We design a scheme for detecting a single photon loss from multi-modal quantum signals transmitted via a fiber or in free space. This consists of a special type of unitary coding transformation, the controlled-squeezing, applied prior to the transmission on the signal composed by information and ancilla modes. At the receiver, the inverse unitary transformation is applied -decoding, and the ancilla modes are measured via photon detection. The outcome reveals whether a photon loss has occurred. Distortion of the information part of the signal caused by an ancilla photon loss can be corrected if the encoding transformation is appropriately selected. Loss of a photon from the information part of the signal can be detected with the probability exponentially close to unity. In contrast to the schemes of decoherence free subspaces and quantum error correction protocols, this methods allows one to make use of entire Hilbert space dimensionality. We discuss possible ways of synthesizing the required encoding-decoding transformations.
It is possible to achieve an arbitrary amount of entanglement between two atoms using only spontaneously emitted photons, linear optics, single photon sources and projective measurements. This is in contrast to all current experimental proposals for entangling two atoms, which are fundamentally restricted to one entanglement bit or ebit.
We propose a scheme for the observation of micro-macro entanglement in photon number based on amplifying and de-amplifying a single-photon entangled state in combination with homodyne quantum state tomography. The created micro-macro entangled state, which exists between the amplification and de-amplification steps, is a superposition of two components with mean photon numbers that differ by approximately a factor of three. We show that for reasonable values of photon loss it should be possible to detect micro-macro photon-number entanglement where the macro system has a mean number of one hun…
We propose an atom-cavity chip that combines laser cooling and trapping of neutral atoms with magnetic microtraps and waveguides to deliver a cold atom to the mode of a fiber taper coupled photonic bandgap (PBG) cavity. The feasibility of this device for detecting single atoms is analyzed using both a semi-classical treatment and an unconditional master equation approach. Single-atom detection seems achievable in an initial experiment involving the non-deterministic delivery of weakly trapped atoms into the mode of the PBG cavity.
Rayleigh criterion has been continuously broken through with modern detecting instruments, many methods on resolving two emitters below the classical diffraction limit has been developed, one of these methods is detecting high order correlation functions of the emitters. We propose a method to resolve the single-photon emitters with only detecting the highest order correlation functions. We find that the variables that characterize the emitters are contained in the highest order correlation functions. Especially when there are more than two emitters, the spatial distribution of the emitters ca…
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. …
We apply input-output theory with quantum pulses [AH Kiilerich, K Mølmer, Phys. Rev. Lett. {\bf 123}, 123604 (2019)] to a model of a new type of two-photon detector consisting of one molecule that can detect two photons arriving sequentially in time. The underlying process is distinct from the usual two-photon absorption process where two photons arriving simultaneously and with frequencies adding up to the resonance frequency are absorbed by a single molecule in one quantum jump. Our detector model includes a Hamiltonian description of the amplification process necessary to convert the micros…
Nondestructive quantum measurements are central for quantum physics applications ranging from quantum sensing to quantum computing and quantum communication. Employing the toolbox of cavity quantum electrodynamics, we here concatenate two identical nondestructive photon detectors to repeatedly detect and track a single photon propagating through a $60\,\mathrm{m}$ long optical fiber. By demonstrating that the combined signal-to-noise ratio of the two detectors surpasses each single one by about two orders of magnitude, we experimentally verify a key practical benefit of cascaded non-demolition…
Single photon detectors are fundamental tools of investigation in quantum optics and play a central role in measurement theory and quantum informatics. Photodetectors based on different technologies exist at optical frequencies and much effort is currently being spent on pushing their efficiencies to meet the demands coming from the quantum computing and quantum communication proposals. In the microwave regime however, a single photon detector has remained elusive although several theoretical proposals have been put forth. In this article, we review these recent proposals, especially focusing …
A strong photon-photon nonlinear interaction is a necessary condition for photon blockade. Moreover, this nonlinearity can also result a bistable behavior in the cavity field. We analyze the relation between detecting field and photon blockade in a superconducting circuit QED system, and show that photon blockade cannot occur when the detecting field is in the bistable regime. This photon blockade is the microwave-photonics analog of the Coulomb blockade. We further demonstrate that the photon transmission through such system can be controlled (from photon blockade to transparency) by the dete…
We show that a photon detector, sensitive to the gradients of electromagnetic fields, or to magnetic fields, should be a useful tool to characterize the quantum properties of spatially-dependent optical fields. We discuss the excitation of an atom on a magnetic dipole or electric quadrupole transitions with the spiral photons of a Laguerre-Gauss (LG) or Bessel beams. We show that these beams are not true hollow beams, due to the presence of magnetic fields and gradients of electric fields on beam axis. This approach paves the way to an analysis at the quantum level of the spatial structure and…
Non-existence of a local hidden variables (LHV) model for a phenomenon benchmarks its use in device-independent quantum protocols. Nowadays photon-number resolving weak-field homodyne measurements allow realization of emblematic gedanken experiments. Alas, claims that we can have no LHV models for such experiments on (a) excitation of a pair of spatial modes by a single photon, and (b) two spatial modes in a weakly squeezed vacuum state, involving constant local oscillator strengths, are unfounded. For (a) an exact LHV model resolves the dispute on the "non-locality of a single photon" in its …
It is not widely appreciated that many subtleties are involved in the accurate measurement of intensity-correlated photons; even for the original experiments of Hanbury Brown and Twiss (HBT). Using a monolithic 4x4 array of single-photon avalanche diodes (SPADs), together with an off-chip algorithm for processing streaming data, we investigate the difficulties of measuring second-order photon correlations g2 in a wide variety of light fields that exhibit dramatically different correlation statistics: a multimode He-Ne laser, an incoherent intensity-modulated lamp-light source and a thermal lig…
An uncertainty relation is introduced for a symmetric arrangement of three mutually unbiased bases in continuous variable phase space, and then used to derive a bipartite entanglement criterion based on the variance of global operators composed of these three phase space variables. We test this criterion using spatial variables of photon pairs, and show that the entangled photons are correlated in three pairs of bases.
A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code. Each computational step is mediated by transfer of quantum information into an ancilla system embedding error-detection capability. Photons are assumed to be subjected to both photon loss and depolarization, and the threshold region of their strengths for scalable quantum computation is obtained, together with the amount of physical resources consumed. Compared to currently known results, the present scheme reduces the resource requirement, while yielding a c…
In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number to improve measurement precision. However, practical constraints prevent arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons w…
We consider a subgroup of unitary transformations on a mode of light induced by a Mach-Zehnder Interferometer and an algebra of observables describing a photon-number detector proceeded by an interferometer. We explore the uncertainty principles between such observables and their usefulness in performing a Bell-like experiment to show a violation of the CHSH inequality, under physical assumption that the detector distinguishes only zero from non-zero number of photons. We show which local settings of the interferometers lead to a maximal violation of the CHSH inequality.
Cavity optomechanical systems are approaching a strong-coupling regime where the coherent dynamics of nanomechanical resonators can be manipulated and controlled by optical fields at the single photon level. Here we propose an interferometric scheme able to detect optomechanical coherent interaction at the single-photon level which is experimentally feasible with state-of-the-art devices.
We report a measurement of the transverse momentum correlation between two photons by detecting only one of them. Our method uses two identical sources in an arrangement, in which the phenomenon of induced coherence without induced emission is observed. In this way, we produce an interference pattern in the superposition of one beam from each source. We quantify the transverse momentum correlation by analyzing the visibility of this pattern. Our approach might be useful for the characterization of correlated photon pair sources and may lead to an experimental measure of continuous variable ent…
In this work we investigate the probabilities of detecting single- and multi-photon coherent states on InGaAs/InP sine-gated and free-run single-photon avalanche diodes. As a result, we conclude that multi-photon state detection cannot be regarded as independent events of absorption of individual single-photon states. However, if a greater number of states are one- and two-photon, then an Independent model is permissible. We conclude that physical processes must occur in the diode structure, determining the correlation when several photons are absorbed simultaneously. We present two models tha…
We discuss how two-photon absorption (TPA) of squeezed and coherent states of light can be detected in measurements of the transmitted light fields. Such measurements typically suffer from competing loss mechanisms such as experimental imperfections and linear scattering losses inside the sample itself, which can lead to incorrect assessments of the two-photon absorption cross section. We evaluate the sensitivity with which TPA can be detected and find that TPA sensitivity of squeezed vacua or squeezed coherent states can become independent of linear losses at sufficiently large photon numbers…
Single-photon entanglement may be the simplest type of entanglement but it is of vice importance in quantum communication. Here we present a practical protocol for distilling the single-photon entanglement from both photon loss and decoherence. With the help of some local single photons, the probability of single photon loss can be decreased and the less-entangled state can also be recovered to maximally entangled state simultaneously. It only requires some linear optical elements which makes it feasible in current experiment condition. This protocol might find applications in current quantum …
The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate 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 confirm that there is no attack. In this paper, under the null hypothesis of no 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 p…
Energy-time entangled photon holes are shown to be relatively insensitive to photon loss due to absorption by atoms whose coherence times are longer than the time delays typically employed in nonlocal interferometry (a fraction of a nanosecond). Roughly speaking, the excited atoms do not retain any significant "which-path" information regarding the time at which a photon was absorbed. High-intensity entangled photon holes can also be amplified under similar conditions. Decoherence does occur from losses at beam splitters, and these results show that photon loss cannot always be adequately mode…
We discuss codes for protecting logical qubits carried by optical fields from the effects of amplitude damping, i.e. linear photon loss. We demonstrate that the correctability condition for one-photon loss imposes limitations on the range of manipulations than can be implemented with passive linear-optics networks.
We design an effect protocol for protecting the single-photon entanglement from photon loss and decoherence. The protocol only requires some auxiliary single photons and the linear optical elements. By operating the protocol, the photon loss can be effectively decreased and the less entangled single photon state can be recovered to the maximally entangled state with some probability. Moreover, the polarization information encoded in the single photon state can be perfectly contained. The protocol can be realized under current experimental condition. As the single photon entanglement is quite i…
Classical versus non-classical photon states for detecting vacuum non-linearity
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿罗森多夫赫尔姆霍兹中心）；The Extreme Light Infrastructure ERIC, ELI Beamlines Facility（极端光基础设施欧洲研究联盟，ELI光束线设施）；Institut für Theoretische Physik, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
Inherent loss is always to be avoided in generating single photons or biphotons, but interestingly it provides opportunities for manipulating the photon wave packet. In this paper we show how inherent loss in parametric down-conversion can be employed to tailor the wave packets of single photons and biphotons. As an example, we propose a scheme to realize a single photon in a single cycle using inherent loss. Our work has potential applications in quantum communication, quantum computation, and quantum interface.
Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly nontrivial in photonic systems as there is no direct analog of quantized Hall conductance for bosonic photons. Here we propose a scheme of investigating topological photonics in superconducting quantum circuits by a simple parametric coupling method, the flexibility of which can lead to the effective \textit{in situ} tunable artificial gauge field for photon…
We discuss the possibilities of studying in detail the dynamics of spontaneous emission of a single photon by a single atom and measuring the transient degree of squeezing by means of full solid angle fluorescence detection.
Single-photon entanglement is of major importance in current quantum communications. However, it is sensitive to photon loss. In this paper, we discuss the protection of single-photon multi-mode W state with noiseless linear amplification. It is shown that the amplification factor is only decided with the transmission coefficient of the variable fiber beam splitters, and it does not change with the number of the spatial mode. This protocol may be useful in current quantum information processing.
We show that it is possible to generate a novel single-photon fringe pattern by using two spatially separated identical bi-photon sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties with potential applications. A striking feature of the fringes is that although the pattern is obtained by detecting only one photon of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon. The fringe shift is characterized by a combination of wavelengths of both photons, which implies tha…
We analyze the optimal state, as given by Berry and Wiseman [Phys. Rev. Lett {\bf 85}, 5098, (2000)], under the canonical phase measurement in the presence of photon loss. The model of photon loss is a generic fictitious beam splitter, and we present the full density matrix calculations, which are more direct and do not involve any approximations. We find for a given amount of loss the upper bound for the input photon number that yields a sub-shot noise estimate.
An on-demand single-photon source is a key requirement for scaling many optical quantum technologies. A promising approach to realize an on-demand single-photon source is to multiplex an array of heralded single-photon sources using an active optical switching network. However, the performance of multiplexed sources is degraded by photon loss in the optical components and the non-unit detection efficiency of the heralding detectors. We provide a theoretical description of a general multiplexed single-photon source with lossy components and derive expressions for the output probabilities of sin…
Using the normally ordered Gaussian form of displaced-squeezed thermal field characteristic of average photon number n, we introduce the photon-added squeezed thermo state (PASTS) and investigate its statistical properties, such as Mandel's Q-parameter, number distribution (as a Legendre polynomial), the Wigner function. We then study its decoherence in a photon-loss channel in term of the negativity of WF by deriving the analytical expression of WF for PASTS. It is found that the WF with single photon-added is always partial negative for the arbitrary values of n and the squeezing parameter r…
Due to their strict photon-number correlation, the twin beams produced in parametric down-conversion (PDC) work well for heralded state generation. Often, however, this state manipulation is distorted by the optical losses in the herald and by the higher photon-number contributions inevitable in the PDC process. In order to find feasible figures of merit for characterizing the heralded states, we investigate their normalized factorial moments of the photon number that can be accessed regardless of the optical losses in the detection. We then perform a measurement of the joint photon statistics…
We model an optical implementation of a CSIGN gate that makes use of the Quantum Zeno effect [1,2] in the presence of photon loss. The raw operation of the gate is severely affected by this type of loss. However, we show that by using the same photon loss codes that have been proposed for linear optical quantum computation (LOQC), the performance is greatly enhanced and such gates can outperform LOQC equivalents. The technique can be applied to other types of nonlinearities, making the implementation of nonlinear optical gates much more attractive.
We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions). We present a systematic code construction that includes the extension of an existing one-photon-loss code to higher numbers of losses. When subject to a photon loss (amplitude damping) channel, the encoded qubits are shown to exhibit a cyclic behaviour where the code and error spaces each correspond to certain multiples of losses, half of which can be correc…
We derive frequency correlation and exit probability expressions for photons generated via spontaneous parametric downconversion (SPDC) in nonlinear waveguides that exhibit linear scattering loss. Such loss is included within a general Hamiltonian formalism by connecting waveguide modes to reservoir modes with a phenomenological coupling Hamiltonian, the parameters of which are later related to the usual loss coefficients. In the limit of a low probability of SPDC pair production, the presence of loss requires that we write the usual lossless generated pair state as a reduced density operator,…
Conference key agreement (CKA) is an information processing task where more than two parties want to share a common secret key. Here, we present a loss-resilient protocol for CKA, based on redundant encoding and error correction. Our protocol provides a speed-up in transmission rate over the existing lossy CKA protocol. However, encoding and error correction come with extra cost. We show that, using photon sources with creation probability p > 0.3, our protocol's secret key rate can overcome the existing protocol's. Hence, high probability entangled photon sources are required for realistic im…
The so-called NOON states are quantum optical resources known to be useful especially for quantum lithography and metrology. At the same time, they are known to be very sensitive to photon losses and rather hard to produce experimentally. Concerning the former, here we present a scheme where NOON states are the elementary resources for building quantum error correction codes against photon losses, thus demonstrating that such resources can also be useful to suppress the effect of loss. Our NOON-code is an exact code that can be systematically extended from one-photon to higher-number losses. I…
Measuring the quantum dynamics of a mechanical system, when few phonons are involved, remains a challenge. We show that a superconducting microwave resonator linearly coupled to the mechanical mode constitutes a very powerful probe for this scope. This new coupling can be much stronger than the usual radiation pressure interaction by adjusting a gate voltage. We focus on the detection of phonon blockade, showing that it can be observed by measuring the statistics of the light in the cavity. The underlying reason is the formation of an entangled state between the two resonators. Our scheme real…
The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing $n$-photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multi-photon Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance-matc…
The act of measuring optical emissions from two remote qubits can entangle them. By demanding that a photon from each qubit reaches the detectors, one can ensure than no photon was lost. But the failure rate then rises quadratically with loss probability. In [1] this resulted in 30 successes per billion attempts. We describe a means to exploit the low grade entanglement heralded by the detection of a lone photon: A subsequent perfect operation is quickly achieved by consuming this noisy resource. We require only two qubits per node, and can tolerate both path length variation and loss asymmetr…
We introduce a quantum channel describing photon losses depending on the degree of polarization mixedness. This can be regarded as a model of quantum channel with correlated errors between discrete and continuous degrees of freedom. We consider classical information over a continuous alphabet encoded on weak coherent states as well as classical information over a discrete alphabet encoded on single photons using dual rail representation. In both cases we study the one-shot capacity of the channel and its behaviour in terms of correlation between losses and polarization mixedness.
Single photon detection is a key resource for sensing at the quantum limit and the enabling technology for measurement based quantum computing. Photon detection at optical frequencies relies on irreversible photo-assisted ionization of various natural materials. However, microwave photons have energies 5 orders of magnitude lower than optical photons, and are therefore ineffective at triggering measurable phenomena at macroscopic scales. Here, we report the observation of a new type of interaction between a single two level system (qubit) and a microwave resonator. These two quantum systems do…
We propose and analyze a method to detect and characterize the drift of a nonstationary quantum source. It generalizes a standard measurement for detecting phase diffusion of laser fields to quantum systems of arbitrary Hilbert space dimension, qubits in particular. We distinguish diffusive and systematic drifts, and examine how quickly one can determine that a source is drifting. We show that for single-photon wavepackets our measurement is implemented by the Hong-Ou-Mandel effect.
We present the quantum theory of the measurement of bosonic particles by multipixel detectors. For the sake of clarity, we specialize on beams of photons. We study the measurement of different spatial beam characteristics, as position and width. The limits of these measurements are set by the quantum nature of the light field. We investigate how both, detector imperfections and finite pixel size affect the photon counting distribution. An analytic theory for the discretized measurement scheme is derived. We discuss the results and compare them to the theory presented by Chille et al. in "Quant…
A photonic cluster state with a tree-type entanglement structure constitutes an efficient resource for quantum error correction of photon loss. But the generation of a tree cluster state with an arbitrary size is notoriously difficult. Here, we propose a protocol to deterministically generate photonic tree states of arbitrary size by using only a single quantum emitter. Photonic entanglement is established through both emission and re-scattering from the same emitter, enabling fast and resource-efficient entanglement generation. The same protocol can also be extended to generate more general t…
We propose a protocol for detecting a single atom in a cavity with the help of the $χ^{(2)}$ nonlinear medium. When the $χ^{(2)}$ nonlinear medium is driven by an external laser field, the cavity mode will be squeezed, and thus one can obtain an exponentially enhanced light-matter coupling. Such a strong coupling between the atom and the cavity field can significantly change the output photon flux, the quantum fluctuations, the quantum statistical property, and the photon number distributions of the cavity field. This provides practical strategies to determine the presence or absence of an ato…
We have studied theoretical un-symmetric multi-photon subtracted twin beam state and demonstrated a method for generating states that resembles to high photon number states with the increase in the number of subtracted photons through Wigner distribution function, which can be reconstructed experimentally by Homodyne measurement. A crucial point is high non-classicality is obtained by photon subtraction when mean photons per mode of twin beam state is low. We have calculated photon statistics from the phase space distribution function and found sub-poissonian behaviour in the same low mean pho…
We consider quantum error-correction codes for multimode bosonic systems, such as optical fields, that are affected by amplitude damping. Such a process is a generalization of an erasure channel. We demonstrate that the most accessible method of transforming optical systems with the help of passive linear networks has limited usefulness in preparing and manipulating such codes. These limitations stem directly from the recoverability condition for one-photon loss. We introduce a three-photon code protecting against the first order of amplitude damping, i.e. a single photon loss, and discuss its…
Photon loss is destructive to the performance of quantum photonic devices and therefore suppressing the effects of photon loss is paramount to photonic quantum technologies. We present two schemes to mitigate the effects of photon loss for a Gaussian Boson Sampling device, in particular, to improve the estimation of the sampling probabilities. Instead of using error correction codes which are expensive in terms of their hardware resource overhead, our schemes require only a small amount of hardware modifications or even no modification. Our loss-suppression techniques rely either on collecting…
