）,we directly derive the compact expression of the SCS＇s photon-number distribution（PND）.Besides the known oscillation characteristics,we find that the PND is a periodic function with a period of π and extremely sensitive to phase.If the squeezing is strong enough,and the compound phase which is relevant to the complex squeezing and displacement parameters are assigned appropriate values,different oscillation behaviours in PND for even and odd photon numbers appear,respectively.

Photon-number distribution of two-mode squeezed thermal states by entangled state representation

Using the entangled state representation, we convert a two-mode squeezed number state to a Hermite polynomial excited squeezed vacuum state. We first analytically derive the photon number distribution of the two-mode squeezed thermal states. It is found that it is a Jacobi polynomial; a remarkable result. This result can be directly applied to obtaining the photon number distribution of non-Gaussian states generated by subtracting from （adding to） two-mode squeezed thermal states.

Calculation and analysis of the number of return photons from sodium laser beacon excited by the long pulse laser with circular polarization

The number of return photons from sodium laser beacon（SLB） greatly suffers down-pumping, recoil, and geomagnetic field when the long pulse laser with circular polarization interacts with sodium atoms in the mesosphere. Considering recoil and down-pumping effects on the number of return photons from SLB, the spontaneous radiation rates are obtained by numerical computations and fittings. Furthermore, combining with the geomagnetic field effects, a new expression is achieved for calculating the number of return photons. By using this expression and considering the stochastic distribution of laser intensity in the mesosphere under different turbulence models for atmosphere, the number of return photons excited by the narrow-band single mode laser and that by the narrow-band three-mode laser are respectively calculated. The results show that the narrow-band three-mode laser with a specific spectrum structure has a higher spontaneous radiation rate and more return photons than a narrow-band single mode laser. Of note, the effect of the atmospheric turbulence on the number of return photons is remarkable. Calculation results indicate that the number of return photons under the HV5/7 model for atmospheric turbulence is much higher than that under the Greenwood and Mod HV models.

Passive decoy state SARG04 quantum-key-distribution with practical photon-number resolving detectors

SARG04 protocol has its advantages in defending photon number splitting attack, benefited from two-photon pulses part. In this paper, we present a passive decoy state SARG04 scheme combining with practical photon number resolving （PNR） detectors. Two kinds of practical detectors, transition-edge sensor and time-multiplexing detector, are taken into consideration. Theoretical analysis shows that both of them are compatible with the passive decoy state SARG04. Compared with the original SARG04, two detectors can boost the key generation rate and maximal secure distance obviously. Meanwhile, the result shows that quantum efficiency and dark count of the detector influence the maximal distance slightly, which indicates the prospect of implementation in real quantum key distribution system with imperfect practical PNS detectors.

Bidirectional transfer of quantum information for unknown photons via cross-Kerr nonlinearity and photon-number-resolving measurement

We propose an arbitrary controlled-unitary （CU） gate and a bidirectional transfer scheme of quantum information （BTQI） for unknown photons. The proposed CU gate utilizes quantum non-demolition photon-number-resolving measure- ment based on the weak cross-Kerr nonlinearities （XKNLs） and two quantum bus beams; the proposed CU gate consists of consecutive operations of a controlled-path gate and a gathering-path gate. It is almost deterministic and is feasible with current technology when a strong amplitude of the coherent state and weak XKNLs are employed. Compared with the existing optical multi-qubit or controlled gates, which utilize XKNLs and homodyne detectors, the proposed CU gate can increase experimental realization feasibility and enhance robustness against decoherence. According to the CU gate, we present a BTQI scheme in which the two unknown states of photons between two parties （Alice and Bob） are mutually swapped by transferring only a single photon. Consequently, by using the proposed CU gate, it is possible to experimentally implement the BTQI scheme with a certain probability of success.

Oscillation behaviour in the photon-number distribution of squeezed coherent states

From the normally ordered form of the density operator of a squeezed coherent state(SCS),we directly derive the compact expression of the SCS’s photon-number distribution(PND).Besides the known oscillation characteristics,we find that the PND is a periodic function with a period of π and extremely sensitive to phase.If the squeezing is strong enough,and the compound phase which is relevant to the complex squeezing and displacement parameters are assigned appropriate values,different oscillation behaviours in PND for even and odd photon numbers appear,respectively.

有限大小量子Dicke-Stark模型的动力学性质

利用相干态的超完备性,可以有效解决光子数空间的截断问题,在有限的相干态空间中即可得到精确的计算结果.本文在相干态空间中计算了Dicke-Stark模型的数值精确解,继而讨论了该模型的量子相变和时间演化动力学.通过计算Dicke-Stark模型基态的平均光子数和平均角动量,发现了量子相变现象,量子相变临界点会随非线性Stark作用发生移动.计算得到Dicke-Stark模型平均光子数和平均角动量随耦合强度和时间演化的相图,有助于了解有限大小Dicke-Stark模型的动力学性质.

层积云背景下量子干涉雷达最优平均光子数自适应策略

量子干涉雷达(Quantum Interference Radar,QIR)是以量子力学为基础,利用量子纠缠效应进行目标探测的一种新型雷达体制,QIR探测光子数的变化会对雷达分辨率和系统生存函数产生影响。为了降低层积云液态水含量对QIR探测性能的影响,提出了基于诱骗态量子密钥协议的最优平均光子数自适应(Photon Number Adaptive,PNA)调整策略。建立了层积云液态水含量、传输距离与最优平均光子数之间的关系,对自适应调整前后的QIR分辨率和信道生存函数进行了比较。理论分析和仿真结果表明,当脉冲信号波长一定,层积云粒子浓度为1.579×10^(4)cm^(-3),层积云液态水含量为0.5 g/cm3时,采用PNA策略之后,QIR角度分辨率值由1.289下降至1.028,QIR系统角度分辨率和空间分辨率均得到有效提高;当层积云液态水含量为0.1034 g/cm^(3)时,采用PNA策略之后,信道生存函数由0.2292提高到0.4167。因此,通过PNA策略自适应地调整系统发送端信号脉冲所含的平均光子数,能够提高QIR在层积云背景下探测的可靠性。

基于多光子叠加态的交叉相位调制耦合参数测量

继纠缠之后,粒子间相互作用已成为量子增强的重要资源.在不利用纠缠资源的前提下,已有研究工作利用单光子叠加态与相干态的相互作用实现了精度为海森堡极限的参数测量,然而海森堡极限并不是这个相互作用模型的测量精度极限.为了得到更高的测量精度,将单光子叠加态替换为多光子叠加态,在弱测量框架下对信号光量子态进行后选择与量子态筛选.将单光子叠加态替换为多光子叠加态,能为测量结果带来全方位提升.提出基于多光子叠加态的交叉相位调制耦合参数测量的物理方案,该物理方案具有搭建难度低及操作简单的优点.

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.

Estimation of photon counting statistics with imperfect detectors

The study on photon counting statistics is of fundamental importance in quantum optics. We theoretically analyzed the imperfect detection of an arbitrary quantum state. We derived photon counting formulae for six typical quantum states （i.e., Fock, coherent, squeeze-vacuum, thermal, odd and even coherent states） with finite quantum efficiencies and dark counts based on multiple on/off detector arrays. We applied the formulae to the simulation of multiphoton number detections and obtained both the simulated and ideal photon number distributions of each state. A comparison between the results by using the fidelity and relative entropy was carried out to evaluate the detection scheme and help select detectors for different quantum states.