non-Gaussian Entanglement Research Articles

Non-Gaussian nature and entanglement of spontaneous parametric nondegenerate triple-photon generation

How to prepare deterministically non-Gaussian entangled states is a fundamental question for continuous-variable quantum information technology. Here, we theoretically demonstrate through numerical methods that the triple-photon state generated by three-photon spontaneous parametric down-conversion is a pure super-Gaussian resource of non-Gaussian entanglement. Interestingly, the degree of entanglement between the modes of the triple-photon state is stronger than that corresponding to the two-mode squeezed vacuum state produced by a quadratic Hamiltonian with the same parameters. Furthermore, we propose a model to prepare two-mode non-Gaussian entangled states with tunable non-Gaussianity based on quadrature projection measurements.

Continuous-variable quantum repeater based on quantum scissors and mode multiplexing

Quantum repeaters are indispensable for high-rate, long-distance quantum communications. The vision of a future quantum internet strongly hinges on realizing quantum repeaters in practice. Numerous repeaters have been proposed for discrete-variable (DV) single-photon-based quantum communications. Continuous variable (CV) encodings over the quadrature degrees of freedom of the electromagnetic field mode offer an attractive alternative. For example, CV transmission systems are easier to integrate with existing optical telecom systems compared to their DV counterparts. Yet, repeaters for CV have remained elusive. We present a novel quantum repeater scheme for CV entanglement distribution over a lossy bosonic channel that beats the direct transmission exponential rate-loss tradeoff. The scheme involves repeater nodes consisting of a) two-mode squeezed vacuum (TMSV) CV entanglement sources, b) the quantum scissors operation to perform nondeterministic noiseless linear amplification of lossy TMSV states, c) a layer of switched, mode multiplexing inspired by second-generation DV repeaters, which is the key ingredient apart from probabilistic entanglement purification that makes DV repeaters work, and d) a non-Gaussian entanglement swap operation. We report our exact results on the rate-loss envelope achieved by the scheme.

Non-Gaussian quantum states of a multimode light field

Even though Gaussian quantum states of multimode light are promising quantum resources due to their scalability, non-Gaussianity is indispensable for quantum technologies, in particular to reach quantum computational advantage. However, embodying non-Gaussianity in a multimode Gaussian state remains a challenge as controllable non-Gaussian operations are hard to implement in a multimode scenario. Here, we report the first generation of non-Gaussian quantum states of a multimode light field by subtracting a photon in a desired mode from multimode Gaussian states, and observe negativity of the Wigner function. For entangled Gaussian states, we observe that photon subtraction makes non-Gaussianity spread among various entangled modes. In addition to applications in quantum technologies, our results shed new light on non-Gaussian multimode entanglement with particular emphasis on quantum networks.

Non-Gaussian macroscopic entanglement of motion in a hybrid electromechanical device

We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We show that the generated macroscopic entangled states are non-Gaussian and its lifetime is limited by coherence time of the qubit. The entanglement is attainable in a wide range of parameters with appropriate control of the qubit. We confirm performance of our scheme by numerically solving the quantum optical master equation including sources of noise. The effect of imperfections, such as asymmetries in the coupling rates as well as mechanical thermal noise are studied and shown how they affect the amount and lifetime of the entangled state. Due to the nonlinear nature of the qubit, the initial Gaussian state of mechanical resonators evolves into a quasi-stationary non-Gaussian state, which is essential for universal quantum information processing in continuous variable systems. This work, therefore, provides the first step towards a universal continuous variable quantum network.

Repeaters for continuous-variable quantum communication

Optical telecommunication is at the heart of today's internet and is currently enabled by the transmission of intense optical signals between remote locations. As we look to the future of telecommunication, quantum mechanics promise new ways to be able to transmit and process that information. Demonstrations of quantum key distribution and quantum teleportation using multi-photon states have been performed, but only over ranges limited to one hundred kilometers. To go beyond this, we need repeaters that are compatible with these quantum multi-photon continuous variables pulses. Here we present a design for a continuous variable quantum repeaters that can distribute entangled and pure two-mode squeezed states over arbitrarily long distances with a success probability that scales only polynomially with distance. The proposed quantum repeater is composed from several basic known building blocks such as non-Gaussian operations for entanglement distillation and an iterative Gaussification protocol (for retaining the Gaussian character of the final state), but complemented with a heralded non-Gaussian entanglement swapping protocol, which allows us to avoid extensive iterations of quantum Gaussification. We characterize the performance of this scheme in terms of key rates for quantum key distribution and show a secure key can be generated over thousands of kilometers.

Displaced photon-number entanglement tests

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.

Entanglement and squeezing in continuous-variable systems

We introduce a multi-mode squeezing coefficient to characterize entanglement in N-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the 2N-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement.

Higher-order nonclassical effects in fluctuating-loss channels

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.

Conditional superpositions of Gaussian operations on different modes of light

We propose a conditional implementation of superpositions of Gaussian operations on different modes of light. These operations are conditional entanglers generating non-Gaussian entanglement between two modes of propagating light beams. The all-optical operations emulate weak effects of highly nonlinear operations only available when light interacts with individual atoms. In particular, we propose schemes to implement superposition of coherent displacements and squeezings on two beams of light and discuss physical properties of generated non-Gaussian entanglement. These methods together with high quality of optical tomography of highly nonclassical states allow one to understand non-Gaussian entangling processes.

Classical light sources with tunable temporal coherence and tailored photon number distributions

We demonstrate the generation of classical incoherent light with electronic control over its temporal characteristics and photon number distribution. The tunability of the temporal coherence is shown, under both classical and quantum detection, through second order correlation ($G^2(\tau)$) measurements. The tailoring of desired classical photon number distributions is illustrated by creating two representative light sources - one thermal and the other a specific classical, non-Gaussian state. Such generation of classical light sources, quite different from existing natural light sources, is likely to be a useful resource in quantum information processing. As a particular application in this direction we outline how a non-Gaussian state generated in this manner may be mixed with an appropriate non-classical Gaussian state at a beamsplitter, to generate non-Gaussian entanglement.

Analytical approach and reconstruction of the density matrix of coupled oscillators

We present an analytical approach to solve the wave function and reconstruct the density matrix for a linear x–x coupled oscillator system. The method is available both for weak and strong coupling systems. Employing our method, we analyse the probability distribution function, dynamical recurrence and non-Gaussian entanglement. Including the dissipation, we reconstruct the density matrix in the Liouville-space. Supplying both analytical and numerical treatment, we obtain the steady-state solution of the density matrix and discuss the effect of resonant excitation.

Direct measurement of the biphoton Wigner function through two-photon interference

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non–classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable quantum systems, consisting of biphotons generated by parametric down conversion. A consequence of our results is that a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics using simple optical set-ups.

Non-Gaussian continuous-variable entanglement and steering

Two Kerr-squeezed optical beams can be combined in a beam splitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient, and proven technology of homodyne detection may be used for their characterization. A physical demonstration maintaining the important features of the model could be realized using optical fibers, beam splitters, and homodyne detection.

Entanglement distillation for continuous variables in a thermal environment: Effectiveness of a non-Gaussian operation

We study the task of distilling entanglement by a coherent superposition operation $t\hat{a}+r\hat{a}^\dagger$ applied to a continuous-variable state under a thermal noise. In particular, we compare the performances of two different strategies, i.e., the non-Gaussian operation $t\hat{a}+r\hat{a}^\dagger$ is applied before or after the noisy Gaussian channel. This is closely related to a fundamental problem of whether Gaussian or non-Gaussian entanglement can be more robust under a noisy channel and also provides a useful insight into the practical implementation of entanglement distribution for a long-distance quantum communication. We specifically look into two entanglement characteristics, the logarithmic negativity as a measure of entanglement and the teleportation fidelity as a usefulness of entanglement, for each distilled state. We find that the non-Gaussian operation after (before) the thermal noise becomes more effective in the low (high) temperature regime.

Photonic families of non-Gaussian entangled states and entanglement criteria for continuous-variable systems

We consider two classes of non-Gaussian entangled states generated from the product of number states with the action of the beamsplitter or the two-mode squeezer. It is shown that, for many of these states, the covariance matrix is compatible with the covariance matrix of separable Gaussian states and their separability cannot be verified by the measurements of the first and second moments of canonical variables. We identify a couple of continuous-variable entanglement criteria with higher order moments to verify these non-Gaussian entanglement.

Efficient Entanglement Criteria beyond Gaussian Limits Using Gaussian Measurements

We present a formalism to derive entanglement criteria beyond the Gaussian regime that can be readily tested by only homodyne detection. The measured observable is the Einstein-Podolsky-Rosen (EPR) correlation. Its arbitrary functional form enables us to detect non-Gaussian entanglement even when an entanglement test based on second-order moments fails. We illustrate the power of our experimentally friendly criteria for a broad class of non-Gaussian states under realistic conditions. We also show rigorously that quantum teleportation for continuous variables employs a specific functional form of EPR correlation.

Local Gaussian operations can enhance continuous-variable entanglement distillation

Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.

Sideband entanglement in collective resonance fluorescence

We examine the quantum correlation between the Mollow sidebands in the collective resonance fluorescence from a strongly driven ensemble of two-level atoms. By using the criterion proposed by Shchukin and Vogel, we show that non-Gaussian entanglement exists between the two separated sidebands. The responsible mechanism is traced to the spontaneous parametric process, in which the nonclassical correlation is established. This suggests that the collective resonance fluorescence provides a continuous source for the non-Gaussian entangled light and thus has great potentials for various applications in quantum information and quantum computation.

Generation and distillation of non-Gaussian entanglement from nonclassical photon statistics

With a product state of the form $${{\rho}_{\rm in} = {\rho}_{a} \otimes |0 \rangle_b {_b} \langle 0|}$$ as input to a beam splitter, the output two-mode state ? out is shown to be negative under partial transpose (NPT) whenever the photon number distribution (PND) statistics { p(n a ) } associated with the possibly mixed state ? a of the input a-mode is antibunched or otherwise nonclassical, i.e., whenever { p(n a ) } fails to respect any one of an infinite sequence of necessary and sufficient classicality conditions. Negativity under partial transpose turns out to be a necessary and sufficient test for entanglement of ? out which is generically non-Gaussian. The output of a PND distribution is further shown to be distillable if any one of an infinite sequence of three term classicality conditions is violated.

Robustness of Non-Gaussian Entanglement against Noisy Amplifier and Attenuator Environments

The recently developed Kraus representation for bosonic Gaussian channels is employed to study analytically the robustness of non-Gaussian entanglement against evolution under noisy attenuator and amplifier environments, and compare it with the robustness of Gaussian entanglement. Our results show that some non-Gaussian states with one ebit of entanglement are more robust than all Gaussian states, even the ones with arbitrarily large entanglement, a conclusion of direct consequence to the recent conjecture by Allegra et al. [Phys. Rev. Lett. 105, 100503 (2010)].