A new method is described for determining the quantum correlations at different times in optical pulses by using balanced homodyne detection. The signal pulse and sequences of ultrashort test pulses are superimposed, where for chosen distances between the test pulses their relative phases and intensities are varied from measurement to measurement. The correlation statistics of the signal pulse is obtained from the time-integrated difference photocurrents measured.
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.
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 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…
A pulsed balanced homodyne detector has been developed for precise measurements of electric field quadratures of pulsed optical quantum states. A high level of common mode suppression (> 85 dB) and low electronic noise (730 electrons per pulse) provide a signal to noise ratio of 14 dB for the measurement of the quantum noise of individual pulses. Measurements at repetition rates up to 1 MHz are possible. As a test, quantum tomography of the coherent state is performed and the Wigner function and the density matrix are reconstructed with a 99.5% fidelity. The detection system can also be used f…
Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classi…
Traditional method for measuring continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses resulted from many factors such as detector's quantum efficiency and mode mismatching between detected field and local oscillator. In this paper, we propose and analyze a new measurement method, which is realized by assisting the balanced homodyne detections with a high gain phase sensitive parametric amplifier. The employment of the high gain parametric amplifier helps to tackle the vacuum quantum noise originat…
Using coherent phase states, parameterized phase state distributions for a single-mode radiation field are introduced and their integral relation to the phase-parameterized field-strength distributions is studied. The integral kernel is evaluated and the problem of direct sampling of the coherent phase state distributions using balanced homodyne detection is considered. Numerical simulations show that when the value of the smoothing parameter is not too small the coherent phase state distributions can be obtained with sufficiently well accuracy. With decreasing value of the smoothing parameter…
In this paper we investigate the security of a quantum cryptographic scheme which utilizes balanced homodyne detection and weak coherent pulse (WCP). The performance of the system is mainly characterized by the intensity of the WCP and postselected threshold. Two of the simplest intercept/resend eavesdropping attacks are analyzed. The secure key gain for a given loss is also discussed in terms of the pulse intensity and threshold.
Optical homodyne detection has found use in a range of quantum technologies as both a characterisation tool and as a way to post-selectively generate non-linearities. So far optical implementations have been limited to bulk optics. Here we present the first homodyne detector fully integrated with silicon photonics and suitable for measurements of the quantum state of the electromagnetic field. This high speed, compact detector shows low noise operation, with 10 dB of clearance between shot noise and electronic noise, up to a speed of 160 MHz. These performances are suitable for on-chip charact…
A single-photon Fock state has been generated by means of conditional preparation from a two-photon state emitted in the process of spontaneous parametric down-conversion. A recently developed high-frequency homodyne tomography technique has been used to completely characterize the Fock state by means of a pulse-to-pulse analysis of the detectors' difference photocurrent. The density matrix elements of the generated state have been retrieved with a final detection efficiency of about 57%. A comparison has been performed between the phase-averaged tomographic reconstructions of the Wigner funct…
We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed non-degenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.
Pulsed homodyne quantum tomography usually requires a high detection efficiency limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency ($<50\%$) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian type. This result is obtained by applying the so-called "minimax" adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our…
The homodyne detection is one of the most basic tools for identifying the quantum state of light. It has been used to detect useful non-local properties, such as entanglement for the quantum teleportation and distillability of a secret key in quantum key distribution. In so doing, the detection scheme employs a bright optical pulse, called the local oscillator (LO) pulse, and the LO pulse is usually transmitted along with the signal pulses. The LO pulse is presumed to be a coherent state with an infinite intensity. However, it is difficult in practice to hold this presumption owing to noise in…
Characterising quantum states of light in the 2 $μm$ band requires high-performance shot-noise limited detectors. Here, we present the characterisation of a homodyne detector that we use to observe vacuum shot-noise via homodyne measurement with a 2.07 $μm$ pulsed mode-locked laser. The device is designed primarily for pulsed illumination. It has a 3 dB bandwidth of 13.2 MHz, total conversion efficiency of 58% at 2.07 $μm$ and a common-mode rejection ratio of 48 dB at 39.5 MHz. The detector begins to saturate at 1.8 mW with 9 dB of shot-noise clearance at 5 MHz. This demonstration enables the …
We present a QKD system with fainted pulses using self-homodyne coherent detection in optical fibers at 1543nm. BB84 protocol key is encoded in the optical phase using a twoelectrode Mach-Zehnder modulator, producing a QPSK modulation.
The effect of the detector electronic noise in an optical homodyne tomography experiment is shown to be equivalent to an optical loss if the detector is calibrated by measuring the quadrature noise of the vacuum state. An explicit relation between the electronic noise level and the equivalent optical efficiency is obtained and confirmed in an experiment with a narrowband squeezed vacuum source operating at an atomic rubidium wavelength.
Homodyne tomography provides a way for measuring generic field-operators. Here we analyze the determination of the most relevant quantities: intensity, field, amplitude and phase. We show that tomographic measurements are affected by additional noise in comparison with the direct detection of each observable by itself. The case of of coherent states has been analyzed in details and earlier estimations of tomographic precision are critically discussed.
Spectral homodyne detection, a widely used technique for measuring quantum properties of light beams, cannot retrieve all the information needed to reconstruct the quantum state of spectral field modes. We show that full quantum state reconstruction can be achieved with the alternative measurement technique of resonator detection. We experimentally demonstrate this difference by engineering a quantum state with features that go undetected by homodyne detection but are clearly revealed by resonator detection.
We report an experimental quantum key distribution that utilizes balanced homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, it allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. When the average photon number was 0.1, an error rate of 0.08 and "effective" quantum efficiency of 0.76 were obtained.
We propose a general method for measuring an arbitrary observable of a multimode electromagnetic field using homodyne detection with a single local oscillator. In this method the local oscillator scans over all possible linear combinations of the modes. The case of two modes is analyzed in detail and the feasibility of the measurement is studied on the basis of Monte-Carlo simulations. We also provide an application of this method in tomographic testing of the GHZ state.
The role of squeezing in quantum key distribution with continuous variables based on homodyne detection and post-selection is investigated for several specific eavesdropping strategies. It is shown that amplitude squeezing creates strong correlations between the signals of the legitimate receiver and a potential eavesdropper. Post-selection of the received pulses can therefore be used to reduce the eavesdropper's knowledge of the raw key, which increases the secret key rate by orders of magnitude over large distances even for modest amounts of squeezing.
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…
We experimentally verify uncertainty relations for mixed states in the tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of single-mode radiation field are discussed in details as paradigm of mixed quantum state. By considering the connection between generalised uncertainty relations and optical tomograms is seen that the purity of the states can be retrieved by statistical analysis of the homodyne data. The purity parameter assumes a relevant role in quantum information where the effective fidelities of protocols depend critical…
A review is given on phase-sensitive measurements, such as homodyne detection, for radiation fields and material systems. Methods of quantum-state reconstruction are considered for radiation fields, including multimode and pulsed radiation. For matter systems, methods are reported for the reconstruction of quantum states of molecular vibrations, the quantized motion of trapped atoms, Bose-Einstein condensates, atomic matter waves, electron motion, spin and angular momentum systems, and crystal lattices.
We discuss excess noise contributions of a practical balanced homodyne detector in Gaussian-modulated coherent-state (GMCS) quantum key distribution (QKD). We point out the key generated from the original realistic model of GMCS QKD may not be secure. In our refined realistic model, we take into account excess noise due to the finite bandwidth of the homodyne detector and the fluctuation of the local oscillator. A high speed balanced homodyne detector suitable for GMCS QKD in the telecommunication wavelength region is built and experimentally tested. The 3dB bandwidth of the balanced homodyne …
We propose an efficient strategy to attack a continuous-variable quantum key distribution (CV-QKD) system, that we call homodyne detector blinding. This attack strategy takes advantage of a generic vulnerability of homodyne receivers: a bright light pulse sent on the signal port can lead to a saturation of the detector electronics. While detector saturation has already been proposed to attack CV-QKD, the attack we study in this paper has the additional advantage of not requiring an eavesdropper to be phase locked with the homodyne receiver. We show that under certain conditions, an attacker ca…
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 …
I propose an approach to adaptive homodyne detection of digitally modulated quantum optical pulses in which the phase of the local oscillator is chosen to maximize the average information gain, i.e., the mutual information, at each step of the measurement. I study the properties of this adaptive detection scheme by considering the problem of classical information content of ensembles of coherent states. Using simulations of quantum trajectories and visualizations of corresponding measurement operators, I show that the proposed measurement scheme adapts itself to the features of each ensemble. …
In this work we analyse the structure of highly-entangled multimode squeezed states, such as those generated by broadband pulses undergoing type-II parametric down-conversion (PDC). Such down-conversion has previously been touted as a natural and efficient means of cluster-state generation, and therefore a viable future pathway to quantum computation. We first detail how broadband PDC processes lead directly to a series of orthogonal supermodes that are linear combinations of the original frequency modes. We then calculate the total squeezing of the multimode entangled states when they are ass…
The quantum spin states of atomic ensemble are of special interesting for both fundamental studies and precision measurement applications. Here, we propose a scheme to prepare collective quantum states of an atomic ensemble placed in an optical cavity via homodyne measurement of probing light field. The effective interactions of atoms mediated by photons are enhanced by the optical cavity, and the output probe light could also be entangled with the collective spin states. By selectively measuring the quadrature of output light, we can prepare various quantum states, including superposition sta…
Self-testing and Semi-Device Independent protocols are becoming the preferred choice for quantum technologies, being able to certify their quantum nature with few assumptions and simple experimental implementations. In particular for Quantum Random Number Generators the possibility of monitoring in real time the entropy of the source only by measuring the input/output statistics is a characteristic that no other classical system could provide. The cost of this new possibility is not necessarily increased complexity and reduced performance. Indeed, here we show that with a simple optical setup …
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…
Imperfect devices in commercial quantum key distribution systems open security loopholes that an eavesdropper may exploit. An example of one such imperfection is the wavelength dependent coupling ratio of the fiber beam splitter. Utilizing this loophole, the eavesdropper can vary the transmittances of the fiber beam splitter at the receiver's side by inserting lights with wavelengths different from what is normally used. Here, we propose a wavelength attack on a practical continuous-variable quantum key distribution system using homodyne detection. By inserting light pulses at different wavele…
We present a comprehensive theory and an easy to follow method for the design and construction of a wideband homodyne detector for time-domain quantum measurements. We show how one can evaluate the performance of a detector in a specific time-domain experiment based on electronic spectral characteristic of that detector. We then present and characterize a high-performance detector constructed using inexpensive, commercially available components such as low-noise high-speed operational amplifiers and high-bandwidth photodiodes. Our detector shows linear behavior up to a level of over 13 dB clea…
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 …
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…
The purpose of this paper is to propose quantum filters for a two-level atom driven by two continuous-mode counter-propagating photons and under continuous measurements. Two scenarios of multiple measurements, 1) homodyne detection plus photodetection, and 2) two homodyne detections, are discussed. Filtering equations for both cases are derived explicitly. As demonstration, the two input photons with rising exponential and Gaussian pulse shapes are used to excite a two-level atom under two homodyne detection measurements. Simulations reveal scaling relations between atom-photon coupling and ph…
Measurements of single-mode phase observables are studied in the spirit of the quantum theory of measurement. We determine the minimal measurement models of phase observables and consider methods of measuring such observables by using a double homodyne detector. We show that, in principle, the canonical phase distribution of the signal state can be measured via double homodyne detection by first processing the state using a two-mode unitary channel.
We propose to experimentally test the nonclassicality of quantum states through homodyne tomography. For single-mode states we check violations of inequalities involving the photon-number probability. For two-mode states we test the nonclassicality by reconstructing some suitable number-operator functions. The test can be performed with available quantum efficiency of homodyne detection, by measuring the pertaining quantities on the corresponding noisy states.
We review the continuous monitoring of a qubit through its spontaneous emission, at an introductory level. Contemporary experiments have been able to collect the fluorescence of an artificial atom in a cavity and transmission line, and then make measurements of that emission to obtain diffusive quantum trajectories in the qubit's state. We give a straightforward theoretical overview of such scenarios, using a framework based on Kraus operators derived from a Bayesian update concept; we apply this flexible framework across common types of measurements including photodetection, homodyne, and het…
An experimental set-up for the measurement of the Casimir effect at separations larger than a few microns is presented. The apparatus is based on a mechanical resonator and uses a homodyne detection technique to sense the Casimir force in the plane-parallel configuration. First measurements in the 3-10 micrometer range show an unexpected large force probably due to patch effects.
Single-photon entangled states, i.e. states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one not only to say whether a given state is path-entangled but also that entanglement lies in…
We present a theoretical study of ghost imaging based on correlated beams arising from parametric down-conversion, and which uses balanced homodyne detection to measure both the signal and idler fields. We analytically show that the signal-idler correlations contain the full amplitude and phase information about an object located in the signal path, both in the near-field and the far-field case. To this end we discuss how to optimize the optical setups in the two imaging paths, including the crucial point regarding how to engineer the phase of the idler local oscillator as to observe the desir…
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 present a multimode theory of non-Gaussian operation induced by an imperfect on/off-type photon detector on a splitted beam from a wideband squeezed light. The events are defined for finite time duration $T$ in the time domain. The non-Gaussian output state is measured by the homodyne detector with finite bandwidh $B$. Under this time- and band-limitation to the quantm states, we develop a formalism to evaluate the frequency mode matching between the on/off trigger channel and the conditional signal beam in the homodyne channel. Our formalism is applied to the CW and pulsed schemes. We expl…
We perform the quantum analysis of the light emitted by a synchronously pumped optical parametric oscillator operating in the above threshold regime, i.e. when the peak power of pulsed pumping exceeds the threshold of continuous generation. We show that both regimes (below and above threshold) are realized at different times within each pulse of the signal field. We show that the quantum fluctuations of signal and pump pulses are correlated between nearby pulses at times that are placed in the same position relative to the center of the pulses, whereas fluctuations are totally not correlated a…
We present a detailed analysis of the multimode quantum state embedded in an optical frequency comb generated by a Synchronously Pumped Optical Parametric Oscillator (SPOPO). The full covariance matrix of the state is obtained with homodyne detection where the local oscillator is spectrally controlled with pulse shaping techniques. The resulting matrix reveals genuine multipartite entanglement. Additionally, the beam is comprised of several independent eigenmodes that correspond to specific pulse shapes. The experimental data is confirmed with numerical simulations. Finally, the potential to c…
