W. J. Munro
We identify what ideal correlated photon number states are to required to maximize the discrepancy between local realism and quantum mechanics when a quadrature homodyne phase measurement is used. Various Bell inequality tests are considered.
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We suggest to use the photon homodyne detection experimental data for checking the Heisenberg and Schrödinger-Robertson uncertainty relations, by means of measuring optical tomograms of the photon quantum states.
Optical satellite links open up new prospects for realizing quantum physical experiments over unprecedented length scales. We analyze and affirm the feasibility of detecting quantum squeezing in an optical mode with homodyne detection of only one bit resolution, as is found in satellites already in orbit. We show experimentally that, in combination with a coherent displacement, a binary homodyne detector can still detect quantum squeezing efficiently even under high loss. The sample overhead in comparison to non-discretized homodyne detection is merely a factor of 3.3.
We observe -9.01$\pm$0.14 dB of squeezing and +15.12$\pm$0.14 dB of antisqueezing with a local oscillator phase locked in homodyne measurement. In reference [1], two main factors are pointed out which degrade the observed squeezing level: phase fluctuation in homodyne measurement and intracavity losses of an optical parametric oscillator for squeezing. We have improved the phase stability of homodyne measurement and have reduced the intracavity losses. We measure pump power dependences of the squeezing and antisqueezing levels, which show good agreement with theoretical calculations taking acc…
We experimentally study a homodyne detection technique for the characterization of a quadrature squeezed field where the correlated bands, here created by four-wave mixing in a hot atomic vapor, are separated by a large frequency gap of more than 6 GHz. The technique uses a two-frequency local oscillator to detect the fluctuations of the correlated bands at a frequency accessible to the detection electronics. Working at low detection frequency, the method allows for the determination of both the amplitude and the phase of the squeezing spectrum. In particular, we show that the quadrature squee…
We describe a simple and efficient setup to generate and characterize femtosecond quadrature-entangled pulses. Quantum correlations equivalent to about 2.5 dB squeezing are efficiently and easily reached using the non-degenerate parametric amplification of femtosecond pulses through a single-pass in a thin (0.1 mm) potassium niobate crystal. The entangled pulses are then individually sampled to characterize the non-separability and the entropy of formation of the states. The complete experiment is analysed in the time-domain, from the pulsed source of quadrature entanglement to the time-resolv…
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coheren…
We consider the measuring procedure that in principle allows to avoid the homodyne detection for the simultaneous selection of both quadrature components in the far-field. The scheme is based on the use of the coherent sources of the non-classical light. The possibilities of the procedure are illustrated on the basis of the use of pixellised sources, where the phase-locked sub-Poissonian lasers or the degenerate optical parametric oscillator generating above threshold are chosen as the pixels. The theory of the pixellised source of the spatio-temporal squeezed light is elaborated as a part of …
Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely recognized for its ease of implementation, efficiency with respect to error correction, and its compatibility with modern optical communication devices. However, recent studies report that the application of homodyne detection obtains poor tolerance to excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks. In this paper, we propose a homodyne detection protocol using the quadrature phase shift keying tec…
We propose a simple optomechanical model in which a mechanical oscillator quadrature could be "cooled" well below its equilibrium temperature by applying a suitable feedback to drive the orthogonal quadrature by means of the homodyne current of the radiation field used to probe its position.
Quantified convergence of general homodyne measurements with applications to continuous variable quantum computing
本文研究了宽谱混频测量在连续变量量子计算中的收敛性，并通过实验验证了其在量子态制备和纠错中的应用价值。
We present a protocol that produces a conditionally prepared state that can be used for a Bell test based on homodyne detection. Based on the results of Munro [PRA 1999], the state is near-optimal for Bell-inequality violations based on quadrature-phase homodyne measurements that use correlated photon-number states. The scheme utilizes the Gaussian entanglement distillation protocol of Eisert et. al. [Annals of Phys. 2004] and uses only beam splitters and photodetection to conditionally prepare a non-Gaussian state from a source of two-mode squeezed states with low squeezing parameter, permitt…
We obtain the standard quadrature-phase positive operator-valued measure (POVM) for homodyne detection directly and rigorously from the POVM for photon counting without directly employing the mean field approximation for the local oscillator. In addition we obtain correction terms for the quadrature-phase POVM that are applicable for relatively weak local oscillator field strengths and typical signal states.
Squeezing enhanced homodyne weak force sensing in cavity optomechanics
通过变分零差读出和量子压缩，在腔光力学系统中实现超越标准量子极限的弱力灵敏度提升。
We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beamsplitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6-dB squeezed light and an homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent generation of single-mode non-gaussian states, confirms that this method opens a promising avenue towards a complete experimental B…
Evaluating the performance of a weak-field homodyne receiver in quadrature phase-shift keying optical communication
本文提出一种弱场接收机作为替代现有光学同相检波器，通过四进制通信证明其在相位编码中的有效性，提升信息传输率和密钥生成速率。
Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules: local complement operation and vertex deletion (single quadrature-amplitude $\hat{x}$ measurement), the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.
We show that hybrid local measurements combining homodyne measurements and photodetection provide violations of a Bell inequality with arbitrarily low photodetection efficiency. This is shown in two different scenarios: when one part receives an atom entangled to the field mode to be measured by the other part and when both parts make similar photonic measurements. Our findings promote the hybrid measurement scenario as a candidate for loophole-free Bell tests beyond previous expectations.
We demonstrate that different kind of mesoscopic quantum states of light can be efficiently generated from a simple iterative scheme using homodyne heralding. These states exhibit strong non-classical features, and are of great interest for many applications such as quantum error-correcting codes or fundamental testings. On this basis we propose a protocol allowing a large loophole-free violation of a CHSH-type Bell inequality with a remarkable robustness to line losses.
We present a scheme for demonstrating violation of Bell's inequalities using a spin-1/2 system entangled with a pair of classically distinguishable wave packets in a harmonic potential. In the optical domain, such wave packets can be represented by coherent states of a single light mode. The proposed scheme involves standard spin-1/2 projections and measurements of the position and the momentum of the harmonic oscillator system, which for a light mode can be realized by means of homodyne detection. We discuss effects of imperfections, including non-unit efficiency of the homodyne detector, and…
Realistic Bell tests with homodyne measurements
本研究针对零差测量受限的光子贝尔实验，通过数值优化CHSH不等式与分箱策略，证实有界光子数态可产生大幅贝尔违背，含噪损真实条件下仍有效，并提出具体实现方案，拓展了零差探测贝尔实验的研究路径。
Broadband pulsed quadrature measurements with calorimeters
研究宽带模式下正交算符的测量问题，提出利用量热计探测总能量的宽带脉冲零差检测方法，并证明其随本振振幅增大可收敛至理想正交测量。
We show that homodyne measurements can be used to demonstrate violations of Bell's inequality with Gaussian states, when the local rotations used for these types of tests are implemented using nonlinear unitary operations. We reveal that the local structure of the Gaussian state under scrutiny is crucial in the performance of the test. The effects of finite detection efficiency is thoroughly studied and shown to only mildly affect the revelation of Bell violations. We speculate that our approach may be extended to other applications such as entanglement distillation where local operations are …
Robust Bell Nonlocality from Gottesman-Kitaev-Preskill States
GKP编码通过锁相检测揭示了有限压缩的GHZ和W态的多参与者非局域性，克服了连续变量系统中锁相检测的限制。
A simple scheme for conditional generation of nonclassical light with sub-Poissonian photon-number statistics is proposed. The method utilizes entanglement of signal and idler modes in two-mode squeezed vacuum state generated in optical parametric amplifier. A quadrature component of the idler mode is measured in balanced homodyne detector and only those experimental runs where the absolute value of the measured quadrature is higher than certain threshold are accepted. If the threshold is large enough then the conditional output state of signal mode exhibits reduction of photon-number fluctuat…
We have theoretically investigated the possibility of using any of several continuous-variable Bell-type inequalities - for which the dichotomic measurements are achieved with coarse-grained quadrature (homodyne) measurements - in a multi-party configuration where each participant is given a section, in the frequency domain, of the output of an optical parametric oscillator which has been synchronously-pumped with a frequency comb. Such light sources are undergoing intense study due to their novel properties, including the potential for production of light entangled in many hundreds of physica…
A classical model is presented for the features of parametric down-conversion and homodyne detection relevant to recent proposed ``loophole-free'' Bell tests. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If cit is not, then the experiments will fail in their initial concept, since both quantum theorists and local r…
We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to fully non-destructive non-informative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using str…
Exact Conditional Momentum Moments for Nonlinear Homodyne Trajectories
本文针对多项式单正交哈密顿量等构成的连续监测系统，推导了其任意有限阶正交矩条件动力学的精确有限维随机表示，提供了一种高效的非线性零差轨迹研究方法。
We examine the moment-reconstruction performance of both the homodyne and heterodyne (double-homodyne) measurement schemes for arbitrary quantum states and introduce moment estimators that optimize the respective schemes for any given data. In the large-data limit, these estimators are as efficient as the maximum-likelihood estimators. We then illustrate the superiority of the heterodyne measurement for the reconstruction of the first and second moments by analyzing Gaussian states and many other significant non-classical states.
Homodyne measurement is a corner-stone of quantum optics. It measures the fundamental variables of quantum electrodynamics - the quadratures of light, which represent the cosine-wave and sine-wave components of an optical field and constitute the quantum optical analog of position and momentum. Yet, standard homodyne, which is used to measure the quadrature information, suffers from a severe bandwidth limitation: While the bandwidth of optical states can easily span many THz, standard homodyne detection is inherently limited to the electrically accessible, MHz to GHz range, leaving a dramatic …
We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as non-unit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's ineq…
Controlling the quadrature measured by a homodyne detector is a universal task in continuous-variable quantum optics. However, deriving an error signal that is linear across theentire range of quadrature angles remains an open experimental problem. Here we propose a scheme to produce such an error signal through the use of a universally tunable modulator.
Recent proposed ``loophole-free'' Bell tests are discussed in the light of classical models for the relevant features of optical parametric amplification and homodyne detection. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If it is not, then the experiments will fail in their initial concept, since both quantum the…
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterody…
The eight-port homodyne detector is an optical circuit designed to perform the monitoring of two quadratures of an optical field, the signal. By using quantum Bose fields and quantum stochastic calculus, we give a complete quantum description of this apparatus, when used as quadrature detector in continuous time. We can treat either the travelling waves in the optical circuit, either the observables involved in the detection part: two couples of photodiodes, postprocessing of the output currents. The analysis includes imperfections, such as not perfectly balanced beam splitters, detector effic…
Automated generation of photonic circuits for Bell tests with homodyne measurements
本文提出自动化框架，利用深度强化学习和量子光学模拟设计光子电路，实现显著违反CHSH不等式的贝尔测试实验。
We present a homodyne detection scheme to verify Bell's inequality on correlated optical beams at the output of a nondegenerate parametric amplifier. Our approach is based on tomographic measurement of the joint detection probabilities, which allows high quantum efficiency at detectors. A self-homodyne scheme is suggested to simplify the experimental set-up.
Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by measuring the field amplitudes at different optical phases using homodyne detection. The quadrature-phase homodyne measurement outputs a continuous variable, so to reduce the computational cost of tomography, researchers often discretize the measurements. We show that this can be done without significantly degrading the fidelity between the estimated state …
Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.
On balanced homodyne measurement -- simple proof of wave function collapse
本文用初等微积分证明平衡零差探测器测量信号的正交相位振幅，并指出测量后复合态坍缩近似于信号坍缩到对应本征态。
Homodyne measurements are a widely used quantum measurement. Using a coherent state of large amplitude as the local oscillator, it can be shown that the quantum homodyne measurement limits to a field quadrature measurement. In this work, we give an example of a general idea: injecting non-classical states as a local oscillator can led to non-classical measurements. Specifically we consider injecting a superposition of coherent states, a Schrödinger cat state, as a local oscillator. We derive the Kraus operators and the positive operator-valued measure (POVM) in this situation.
We investigate the violation of local realism in Bell tests involving homodyne measurements performed on multimode continuous-variable states. By binning the measurement outcomes in an appropriate way, we prove that the Mermin-Klyshko inequality can be violated by an amount that grows exponentially with the number of modes. Furthermore, the maximum violation allowed by quantum mechanics can be attained for any number of modes, albeit requiring a quantum state that is rather unrealistic. Interestingly, this exponential increase of the violation holds true even for simpler states, such as multip…
Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature values. In this paper we explore the possibility of operating a conjugate homodyne detection system in "photon counting" mode to implement discrete-variable (DV) quantum key distribution (QKD) protocols. A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures X and P of the incoming quantum state. In classical electrodynamics, X^2 + P^2 is …
A combined ferrite parametric amplifier and millimeter-wave homodyne interferometer are proposed as an ambient temperature Bell Test. It is shown that the non-linear magnetic susceptibility of the yttrium iron garnet (YIG) ferrite, on account of its narrow line-width Larmor precessional resonance, make it an ideal material for the creation of entangled photons. These can be measured using a homodyne interferometer, as the much larger number of thermally generated photons associated with ambient temperature emission can be screened out. The proposed architecture may enable YIG quantum technolog…
We report on the successful implementation of a new approach to locking the frequencies of an OPO-based squeezed-vacuum source and its driving laser. The technique allows the simultaneous measurement of the phase-shifts induced by a cavity, which may be used for the purposes of frequency-locking, as well as the simultaneous measurement of the sub-quantum-noise-limited (sub-QNL) phase quadrature output of the OPO. The homodyne locking technique is cheap, easy to implement and has the distinct advantage that subsequent homodyne measurements are automatically phase-locked. The homodyne locking te…
It is a long-standing belief, as pointed out by Bell in 1986, that it is impossible to use a two-mode Gaussian state possessing a positive-definite Wigner function to demonstrate nonlocality as the Wigner function itself provides a local hidden-variable model. In particular, when one performs continuous-variable (CV) quadrature measurements upon a routinely generated CV entanglement, namely, the two-mode squeezed vacuum (TMSV) state, the resulting Wigner function is positive-definite and as such, the TMSV state cannot violate any Bell inequality using CV quadrature measurements. We show here, …
We derive sampling functions for estimation of quantum state fidelity with Schrödinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity with squeezed Fock states that can approximate the cat-like states and can be generated from Gaussian squeezed states by conditional photon subtraction. The fidelities can be determined by averaging the sampling functions over quadrature statistics measured by homodyne detection. The sampling functions are designed such that they can compensate for losses and i…
A new scheme is described for pulsed squeezed light generation using femtosecond pulses parametrically deamplified through a single pass in a thin (0.1mm) potassium niobate KNbO3 crystal, with a significant deamplification of about -3dB. The quantum noise of each individual pulse is registered in the time domain using a single-shot homodyne detection operated with femtosecond pulses and the best squeezed quadrature variance was measured to be 1.87 dB below the shot noise level. Such a scheme provides the basic ressource for time-resolved quantum communication protocols.
We provide a detailed analysis of the recently proposed setup for a loophole-free test of Bell inequality using conditionally generated non-Gaussian states of light and balanced homodyning. In the proposed scheme, a two-mode squeezed vacuum state is de-gaussified by subtracting a single photon from each mode with the use of an unbalanced beam splitter and a standard low-efficiency single-photon detector. We thoroughly discuss the dependence of the achievable Bell violation on the various relevant experimental parameters such as the detector efficiencies, the electronic noise and the mixedness …
We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum non locality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH non locality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection-inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly non classical states of bosonic systems.
We study the problem of determining the photon number statistics of an unknown quantum state by simultaneously measuring conjugate quadratures with double homodyne detectors. Classically, the sum of the squared outputs of the two homodyne detectors is proportional to the intensity (thus the photon number) of the input light. Quantum mechanically, due to vacuum noise, the above photon number measurement is intrinsically noisy. We quantify the information gain in a single-shot measurement and discuss potential applications of this technology in quantum key distribution. We also show that the pho…
Integrated Differential Conjugate Homodyne Detection for Quantum Random Number Generation
提出基于集成光子学与模拟电路的差分共轭零差检测QRNG方案，利用共轭正交平方和可观测量实现高SNC与CMRR，并经Toeplitz哈希和NIST测试验证。
The generation of Bell states of distant objects is of importance for constructing quantum networks. Previous studies have revealed that transient or intermittent Bell states can be generated between remote qubits by exploiting time-continuous measurement on the environments of the systems, e.g., photon counting or homodyne detection. In this paper, we consider a new scheme for achieving long-time sustainable Bell states of two distant qubits mediated by a one-dimension waveguide via continuous photon counting and homodyne detection. In both of cases, different Bell states can be present for d…
We study a model of a two-level system (i.e. a qubit) in interaction with the electromagnetic field. By means of homodyne detection, one field-quadrature is observed continuously in time. Due to the interaction, information about the initial state of the qubit is transferred into the field, thus influencing the homodyne measurement results. We construct random variables (pointers) on the probability space of homodyne measurement outcomes having distributions close to the initial distributions of sigma-x and sigma-z. Using variational calculus, we find the pointers that are optimal. These optim…
We discuss a balanced homodyne detection scheme with imperfect detectors in the framework of the operational approach to quantum measurement. We show that a realistic homodyne measurement is described by a family of operational observables that depends on the experimental setup, rather than a single field quadrature operator. We find an explicit form of this family, which fully characterizes the experimental device and is independent of a specific state of the measured system. We also derive operational homodyne observables for the setup with a random phase, which has been recently applied in …
In a recent continuous-variable quantum memory experiment, one quadrature of light pulse is directly uploaded by the light-atom coupling whereas complementary quadrature is obtained by homodyne measurement of the out-coupled light. Subsequently, information from homodyne mea- surement is written into the memory by feed-back electro-optical control of the atomic state. Using the same experimental set-up, a deterministic noise excess free record of unknown quantum states to continuous-variable quantum atomic memory is proposed. Further, the memory experiment is extended by the pre-squeezing of t…
We consider how to measure collective spin states of an atomic ensemble based on the recent multi-pass approaches for quantum interface between light and atoms. We find that a scheme with two passages of a light pulse through the atomic ensemble is efficient to implement the homodyne tomography of the spin state. Thereby, we propose to utilize optical pulses as a phase-shifter that rotates the quadrature of the spins. This method substantially simplifies the geometry of experimental schemes.
A Quantum Theory of Temporally Mismatched Homodyne Measurements with Applications to Optical Frequency Comb Metrology
本文针对现有量子理论无法描述具有大模式失配和有限强度本地振荡器的光学频率梳测量问题，推导了任意模式重叠下的零差探测测量算符，并据此设计最大化信噪比的滤波器，为将频率梳干涉测量扩展到非经典光态计量等场景奠定基础。
We propose a whole family of physical states that yield a violation of the Bell CHSH inequality arbitrarily close to its maximum value, when using quadrature phase homodyne detection. This result is based on a new binning process called root binning, that is used to transform the continuous variables measurements into binary results needed for the tests of quantum mechanics versus local realistic theories. A physical process in order to produce such states is also suggested. The use of high-efficiency spacelike separated homodyne detections with these states and this binning process would resu…
A single photon, delocalized over two optical modes, is characterized by means of quantum homodyne tomography. The reconstructed four-dimensional density matrix extends over the entire Hilbert space and thus reveals, for the first time, complete information about the dual-rail optical quantum bit as a state of the electromagnetic field. The experimental data violate the Bell inequality albeit with a loophole similar to the detection loophole in photon counting experiments.
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