Continuous variable quantum teleportation with sculptured and noisy non-Gaussian resources

Quantum teleportation has achieved significant progress in the optical frequency domain but faces persistent challenges, including high transmission losses and limited transmittance. In contrast, the microwave frequency domain offers distinct advantages, such as reduced absorption losses, lower energy consumption, and compatibility with superconducting quantum technologies. To overcome the limitations of optical quantum teleportation, this study presents a microwave-based continuous-variable quantum teleportation (CVQT) scheme designed for open-air environments at room temperature. The proposed approach employs microwave two-mode squeezed states, with entanglement enhanced through quantum scissors operations to mitigate environmental degradation. Numerical simulations demonstrate that the maximum transmission distance of microwave entangled states for CVQT is about 200 m at room temperature. The results also indicate that the microwave CVQT scheme achieves lower attenuation and higher fidelity over short distances compared to optical frequency CVQT under similar weather conditions. Moreover, microwave quantum states exhibit reduced sensitivity to weather-induced variations, highlighting their robustness and practicality for open-air quantum communication applications.

The progress in quantum operations of continuous-variable (CV) schemes can be reduced to that in CV quantum teleportation. The fidelity of quantum teleportation of an optical setup is limited by the finite degree of quantum correlation that can be prepared with a pair of finitely squeezed states. Reports of improvement of squeezing level have appeared recently, and we adopted the improved methods in our experimental system of quantum teleportation. As a result, we teleported a coherent state with a fidelity $F=0.83\ifmmode\pm\else\textpm\fi{}0.01$, which is better than any other figures reported to date, to our knowledge. In this paper, we introduce a measure ${n}_{s}$, the number of teleportations expected to be carried out sequentially. Our result corresponds to ${n}_{s}=5.0\ifmmode\pm\else\textpm\fi{}0.4$. It suggests that our improvement would enable us to proceed toward more advanced quantum operations involving multiple steps.

A quantum internet connects remote quantum processors that need interact and exchange quantum signals over a long distance through photonic channels. However, these quantum nodes are usually composed of quantum systems with emitted photons unsuitable for long-distance transmission. Therefore, quantum wavelength conversion to telecom is crucial for long-distance quantum networks based on optical fiber. Here we propose wavelength conversion devices for single-photon polarization qubits using continuous variable quantum teleportation, which can efficiently convert qubits between near-infrared (780/795 nm suitable for interacting with atomic quantum nodes) and telecom wavelength (1300-1500 nm suitable for long-distance transmission). The teleportation uses entangled photon sources (i.e., non-degenerate two-mode squeezed state) that can be generated by four-wave mixing in rubidium atomic vapor cells, with a diamond configuration of atomic transitions. The entangled fields can be emitted in two orthogonal polarizations with locked relative phase, making them especially suitable for interfacing with single-photon polarization qubits. Our work paves the way for the realization of long-distance quantum networks.

We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter r and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter r.

Summary form only given. The concept of quantum teleportation of continuous variables was suggested by Vaidman [see Phys. Rev. A, vol. 49, p. 1473, 1994]. The protocol for this kind of teleportation was elaborated and demonstrated experimentally by Kimble with collaborators [see Science, vol. 282, p. 706, 1998]. In this scheme the state being teleported is that of a single transverse mode of the electromagnetic field with finite frequency bandwidth. We describe the quantum teleportation scheme that allows one to teleport the quantum state of the wavefront of an electromagnetic wave. In other words we propose teleportation of the quantum state of a spatially multimode electromagnetic field.

Satellite-based quantum communication is critical in establishing a global quantum network for its ability to achieve thousand-kilometer-level tasks without the requirement of quantum relay. The free-space channel, however, is affected by diffraction, regular refraction, and atmospheric turbulence, which induce random wandering and broadening of the transmitted beam, resulting in the transmittance of fluctuation. In such a scenario, the ability to predict the unknown situation has become a problem worth considering. In this paper, we suggest a machine learning (ML) assisted prediction of continuous-variable quantum teleportation (CVQT) over satellite-ground channel. We apply the prediction algorithm, which involves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -nearest neighbor (KNN) algorithm and decision tree (DT) algorithm, to the squeezing parameter and the satellite altitude. Numerical analysis shows that the predicted parameter can reflect the actual derivation and calculation under certain circumstances within the allowable range of error. Moreover, we apply the prediction algorithm to the case affected by the fluctuating parameter transmittance. The results show that the ML-assisted prediction results are consistent with the actual data when zenith angles, turbulence strengths, and wavelengths are taken into account. It demonstrates the high identifying accuracy without increasing the complexity of the system.

We analyze the statistics of observables in continuous variable quantum\nteleportation in the formalism of the characteristic function. We derive\nexpressions for average values of output state observables in particular\ncumulants which are additive in terms of the input state and the resource of\nteleportation. Working with Squeezed Bell-like states, which may be optimized\nin a free parameter for better teleportation performance we discuss the\nrelation between resources optimal for fidelity and for different observable\naverages. We obtain the values of the free parameter which optimize the central\nmomenta and cumulants up to fourth order. For the cumulants the distortion\nbetween in and out states due to teleportation depends only on the resource. We\nobtain optimal parameters for the second and fourth order cumulants which do\nnot depend on the squeezing of the resource. The second order central momenta\nwhich is equal to the second order cumulants and the photon number average are\noptimized by the same resource. We show that the optimal fidelity resource,\nfound in reference (Phys. Rev. A {\\bf 76}, 022301 (2007)) to depend also on the\ncharacteristics of input, tends for high squeezing to the resource which\noptimizes the second order momenta. A similar behavior is obtained for the\nresource which optimizes the photon statistics which is treated here using the\nsum of the squared differences in photon probabilities of input and output\nstates as the distortion measure. This is interpreted to mean that the\ndistortions associated to second order momenta dominates the behavior of the\noutput state for large squeezing of the resource. Optimal fidelity and optimal\nphoton statistics resources are compared and is shown that for mixtures of Fock\nstates they are equivalent.\n

We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies and phase fluctuations. The inferred fidelity for input coherent states is F = 0.61 +- 0.02, which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69. The teleportation protocol is explained in detail, including a discussion of discrepancy between experiment and theory, as well as of the limitations of the current apparatus.

Quantum teleportation, a transfer protocol of quantum states, is the essence of many sophisticated quantum information protocols. There have been two complementary approaches to optical quantum teleportation: discrete variables (DVs) and continuous variables (CVs). However, both approaches have pros and cons. Here we take a “hybrid” approach to overcome the current limitations: CV quantum teleportation of DVs. This approach enabled the first realization of deterministic quantum teleportation of photonic qubits without post-selection. We also applied the hybrid scheme to several experiments, including entanglement swapping between DVs and CVs, conditional CV teleportation of single photons, and CV teleportation of qutrits. We are now aiming at universal, scalable, and fault-tolerant quantum computing based on these hybrid technologies.

We develop a simple and efficient theoretical model to understand the quantum properties of broadband continuous variable quantum teleportation. We show that, if stated properly, the problem of multimode teleportation can be simplified to teleportation of a single effective mode that describes the input state temporal characteristic. Using that model, we show how the finite bandwidth of squeezing and external noise in the classical channel affect the output teleported quantum field. We choose an approach that is especially relevant for the case of non-Gaussian nonclassical quantum states and we finally back-test our model with recent experimental results.

Quantum teleportation plays an important role in quantum information science. In order to obtain the effect of quantum teleportation of a quantum state by using an entangled resource, the fidelity of teleporting the quantum state should be calculated. Braunstein and Kimble[Phys. Rev. Lett. 80 869 (1998)] derived a formula of calculating the fidelity of quantum teleportation for Gaussian entangled resource and any input state to be teleported. Then, the point is how to calculate the quantum teleportation fidelity for any entangled resource. In this paper, werealize this purpose by using the entangled state representation. First, we derive the Weyl expansion of any density operator by using the completeness relation between coherent state and P-representation. Then using the orthogonal property of entangled state representation and the traditional Kimble-Braunstein scheme of quantum teleportation, we further derive the mean density operator of the output state, which means that we establish the relation between the output density operator and the characteristic functions of the input state to be teleported and the entangled resources. The characteristic function of the output state is also derived which is in the concise form relating these two characteristic functions above. Then we further obtain a new formula for calculating the quantum teleportation fidelity for the coherent state input and any two-mode entangled resource. It is shown that the fidelity of teleportation can be easily calculated when the Q-function of the normally ordering form of entangled resource is known. This is a convenient way of obtaining the fidelity of teleportation. As its applications, some Gaussian and non-Gaussian entangled states are examined to teleport the coherent state, whose results are correct.

We introduce and discuss a set of tunable two-mode states of continuous-variable systems, as well as an efficient scheme for their experimental generation. This novel class of tunable entangled resources is defined by a general ansatz depending on two experimentally adjustable parameters. It is very ample and flexible as it encompasses Gaussian as well as non-Gaussian states. The latter include, among others, known states such as squeezed number states and de-Gaussified photon-added and photon-subtracted squeezed states, the latter being the most efficient non-Gaussian resources currently available in the laboratory. Moreover, it contains the classes of squeezed Bell states and even more general non-Gaussian resources that can be optimized according to the specific quantum technological task that needs to be realized. The proposed experimental scheme exploits linear optical operations and photon detections performed on a pair of uncorrelated two--mode Gaussian squeezed states. The desired non-Gaussian state is then realized via ancillary squeezing and conditioning. Two independent, freely tunable experimental parameters can be exploited to generate different states and to optimize the performance in implementing a given quantum protocol. As a concrete instance, we analyze in detail the performance of different states considered as resources for the realization of quantum teleportation in realistic conditions. For the fidelity of teleportation of an unknown coherent state, we show that the resources associated to the optimized parameters outperform, in a significant range of experimental values, both Gaussian twin beams and photon-subtracted squeezed states.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

We propose a quantum teleportation scheme for tripartite entangled coherent state (ECS) with continuous variable. Our scheme is feasible and economical in the sense that we need only linear optical devices such as beam splitters, phase shifters and photon detectors and employ three bipartite maximally ECSs as quantum channels. We also generalize the tripartite scheme into multipartite case and calculate the minimum average fidelity for the schemes in tripartite and multipartite cases.

Einstein–Podolsky–Rosen correlation and continuous-variable quantum teleportation for the non-Gaussian entangled state with coherent component