non-Gaussian Operations Research Articles

Enabling CV-MDI-QKD for weakly squeezed states using non-Gaussian operations

Enabling CV-MDI-QKD for weakly squeezed states using non-Gaussian operations

Non-Gaussian two mode squeezed thermal states in continuous variable quantum teleportation

We consider a practical scheme for the implementation of non-Gaussian operation, viz., photon subtraction, photon addition, and photon catalysis, on two-mode squeezed thermal state. The generated states are employed as resources in continuous-variable quantum teleportation. The results show that the three non-Gaussian operations can enhance the teleportation fidelity. Considering the success probability of the non-Gaussian operations, we identify single-photon catalysis and single photon subtraction to be optimal for teleporting input coherent states and squeezed vacuum states, at low and intermediate squeezing levels, respectively.

Analyzing performance of f-deformed displaced Fock state in continuous-variable quantum teleportation

Performing non-Gaussian operations, namely photon addition, photon subtraction, photon-addition-then-subtraction, photon-subtraction-then-addition can successfully enhance the fidelity of the continuous-variable quantum teleportation. However, a shortcoming of these non-Gaussian resources is that they are probabilistic in nature. In this article, we investigate the success probability of the non-Gaussian resources for optimal performance of the ideal teleportation protocol. To this end, we first derive the analytical expression for the two-mode entangled channel having f-deformed displaced Fock state or photon-added displaced Fock state or photon-subtracted displaced Fock state at one port and vacuum at another port of a symmetric beam-splitter. The generalized displaced Fock states are obtained by replacing the conventional bosonic functions by the nonlinear f-deformed operators such as A = af(a † a) and B=af(a†a)−1 . The Wigner characteristic functions describing these three aforementioned non-Gaussian states are determined and utilized to attain the teleportation fidelity for input coherent and squeezed vacuum states. It is found that the nonlinear substitution leads to an enhancement in teleportation fidelity beyond the threshold limit. Moreover, the entangled photon-subtracted displaced Fock state demonstrates maximum efficiency as a quantum channel for teleporting single-mode coherent and squeezed states. We provide the squeezing regime values corresponding to the optimal performance of the non-Gaussian states considered, which will be of significant interest to the experimental fraternity. Further, we show that the entangled photon-added displaced Fock states have larger amount of entanglement but the entangled photon-subtracted displaced Fock states have stronger Einstein-Podolsky-Rosen correlation.

Advantage of probabilistic non-Gaussian operations in the distillation of single mode squeezed vacuum state

We consider distillation of squeezing in single mode squeezed vacuum state using three different probabilistic non-Gaussian operations: photon subtraction (PS), photon addition (PA) and photon catalysis (PC). To achieve this, we consider a practical model to implement these non-Gaussian operations and derive the Wigner characteristic function of the resulting non-Gaussian states. Our result shows that while PS and PC operations can distill squeezing, PA operation cannot. Furthermore, we delve into the success probabilities associated with these non-Gaussian operations and identify optimal parameters for the distillation of squeezing. Our current analysis holds significant relevance for experimental endeavors concerned with squeezing distillation.

Metrological detection of entanglement generated by non-Gaussian operations

Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.

Phase estimation via multi-photon subtraction inside the SU(1,1) interferometer

To improve the phase sensitivity, multi-photon subtraction schemes (multi-PSS) within the SU(1,1) interferometer are proposed. The input states are the coherent state and the vacuum state, and the detection method is homodyne detection. The effects of multi-photon subtraction on phase sensitivity, quantum Fisher information (QFI), and quantum Cramér-Rao bound (QCRB) are analyzed under both ideal and photon losses situations. It is shown that the internal subtraction operation can improve the phase sensitivity, which becomes better performance by increasing subtraction number. It can also efficiently improve the robustness of the SU(1,1) interferometer against internal photon losses. By comparing separatively arbitrary photon subtraction on the two-mode inside SU(1,1) interferometer, the performance differences under different conditions are analyzed, including the asymmetric properties of non-Gaussian operations on the phase precision and the QFI. Our proposed scheme represents a valuable method for achieving quantum precision measurements.

Performance optimization of continuous-variable quantum teleportation with generalized photon-varying non-Gaussian operations

Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the protocol. However, for a given type of non-Gaussian operation, the achievable fidelity varies with the parameters associated with the operation. Previous work only focused on particular settings of the parameters, over which an optimization was missing. The potential of such operations is not fully uncovered. Given a fixed non-Gaussian operation, the achievable fidelity also varies with input states. An operation that increases the fidelity for teleporting one class of states might do the contrary for other classes of states. A performance metric, upon which an operation is optimized, suitable for different input states, is also missing. In this work, we build a framework for photon-varying non-Gaussian operations for multimode states, upon which we propose a performance metric suitable for arbitrary teleportation input states. We then apply the new metric to evaluate different types of non-Gaussian operations. Starting from simple multiphoton photon subtraction and photon addition, we find that increasing the number of ancillary photons involved in the operation does not guarantee performance improvement. We then investigate a generalization of the operations mentioned above, finding that operations that approximate a particular form provide the best improvement. The results provided here will be valuable for real-world implementations of quantum teleportation networks and applications that harness the non-Gaussianity of quantum states. Published by the American Physical Society 2024

Simulating quantum field theories on continuous-variable quantum computers

We delve into the use of photonic quantum computing to simulate quantum mechanics and extend its application towards quantum field theory. We develop and prove a method that leverages this form of continuous-variable quantum computing (CVQC) to reproduce the time evolution of quantum-mechanical states under arbitrary Hamiltonians, and we demonstrate the method's remarkable efficacy with various potentials. Our method centers on constructing an , a specially prepared quantum state that induces the desired time evolution on the target state. This is achieved by introducing a non-Gaussian operation using a measurement-based quantum computing approach, enhanced by machine learning. Furthermore, we propose a framework in which these methods can be extended to encode field theories in CVQC without discretizing the field values, thus preserving the continuous nature of the fields. This opens new avenues for quantum computing applications in quantum field theory. Published by the American Physical Society 2024

Classical simulation of non-Gaussian fermionic circuits

We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.

Long-distance high-fidelity continuous-variable quantum key distribution with non-Gaussian operations: An exact closed form solution

In this paper, we derive a closed-form expression for the output state of a CV-QKD protocol in the presence of zero-photon catalysis (ZPC) and a quantum scissor (QS). Then, based on this closed-form solution, we use a direct search algorithm to find the appropriate values of input state and QS parameters, which considerably enhance the range and the fidelity of a CV-QKD protocol. In the special case of pure loss channel, the largest range of the protocol is only 6.5% less than the fundamental limit of repeaterless quantum communication. In addition, examination of the protocol for different values of excess noise, reveals that there is a trade-off between range and fidelity, and a high value of fidelity can be obtained at the cost of a slight reduction in protocol range.

Underwater quantum key distribution with continuous-variable via photon additions

Quantum key distribution with continuous-variable (CVQKD) provides an alternative way for the security improvement of underwater optical communication, but facing into the awkward situation of short distance. For this reason, here we exploit photon addition operation at the emitter into enhancing the performance of underwater CVQKD. Based on numerical simulation, it is shown that applying photon-addition non-Gaussian operation between entangled resource and the sender can further enhance both the secure key rate and the transmission distance, compared to apply photon subtraction operation between entangled resource and the receiver. In addition, the influence of seawater quality factors in underwater CVQKD system is also considered, so as to provide technical support for underwater safety communication.

Continuous-variable quantum key distribution based on non-Gaussian operations with on-off detection.

Quantum key distribution (QKD) with continuous variable (CV) is an effective method for achieving the high key rate, but is also limited to a short transmission distance. To overcome this limitation, some solutions have been proposed, including non-Gaussian operations, such as photon addition and photon subtraction using ideal photon source and number-resolving detection. Here we consider the effect of non-Gaussian operation for realistic photon source and ideal on-off photon detection. In the realistic case, it is shown that the performance of CVQKD can not be improved by both photon-subtraction/addition on the right side before the entangled source reaches the channel and photon-subtraction on the left side preceding the entangled source to the sender Alice before performing heterodyne detection, but be enhanced by the photon addition on the left side in a long distance case. These results may provide a useful reference for quantum information with continuous variable.

Non-Gaussian approach: Withstanding loss and noise of multi-scattering underwater channel for continuous-variable quantum teleportation

Underwater quantum communication plays a crucial role in ensuring secure data transmission and extensible quantum networks in underwater environments. However, the implementation of such applications encounters challenges due to the light attenuation caused by the complicated natural seawater. This paper focuses on employing a model based on seawater chlorophyll-a concentration to characterize the absorption and scattering of light through quantum channels. We propose a multi-scattering random channel model, which demonstrates characteristics of the excess noise in different propagation directions of communication links. Furthermore, we consider the fidelity of a continuous-variable quantum teleportation through seawater channel. To enhance transmission performance, non-Gaussian operations have been conducted. Numerical simulations show that incorporating non-Gaussian operations enables the protocol to achieve higher fidelity transmission or lower fidelity fading rates over longer transmission distances.

Enhanced entanglement and quantum teleportation of two-mode squeezed vacuum state via multistage non-Gaussian operations

The improvement of quantum features and processes, prominent as entanglement and quantum teleportation, of the two-mode squeezed vacuum state (TMSVS) in the small squeezed parameter domain is of great importance. Therefore, it has attracted the attention of scientists in the field of quantum information in recent years. In this paper, we introduce a new optical scheme to enhance the degree of entanglement and quantum teleportation fidelity of such a state using ordinary quantum devices including beam splitters and photon-number-resolving detectors. The scheme allows us to sequentially perform non-Gaussian operations, namely, photon addition, photon subtraction, quantum optical catalysis, and combinations of these techniques, into both modes of the TMSVS. The investigated results show that the degree of entanglement and fidelity in the novel two-mode non-Gaussian state is enhanced, especially in the small regions of the squeezed parameter compared with the original TMSVS and non-Gaussian states constructed from it in previous works. They also indicate that the enhanced zones recede to the small squeezed parameter areas with increasing the number of stages of the non-Gaussian effect.

Teleportation protocols with non-Gaussian operations: Conditional photon subtraction versus cubic phase gate

In our paper, we compare three teleportation protocols: The original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schr\"odinger cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.

Teleportation of hybrid entangled states with continuous-variable entanglement

Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation.

Phase estimation of an SU(1,1) interferometer with a coherent superposition squeezed vacuum in a realistic case.

The phase sensitivity of SU(1,1) interferometer is investigated using a coherent state and an m-coherent superposition squeezed vacuum states as inputs and the intensity detection. Photon-subtraction, photon-addition and photon superposition are three special cases. Both ideal and realistic cases are considered. It is shown that the coefficient s of coherent superposition can modulate the performance of phase sensitivity, especially in a small squeezing region. Even in the presence of photon losses, the three-kind of non-Gaussian operations can achieve the improvement of measure precision, and the photon addition presents the best robustness compared to the photon subtraction and coherent superposition. For small squeezing, the first-order non-Gaussian operation may be the most preferred in improving phase sensitivity if considering the limitations of experimental conditions. Our results may be helpful for the practical application of quantum information.

Teleportation of discrete-variable qubits via continuous-variable lossy channels

The Continuous-Variable (CV) quantum state of light allows for the teleportation of a Discrete-Variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource channel is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold of 0.5 dB. In this work, we present a new non-deterministic teleportation protocol that combines a Gaussian CV resource channel with a modified form of the Bell State Measurement that accommodates a DV-qubit fidelity beyond the classical limit for channel losses up to 20~dB. Beyond this orders of magnitude improvement, we also show how the use of non-Gaussian operations on the CV resource channel can lead to a DV-qubit fidelity approaching unity for any channel loss.

Realistic non-Gaussian-operation scheme in parity-detection-based Mach-Zehnder quantum interferometry

We theoretically analyze phase sensitivity using parity detection based Mach Zehnder interferometer (MZI) with the input states generated by performing non-Gaussian operations, viz., photon subtraction, photon addition, and photon catalysis on a two-mode squeezed vacuum (TMSV) state. Since these non-Gaussian operations are probabilistic, it is of utmost importance to take the success probability into account. To this end, we consider the realistic model of photon subtraction, addition, and catalysis and derive a single expression of the Wigner function for photon subtracted, added, and catalyzed TMSV state. The Wigner function is used to evaluate the lower bound on the phase sensitivity via quantum Cramer-Rao bound and parity detection based phase sensitivity in MZI. We identify the ranges of squeezing and transmissivity parameters where the non-Gaussian states provide better phase sensitivity than the TMSV state. On qualitatively taking the success probability into account, it turns out that the photon addition is the most advantageous non-Gaussian operation. We hope that the generalized Wigner function derived in this work will be useful in various quantum information protocols and state characterization.

Experimental Demonstration of Remotely Creating Wigner Negativity via Quantum Steering.

Non-Gaussian states with Wigner negativity are of particular interest in quantum technology due to their potential applications in quantum computing and quantum metrology. However, how to create such states at a remote location remains a challenge, which is important for efficiently distributing quantum resource between distant nodes in a network. Here, we experimentally prepare an optical non-Gaussian state with negative Wigner function at a remote node via local non-Gaussian operation and shared Gaussian entangled state existing quantum steering. By performing photon subtraction on one mode, Wigner negativity is created in the remote target mode. We show that the Wigner negativity is sensitive to loss on the target mode, but robust to loss on the mode performing photon subtraction. This experiment confirms the connection between the remotely created Wigner negativity and quantum steering. As an application, we present that the generated non-Gaussian state exhibits metrological power in quantum phase estimation.