Search

A scheme for the enhanced generation of higher photon-number states is realized, using an optical time-multiplexing setting that exploits a parametric down-conversion source for an iterative state generation. We use a quantum feedback mechanism for already generated photons to induce self-seeding of the consecutive nonlinear process, enabling us to coherently add photons to the light that propagates in the feedback loop. The addition can be carried out for any chosen number of round trips, resulting in a successive buildup of multiphoton states. Our system is only limited by loop losses. The looped design is rendered possible by a carefully engineered waveguide source that is compatible with and preserves the shape of the propagating mode. We compare the fidelities and success probabilities of our protocol with the common direct heralding of photon-number states. This comparison reveals that, for same the fidelity, our feedback-based setup significantly enhances success probabilities, being vital for an efficient utilization in quantum technologies. Moreover, quantum characteristics of the produced states are analyzed, and the flexibility of producing higher photon-number states with our setup beyond the common direct heralding is demonstrated., Comment: 10 pages. Comments are welcome

Interferometers provide a highly sensitive means to investigate and exploit the coherence properties of light in metrology applications. However, interferometers come in various forms and exploit different properties of the optical states within. In this paper, we introduce a classification scheme that characterizes any interferometer based on the number of involved nonlinear elements by studying their influence on single-photon and photon-pair states. Several examples of specific interferometers from these more general classes are discussed, and the theory describing the expected first-order and second-order coherence measurements for single-photon and single-photon-pair input states is summarized and compared. These theoretical predictions are then tested in an innovative experimental setup that is easily able to switch between implementing an interferometer consisting of only one or two nonlinear elements. The resulting singles and coincidence rates are measured in both configurations and the results are seen to fit well with the presented theory. The measured results of coherence are tied back to the presented classification scheme, revealing that our experimental design can be useful in gaining insight into the properties of the various interferometeric setups containing different degrees of nonlinearity., Comment: 12 pages, 5 figures

Dissimilar notions of quantum correlations have been established, each being motivated through particular applications in quantum information science and each competing for being recognized as the most relevant measure of quantumness. In this contribution, we experimentally realize a form of quantum correlation that exists even in the absence of entanglement and discord. We certify the presence of such quantum correlations via negativities in the regularized two-mode Glauber-Sudarshan function. Our data show compatibility with an incoherent mixture of orthonormal photon-number states, ruling out quantum coherence and other kinds of quantum resources. By construction, the quantumness of our state is robust against dephasing, thus requiring fewer experimental resources to ensure stability. In addition, we theoretically show how multimode entanglement can be activated based on the generated, nonentangled state. Therefore, we implement a robust kind of nonclassical photon-photon correlated state with useful applications in quantum information processing.

We develop a unified theoretical framework for the efficient description of multiphoton states generated and propagating in loop-based optical networks which contain nonlinear elements. These active optical components are modeled as nonlinear media, resembling a two-mode squeezer. First, such nonlinear components can be seeded to manipulate quantum states of light, as such enabling photon addition protocols. And, second, they can function as an amplifying medium for quantum light. To prove the practical importance of our approach, the impact of multiple round trips is analyzed for states propagating in experimentally relevant loop configurations of networks, such as time-multiplexed driven quantum walks and iterative photon-number state generation protocols. Our method not only enables us to model such complex systems but also allows us to propose alternative setups that overcome previous limitations. To characterize the systems under study, we provide exact expressions for fidelities with target states, success probabilities of heralding-type measurements, and correlations between optical modes, including many realistic imperfections. Moreover, we provide an easily implementable numerical approach by devising a vector-type representation of photonic states, measurement operators, and passive and active processes.

We study the quasiprobability representation of quantum light, as introduced by Glauber and Sudarshan, for the unified characterization of quantum phenomena. We begin with reviewing the past and current impact of this technique. Regularization and convolution methods are specifically considered since they are accessible in experiments. We further discuss more general quantum systems for which the concept of negative probabilities can be generalized, being highly relevant for quantum information science. For analyzing quantum superpositions, we apply recently developed approaches to visualize quantum coherence of states via negative quasiprobability representations, including regularized quasiprobabilities for light and more general quantum correlated systems.

The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.

We report on the first experimental reconstruction of an entanglement quasiprobability. In contrast to related techniques, the negativities in our distributions are a necessary and sufficient identifier of separability and entanglement and enable a full characterization of the quantum state. A reconstruction algorithm is developed, a polarization Bell state is prepared, and its entanglement is certified based on the reconstructed entanglement quasiprobabilities, with a high significance and without correcting for imperfections., Comment: close to published paper; including supplement

The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the latter decomposition property has been studied less frequently. In this contribution, we introduce a method for the generalized expansion of quantum states in terms of so-called quasistates. In contrast to the quasiprobability decomposition through nonclassical distributions and pure-state operators, our technique results in classical probabilities and nonpositive semidefinite operators, defining the notion of quasistates, that carry the information about the nonclassical characteristics of the system. Therefore, our method presents a complementary approach to prominent quasiprobability representations. We explore the usefulness of our technique with several examples, including applications for quantum state reconstruction and the representation of nonclassical light. In addition, using our framework, we also demonstrate that inseparable quantum correlations can be described in terms of classical joint probabilities and tensor-product quasistates for an unambiguous identification of quantum entanglement.

Gaussian boson sampling is a promising scheme for demonstrating a quantum computational advantage using photonic states that are accessible in a laboratory and, thus, offer scalable sources of quantum light. In this contribution, we study two-point photon-number correlation functions to gain insight into the interference of Gaussian states in optical networks. We investigate the characteristic features of statistical signatures which enable us to distinguish classical from quantum interference. In contrast to the typical implementation of boson sampling, we find additional contributions to the correlators under study which stem from the phase dependence of Gaussian states and which are not observable when Fock states interfere. Using the first three moments, we formulate the tools required to experimentally observe signatures of quantum interference of Gaussian states using two outputs only. By considering the current architectural limitations in realistic experiments, we further show that a statistically significant discrimination between quantum and classical interference is possible even in the presence of loss, noise, and a finite photon-number resolution. Therefore, we formulate and apply a theoretical framework to benchmark the quantum features of Gaussian boson sampling under realistic conditions.

It is demonstrated that the collapse of the wave function is equivalent to the continuity of measurement outcomes. The latter states that a second measurement has to result in the same outcome as the first measurement of the same observable for a vanishing time between both observations. In contrast to the exclusively quantum-physical collapse description, the equivalent continuity requirement also applies in classical physics, allowing for a comparison of both domains. In particular, it is found that quantum coherences are the single cause for measurable deviations in statistical properties due to the collapse. Therefore, the introduced approach renders it possible to characterize and quantify the unique features of the quantum-physical measurement problem within the framework of modern quantum resource theories and compare them to classical physics., Comment: Comments are welcome

We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to analyze various forms of quantum coherence in different physical systems. Moreover, our framework renders it possible to uncover complex quantum correlations between systems, for example, via quasiprobability representations of multipartite entanglement., Comment: revised version

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first place. For this reason, we derive from first principles equations of motions that describe the classical propagation in quantum systems. A comparison of this classical model with the actual temporal quantum behavior enables us to identify quantum phenomena in the system's dynamics and distinguish them from static quantum features at individual points in time. For instance, we show how Newton's second law emerges as a special case of our general treatment, connecting it to a Schr\"odinger-type equation. As applications of our universal technique, we analyze nonlinear optical processes, semiclassical models, and the multipartite entanglement dynamics of macroscopic ensembles., Comment: extended version, close to published paper

We revisit the representation of generalized quantum observables by establishing a geometric picture in terms of their positive operator-valued measures (POVMs). This leads to a clear geometric interpretation of Born's rule by introducing the concept of contravariant operator-valued measures. Our approach is applied to the theory of array detectors, which is a challenging task as the finite dimensionality of the POVM substantially restricts the available information about quantum states. Our geometric technique allows for a direct estimation of expectation values of different observables, which are typically not accessible with such detection schemes. In addition, we also demonstrate the applicability of our method to quantum-state reconstruction with unbalanced homodyne detection., Comment: 16 pages, 9 figures

We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to indicate such quantum characteristics for the quantum efficiencies present in our setup. In addition, it would require ideal photon-number resolution. Hence, we realize a robust, reliable, and resource-efficient approach to characterize nonclassical light in phase space under realistic conditions.

The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states by comparing the trajectories to their classically correlated counterparts. For this reason, we introduce equations of motions describing the separable propagation of any interacting quantum system, which are derived by requiring separability for all times. The resulting Schroedinger-type equations allow for comparing the trajectories in a separable configuration with the actual behavior of the system and, thereby, identifying inseparable and time-dependent quantum properties. As an example, we study bipartite discrete- and continuous-variable interacting systems. The generalization of our developed technique to multipartite scenarios is also provided., Comment: close to published version

Based on correlations of coherently displaced photon-numbers, we derive entanglement criteria for the purpose to verify non-Gaussian entanglement. Our construction method enables us to verify bipartite and multipartite entanglement of complex states of light. An important advantage of our technique is that the certified entanglement even persists in the presence of arbitrarily high, constant losses. We exploit experimental correlation schemes for the two-mode and multimode scenarios, which allow us to directly measure the desired observables. To detect entanglement of a given state, a genetic algorithm is applied to optimize over the infinite set of our constructed witnesses. In particular, we provide suitable witnesses for several distinct two-mode states. Moreover, a mixed non-Gaussian four-mode state is shown to be entangled in all possible non-trivial partitions., Comment: 14 pages, 7 figures

We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we study the bipartite case and the connection of two typically applied and distinctively different concepts of nonclassicality in quantum optics and quantum information. Our investigation includes the representation of correlated states in terms of quasiprobability matrices, a comparative study of joint and conditional quantum correlations, and an entanglement characterization. It is, for example, shown that our composition approach always includes entanglement as one form of quantum correlations. Yet, other forms of quantum correlations can also occur without entanglement. Finally, we give an outlook towards multimode systems and temporal correlations.

We derive and implement a general method to characterize the nonclassicality in compound discrete- and continuous-variable systems. For this purpose, we introduce the operational notion of conditional hybrid nonclassicality which relates to the ability to produce a nonclassical continuous-variable state by projecting onto a general superposition of discrete-variable subsystem. We discuss the importance of this form of quantumness in connection with interfaces for quantum communication. To verify the conditional hybrid nonclassicality, a matrix version of a nonclassicality quasiprobability is derived and its sampling approach is formulated. We experimentally generate an entangled, hybrid Schr\"odinger cat state, using a coherent photon-addition process acting on two temporal modes, and we directly sample its nonclassicality quasiprobability matrix. The introduced conditional quantum effects are certified with high statistical significance., Comment: Closer to published version

In this paper, we use the characteristic function, i.e., the Fourier transform of the Glauber-Sudarshan phase-space distribution, to find the degree of nonclassicality of a given state. This degree of nonclassicality quantifies the nonclassicality in terms of quantum superpositions. We demonstrate two ways to determine or to estimate the degree of nonclassicality by studying the properties of the characteristic functions. The developed criteria are applied to two examples of squeezed states undergoing a classical mixing or a nonclassical superposition with vacuum., Comment: 13 pages, 6 figures

In a recent contribution, we introduced and applied a detector-independent method to uncover nonclassicality. Here, we extend those techniques and give more details on the performed analysis. We derive a general theory of the positive-operator-valued measure that describes multiplexing layouts with arbitrary detectors. From the resulting quantum version of a multinomial statistics, we infer nonclassicality probes based on a matrix of normally ordered moments. We discuss these criteria and apply the theory to our data which are measured with superconducting transition-edge sensors. Our experiment produces heralded multi-photon states from a parametric down-conversion light source. We show that the known notions of sub-Poisson and sub-binomial light can be deduced from our general approach, and we establish the concept of sub-multinomial light, which is shown to outperform the former two concepts of nonclassicality for our data., Comment: close to published version

We introduce a method for the verification of nonclassical light which is independent of the complex interaction between the generated light and the material of the detectors. This is accomplished by means of a multiplexing arrangement. Its theoretical description yields that the coincidence statistics of this measurement layout is a mixture of multinomial distributions for any classical light field and any type of detector. This allows us to formulate bounds on the statistical properties of classical states. We apply our directly accessible method to heralded multiphoton states which are detected with a single multiplexing step only and two detectors, which are in our work superconducting transition-edge sensors. The nonclassicality of the generated light is verified and characterized through the violation of the classical bounds without the need for characterizing the used detectors., Comment: close to published version

We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems with a fluctuating particle number. To access the quality of the verified entanglement, the operational measure of the entanglement visibility is introduced. As an example, we perform an analytical characterization of quantum systems composed of interacting harmonic oscillators and witness the entanglement via energy measurements. Our analysis shows that the detectable entanglement decays for macroscopic particle numbers without the need for decoherence processes and for all considered coupling regimes. We further study thermal states of the given correlated system together with the temperature dependence of entanglement.

We study the evolution of higher-order nonclassicality and entanglement criteria in atmospheric fluctuating-loss channels. By formulating input-output relations for the matrix of moments, we investigate the influence of such channels on the corresponding quantumness criteria. This generalization of our previous work on Gaussian entanglement [M. Bohmann et al., Phys. Rev. A 94, 010302(R) (2016)] not only exploits second-order-based scenarios, but it also provides a detailed investigation of nonclassicality and entanglement in non-Gaussian and multimode radiation fields undergoing a fluctuating attenuation. That is, various examples of criteria and states are studied in detail, unexpected effects, e.g., the dependency of the squeezing transfer on the coherent displacement, are discovered, and it is demonstrated that non-Gaussian entanglement can be more robust against atmospheric losses than Gaussian one. Additionally, we propose a detection scheme for measuring the considered moments after propagation through the atmosphere. Therefore, our results may help to develop, improve, and optimize non-Gaussian sources of quantum light for applications in free-space quantum communication.

Quantum features of correlated optical modes define a major aspect of the nonclassicality in quantized radiation fields. However, the phase-sensitive detection of a two-mode light field is restricted to interferometric setups and local intensity measurements. Even the full reconstruction of the quantum state of a single radiation mode relies on such detection layouts and the preparation of a well-defined reference light field. In this work, we establish the notion of the essential quantum correlations of two-mode light fields. It refers to those quantum correlations which are measurable by a given device, i.e., the accessible part of a nonclassical Glauber-Sudarshan phase-space distribution, which does not depend on a global phase. Assuming a simple four-port interferometer and photon-number-resolving detectors, we derive the reconstruction method and nonclassicality criteria based on the Laplace-transformed moment-generating function of the essential quasiprobability. With this technique, we demonstrate that the essential quantum correlations of a polarization tomography scheme are observable even if the detectors are imperfect and cannot truly resolve the photon statistics.

Phase-space distributions are widely applied in quantum optics to access the nonclassical features of radiations fields. In particular, the inability to interpret the Glauber-Sudarshan distribution in terms of a classical probability density is the fundamental benchmark for quantum light. However, this phase-space distribution cannot be directly reconstructed for arbitrary states, because of its singular behavior. In this work, we perform a characterization of the Glauber-Sudarshan representation in terms of distribution theory. We address important features of such distributions: (i) the maximal degree of their singularities is studied, (ii) the ambiguity of representation is shown, and (iii) their dual space for nonclassicality tests is specified. In this view, we reconsider the methods for regularizing the Glauber-Sudarshan distribution for verifying its nonclassicality. This treatment is supported with comprehensive examples and counterexamples., Comment: 11 pages, 1 figure

A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent P functional that generalizes the Glauber-Sudarshan P function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system., Comment: 6 pages, 3 figures

The existence of non-local quantum correlations is certainly the most important specific property of the quantum world. However, it is a challenging task to distinguish correlations of classical origin from genuine quantum correlations, especially when the system involves more than two parties, for which different partitions must be simultaneously considered. In the case of mixed states, intermediate levels of correlations must be introduced, coined by the name inseparability. In this work, we revisit in more detail such a concept in the context of continuous-variable quantum optics. We consider a six-partite quantum state that we have effectively generated by the parametric downconversion of a femtosecond frequency comb, the full 12 x 12 covariance matrix of which has been experimentally determined. We show that, though this state does not exhibit "genuine entanglement", it is undoubtedly multipartite-entangled. The consideration of not only the entanglement of individual mode-decompositions but also of combinations of those solves the puzzle and exemplifies the importance of studying different categories of multipartite entanglement.

We provide a rigorous treatment of the entanglement properties of two-mode Gaussian states in atmospheric channels by deriving and analyzing the input-output relations for the corresponding entanglement test. A key feature of such turbulent channels is a non-trivial dependence of the transmitted continuous-variable entanglement on coherent displacements of the quantum state of the input field. Remarkably, this allows one to optimize the entanglement certification by modifying local coherent amplitudes using a finite, but optimal amount of squeezing. In addition, we propose a protocol which, in principle, renders it possible to transfer the Gaussian entanglement through any turbulent channel over arbitrary distances. Therefore, our approach provides the theoretical foundation for advanced applications of Gaussian entanglement in free-space quantum communication.

We study, in theory and experiment, the quantum properties of correlated light fields measured with click-counting detectors providing incomplete information on the photon statistics. We establish a correlation parameter for the conditional statistics, and we derive the corresponding nonclassicality criteria for detecting conditional quantum correlations. Classical bounds for Pearson's correlation parameter are formulated that allow us, once they are violated, to determine nonclassical correlations via the joint statistics. On the one hand, we demonstrate nonclassical correlations in terms of the joint click statistics of light produced by a parametric down conversion source. On the other hand, we verify quantum correlations of a heralded, split single-photon state via the conditional click statistics together with a generalization to higher-order moments. We discuss the performance of the presented nonclassicality criteria to successfully discern joint and conditional quantum correlations. Remarkably, our results are obtained without making any assumptions on the response function, quantum efficiency, and dark-count rate of the photodetectors.

Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in terms of measurable quantities. Witnesses, if properly constructed, succeed in performing this task. We derive a method that is capable to compute witnesses for identifying deterministic evolutions and measurement-induced collapse processes. At the same time, applying the Choi-Jamiolkowski isomorphism, it uncovers the entanglement characteristics of bipartite quantum states. Remarkably, a statistical mixture of unitary evolutions is mapped onto mixtures of maximally entangled states, and classical separable states originate from genuine quantum-state reduction maps. Based on our treatment we are able to witness these opposing attributes at once and, furthermore, obtain an insight into their different geometric structures. The complementarity is further underpinned by formulating a complementary Schmidt decomposition of a state in terms of maximally entangled states and discrete Fourier-transformed Schmidt coefficients., Comment: close to published version

Phase-sensitive properties of light play a crucial role in a variety of quantum optical phenomena, which have been mostly discussed in the framework of photoelectric detection theory. However, modern detection schemes, such as arrays of on-off detectors, are not based on photoelectric counting. We demonstrate that the theory of homodyning with such click counting detectors can be established by using a proper detection model. For practical applications, a variety of typically occurring imperfections are rigorously analyzed and directly observable nonclassicality criteria are studied. Fundamental examples demonstrate the general functionality of our technique. Thus, our approach of homodyne detection with on-off detector systems is able to bridge the gap between imperfect detection and the phase resolution demands for modern applications of quantum light., Comment: 13 pages, 14 figures

We report on the implementation of a time-multiplexed click detection scheme to probe quantum correlations between different spatial optical modes. We demonstrate that such measurement setups can uncover nonclassical correlations in multimode light fields even if the single mode reductions are purely classical. The nonclassical character of correlated photon pairs, generated by a parametric down-conversion, is immediately measurable employing the theory of click counting instead of low-intensity approximations with photoelectric detection models. The analysis is based on second- and higher-order moments, which are directly retrieved from the measured click statistics, for relatively high mean photon numbers. No data postprocessing is required to demonstrate the effects of interest with high significance, despite low efficiencies and experimental imperfections. Our approach shows that such novel detection schemes are a reliable and robust way to characterize quantum-correlated light fields for practical applications in quantum communications., Comment: 6 pages, incl. supplemental material

We study the problem of witnessing entanglement among indistinguishable particles. For this purpose, we derive a set of equations which results in necessary and sufficient conditions for probing multipartite entanglement between arbitrary systems of Bosons or Fermions. The solution of these equations yields the construction of optimal entanglement witnesses for partial and full entanglement in discrete and continuous variable systems. Our approach unifies the verification of entanglement for distinguishable and indistinguishable particles. We provide general solutions for certain observables to study quantum entanglement in systems with different quantum statistics in noisy environments., Comment: 11 pages, 2 figures

Systems of on-off detectors are well established for measuring radiation fields in the regime of small photon numbers. We propose to combine these detector systems with unbalanced homodyning with a weak local oscillator. This approach yields phase-space functions, which represent the click counterpart of the s parametrized quasiprobabilities of standard photoelectric detection theory. This introduced class of distributions can be directly sampled from the measured click counting statistics. Therefore, our technique visualizes nonclassical effects without further data processing. Surprisingly, a small number of on-off diodes can yield more insight than perfect photon number resolution. Quantum signatures in the particle and wave domain of the quantized radiation field, as shown by photon number and squeezed states, respectively, will be uncovered in terms of negativities of the sampled phase-space functions. Application in the vast fields of quantum optics and quantum technology will benefit from our efficient nonclassicality characterization approach., Comment: 4 figures, close to published version

Quantum metrology and quantum information necessitate a profound study of suitable states. Attenuations induced by free-space communication links or fluctuations in the generation of such states limit the quantum enhancement in possible applications. For this reason we investigate quantum features of mixtures of so-called N00N states propagating in atmospheric channels. First, we show that noisy N00N states can still yield a phase resolution beyond classical limitations. Second, we identify entanglement of noisy N00N states after propagation in fluctuating loss channels. To do so, we apply the partial transposition criterion. Our theoretical analysis formulates explicit bounds which are indispensable for experimental verification of quantum entanglement and applications in quantum metrology.

We report the direct -- continuous in phase -- sampling of a regularized $P$ function, the so-called nonclassicality quasiprobability, for squeezed light. Through their negativities, the resulting phase-space representation uncovers the quantum character of the state. In contrast to discrete phase-locked measurements, our approach allows an unconditional verification of nonclassicality by getting rid of interpolation errors due to fixed phases. To realize the equal phase distribution of measured quadratures, a data selection is implemented with quantum random numbers created by measuring the vacuum noise. The continuously measured squeezed field was generated in an optical parametric amplifier. Suitable pattern functions for obtaining the regularized $P$ function are investigated. The significance of detecting negativities in our application is determined. The sampling of nonclassicality quasiprobabilities is shown to be a powerful and universal method to visualize quantum effects within arbitrary quantum states.

Driven by single photon detection requirements especially for quantum information sciences, the theory of arrays of off-on detectors has been well developed and applied. However for a comprehensive characterization of nonclassicality one also needs phase sensitive properties. This missing link is fulfilled by the theory of phase sensitive click counting measurements. This theory is presented. It unifies the balanced homodyne detection for high intensities with the click detection in the few photon regime. We formulate and apply a hierarchy of nonlinear squeezing conditions to probe quantum effects beyond standard squeezing. Imperfections stemming from fluctuations of the local oscillator, detector efficiency, and dark count rates are considered. Experimentally accessible sampling formulas are given which can be applied without time consuming data processing. Our phase-sensitive click detection theory paves the way towards novel applications of nonclassical light in quantum metrology., Comment: close to published EPL version

An analysis is conducted of the multipartite entanglement for Gaussian states generated by the parametric down-conversion of a femtosecond frequency comb. Using a recently introduced method for constructing optimal entanglement criteria, a family of tests is formulated for mode decompositions that extends beyond the traditional bipartition analyses. A numerical optimization over this family is performed to achieve maximal significance of entanglement verification. For experimentally prepared 4-, 6-, and 10-mode states, full entanglement is certified for all of the 14, 202, and 115974 possible nontrivial partitions, respectively., Comment: close to published version, see also viewpoint http://physics.aps.org/articles/v8/10

We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using appropriate measurable witnesses. We derive equations for the construction of optimal witnesses and discuss general properties arising from our approach. As an example, we formulate witnesses for a 4-cluster state and perform a full quantitative analysis of the entanglement structure in the presence of noise and losses. The strength of the method in multimode continuous variable systems is also demonstrated by considering a dephased GHZ-type state., Comment: 12 pages, 1 table and 3 figures

We introduce an experimentally accessible method to measure a unique degree of nonclassicality, based on the quantum superposition principle, for arbitrary quantum states. We formulate witnesses and test a given state for any particular value of this measure. The construction of optimal tests is presented as well as the general numerical implementation. We apply this approach on examples such as squeezed states, and we show how to formulate conditions to certify a particular degree of nonclassicality for single- and multimode radiation fields., Comment: 9 pages, 3 figures

We derive an analytical description for the quantum state preparation using systems of on-off detectors. Our method will apply the true click statistics of such detector systems. In particular, we consider heralded quantum state preparation using correlated light fields, photon addition and photon subtraction processes. Using a post-selection procedure to a particular number of clicks of the detector system, the output states reveal a variety of quantum features. The rigorous description allows the identification and characterization of fundamentally unavoidable attenuations within given processes. We also generalize a known scenario of noiseless amplification with click detectors for the purpose of the preparation of various types of nonclassical states of light. Our exact results are useful for the choice of experimental parameters to realize a target state., Comment: 11 pages, 8 figures, updated references

The nonclassicality of single-mode quantum states is studied in relation to the entanglement created by a beam splitter. It is shown that properly defined quantifications -- based on the quantum superposition principle -- of the amounts of nonclassicality and entanglement are strictly related to each other. This can be generalized to the amount of genuine multipartite entanglement, created from a nonclassical state by an N splitter. As a consequence, a single-mode state of a given amount of nonclassicality is fully equivalent, as a resource, to exactly the same amount of entanglement. This relation is also considered in the context of multipartite entanglement and multimode nonclassicality., Comment: 6 pages, 2 figures

We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize quantum correlations by the statistics measured with systems of on-off detectors. Additionally, we generalize our method to multiple detector systems for measurements of correlations between light fields. We also consider multi-mode radiation fields and isolate nonclassicality in terms of the space time correlations. Finally, we present results for the quantum statistics using on-off detectors operating in nonlinear detection modes.

The generation and the characterization of multipartite entangled light is an important and challenging task in quantum optics. In this paper the entanglement properties of the light emitted from a planar semiconductor microcavity are studied. The intracavity scattering dynamics leads to the emission of light that is described by a fourpartite W state. Its multipartite correlations are identified by using the method of entanglement witnesses. Entanglement conditions are derived, which are based on a general witness constructed from W states. The results can be used to detect entanglement of light that propagates through lossy and even turbulent media., Comment: 9 pages, 3 figures, minor corrections

We introduce a class of bipartite entangled continuous variable states that are positive under partial transposition operation, i.e., PPT bound entangled. These states are based on realistic preparation procedures in optical systems, being thus a feasible option to generate and observe genuinely bipartite bound entanglement in high precision experiments. One fundamental step in our scheme is to perform a non-Gaussian operation over a single-mode Gaussian state; this deGaussification procedure is achieved through a modified single-photon addition, which is a procedure that has currently being investigated in diverse optical setups. Although dependent on a single-photon detection in a idler channel, the preparation can be made unconditional after a calibration of the apparatus. The detection and proof of bound entanglement is made by means of the Range Criterion, theory of Hankel operators and Gerschgorin Disk s perturbation theorems., Comment: 8 pages, 1 figure

We derive a set of algebraic equations, the so-called multipartite separability eigenvalue equations. Based on their solutions, we introduce a universal method for the construction of multipartite entanglement witnesses. We witness multipartite entanglement of $10^3$ coupled quantum oscillators, by solving our basic equations analytically. This clearly demonstrates the feasibility of our method for studying ultra-high orders of multipartite entanglement in complex quantum systems., Comment: published version

Regular quasiprobabilities are introduced for the aim of characterizing quantum correlations of multimode radiation fields. Negativities of these quantum-correlation quasiprobabilities are necessary and sufficient for any quantum correlation encoded in the multimode Glauber-Sudarshan P function. The strength of the method is demonstrated for a two-mode phase randomized squeezed-vacuum state. It has no entanglement, no quantum discord, a positive Wigner function, and a classical reduced single-mode representation. Our method clearly visualizes the quantum correlations of this state., Comment: 7 pages, 3 figures

The emission of entangled light from planar semiconductor microcavities is studied and the entanglement properties are analyzed and quantified. Phase-matching of the intra-cavity scattering dynamics for multiple pump beams or pulses, together with the coupling to external radiation, leads to the emission of a manifold of entangled photon pairs. A decomposition of the emitted photons into two parties leads to a strong entanglement of the resulting bipartite system. For the quantification of the entanglement, the Schmidt number of the system is determined by the construction of Schmidt number witnesses. It is analyzed to which extend the resources of the originally strongly entangled light field are diminished by dephasing in propagation channels., Comment: 9 pages, 5 figures, extended version

We demonstrate the feasibility to completely characterize entanglement by negativities of quasiprobabilities. This requires the complete solution of a sophisticated mathematical problem, the so-called separability eigenvalue problem. Its solution is obtained for a non-Gaussian continuous variable quantum state, a two-mode squeezed state undergoing dephasing. This is a standard scenario for experiments with quantum-correlated radiation fields.