non-Gaussian Operations Research Articles

Mode-selective single-photon addition to a multimode quantum field

Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion (PDC) processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the type-II collinear down conversion, while single-mode condition are retrieved for noncollinear type-I and type-II processes. Numerical results are shown for photon addition in PDC process at near-infrared and telecommunications wavelengths.

Distribution and quantification of remotely generated Wigner negativity

Wigner negativity, as a well-known indicator of nonclassicality, plays an essential role in quantum computing and simulation using continuous-variable systems. The conditional preparation of Wigner-negative states through appropriate non-Gaussian operations on an auxiliary mode is common procedure in quantum optics experiments. Motivated by the demand of real-world quantum network, here we investigate the remote creation and distribution of Wigner negativity in the multipartite scenario from a quantitative perspective. By establishing a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality, we show that the amount of Wigner negativity cannot be freely distributed among different modes. Moreover, for photon subtraction—one of the main experimentally realized non-Gaussian operations—we provide an intuitive method to quantify remotely generated Wigner negativity. Our results pave the way for exploiting Wigner negativity as a valuable resource for numerous quantum information protocols based on non-Gaussian scenario.

Improving entanglement of even entangled coherent states via superposition of number-conserving operations

A scheme for improving entanglement is proposed by repeatedly performing number-conserving generalized superposition of products (GSP) operation, i.e., saa†+ta†am with s2+t2=1, on each modes of even entangled coherent state (EECS). Both Einstein–Podolsky–Rosen (EPR) correlation and concurrence are used as the measures for describing entanglement. It is found that both single-mode and two-mode-symmetric GSP operations can be used for the entanglement improvement. In particular, for the optimal EPR correlation, the GSP-EECS with two-mode-symmetric first-order operations presents a better performance for the entanglement improvement than the cases of high-order GSP operations. Compared to several special non-Gaussian operations, including photon subtraction-then-addition (PSTA) (s=0) and photon-addition-then-subtraction (PATS) (s=1), it is shown that the entanglement of GSP-EECS is always superior to those of both PSTA-EECS and PATS-EECS at a small amplitude level. When the GSP-EECS is used as the entangled resource for teleportation, our optimal teleportation fidelity presents the best performance.

Short-wave infrared continuous-variable quantum key distribution over satellite-to-submarine channels

The trans-media transmission of quantum pulse is one of means of free-space transmission which can be applied in continuous-variable quantum key distribution (CVQKD) system. In traditional implementations for atmospheric channels, the 1500-to-1600-nm pulse is regarded as an ideal quantum pulse carrier. However, the underwater transmission of this pulses tends to suffer from severe attenuation, which inevitably deteriorates the security of the whole CVQKD system. In this paper, we propose an alternative scheme for implementations of CVQKD over satellite-to-submarine channels. We estimate the parameters of the trans-media channels, involving atmosphere, sea surface and seawater and find that the short-wave infrared performs well in the above channels. The 450-nm pulse is used for generations of quantum signal carriers to accomplish quantum communications through atmosphere, sea surface and seawater channels. Numerical simulations show that the proposed scheme can achieve the transmission distance of 600 km. In addition, we demonstrate that non-Gaussian operations can further lengthen its maximal transmission distance, which contributes to the establishment of practical global quantum networks.

Ghost Imaging with Non-Gaussian Quantum Light

Nonlocal point-to-point correlations between two photons have been used to produce ``ghost'' images without placing the camera towards the object. Here we theoretically demonstrate and analyze the advantage of non-Gaussian quantum light in improving the image quality of a ghost imaging system over a traditional Gaussian light source. For any squeezing degree, the signal-to-noise ratio (SNR) of the ghost image can be enhanced by the non-Gaussian operations of photon addition and subtraction on a two-mode squeezed light source. We find striking evidence that using non-Gaussian coherent operations, the SNR can be promoted to a high level even within the extremely weak squeezing regime. The resulting insight provides experimental recipes of quantum imaging using non-Gaussian light for illumination.

Non-Gaussian operations in measurement-device-independent quantum key distribution

Non-Gaussian operations in continous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis and subtraction on squeezed coherent states on CV measurement device independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we observe that zero photon catalysis on two mode squeezed coherent state (TMSC) is an optimial choice for CV MDI QKD, while single photon subtraction is also a good candidate; both of them offering nearly 70 km of transmission distances. We also derive a single generalized covariance matrix for the aforementioned states which will be useful in several other aspects of CV quantum information processing.

Non-Clifford gate on optical qubits by nonlinear feedforward

In a continuous-variable optical system, the Gottesman-Kitaev-Preskill (GKP) qubit is a promising candidate for fault-tolerant quantum computation. To implement non-Clifford operations on GKP qubits, non-Gaussian operations are required. In this context, the implementation of a cubic phase gate by combining nonlinear feedforward with ancillary states has been widely researched. Recently, however, it is pointed out that the cubic phase gate is not the most suitable for non-Clifford operations on GKP qubits. In this work, we show that we can achieve linear optical implementation of non-Clifford operations on GKP qubit with high fidelity by applying the nonlinear feedforward originally developed for the cubic phase gate and using a GKP-encoded ancillary state. Our work shows the versatility of nonlinear feedforward technique important for optical implementation of the fault-tolerant continuous-variable quantum computation.

Non-Gaussian Quantum States and Where to Find Them

Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description. Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements. In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states. We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variable systems. We then use this framework in various ways to explore the structure of the state space. We explain how non-Gaussian states can be characterised not only through the negative values of their Wigner function, but also via other properties such as quantum non-Gaussianity and the related stellar rank. For multimode systems, we are naturally confronted with the question of how non-Gaussian properties behave with respect to quantum correlations. To answer this question, we first show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state. Then, we highlight that these measured modes must be correlated via specific quantum correlations to the remainder of the system to create quantum non-Gaussian or Wigner-negative states. On the other hand, non-Gaussian operations are also shown to enhance or even create quantum correlations. Finally, we will demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage. At the end of the Tutorial, we also provide an overview of several experimental realisations of non-Gaussian quantum states in quantum optics and beyond.

Universal hybrid quantum computing in trapped ions

Using discrete and continuous variable subsystems, hybrid approaches to quantum information could enable more quantum computational power for the same physical resources. Here, we propose a hybrid scheme that can be used to generate the necessary Gaussian and non-Gaussian operations for universal continuous variable quantum computing in trapped ions. This scheme utilizes two linear spin-motion interactions to generate a broad set of nonlinear effective spin-motion interactions including one- and two-mode squeezing, beam splitter, and trisqueezing operations in trapped ion systems. We discuss possible experimental implementations using laser-based and laser-free approaches.

Remote Generation of Magnon Schrödinger Cat State via Magnon-Photon Entanglement

The magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even or odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with the magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters, they are generated with both high fidelity and nonclassicality, as well as with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been discussed, where the lifetime of the created magnon cat states is expected to be t∼1 μs.

Performance Improvement of Atmospheric Continuous-Variable Quantum Key Distribution with Untrusted Source.

Atmospheric continuous-variable quantum key distribution (ACVQKD) has been proven to be secure theoretically with the assumption that the signal source is well protected by the sender so that it cannot be compromised. However, this assumption is quite unpractical in realistic quantum communication system. In this work, we investigate a practical situation in which the signal source is no longer protected by the legitimate parts, but is exposed to the untrusted atmospheric channel. We show that the performance of ACVQKD is reduced by removing the assumption, especially when putting the untrusted source at the middle of the channel. To improve the performance of the ACVQKD with the untrusted source, a non-Gaussian operation, called photon subtraction, is subsequently introduced. Numerical analysis shows that the performance of ACVQKD with an untrusted source can be improved by properly adopting the photon subtraction operation. Moreover, a special situation where the untrusted source is located in the middle of the atmospheric channel is also considered. Under direct reconciliation, we find that its performance can be significantly improved when the photon subtraction operation is manipulated by the sender.

Continuous variable measurement-device-independent quantum key distribution based on photon subtraction and optical amplifiers

Aiming at the problems of low secret key rate, short transmission distance and low detection efficiency of continuous-variable quantum key distribution protocol, we propose a measurement-device-independent continuous-variable quantum key distribution(MDI-CVQKD) protocol based on photon subtraction and noiseless linear amplifiers (NLA). The protocol uses non-Gaussian operation, in particular, photon subtraction to improve the entanglement between quantum states, and NLA is used to amplify quantum states to compensate for channel attenuation. In this paper, the principle of the protocol is analyzed theoretically, and the relationship between the secret key rate and the secure transmission distance is derived through the covariance matrix between quantum states. Simulation results show that the proposed protocol can not only improve the entanglement between quantum states, but also extend the transmission distance of key distribution and improve the performance of key distribution system.

Generating antibunching light by beam-splitting photon number resolved detection from the superbunching squeezed vacuum

Beam-splitting photon number resolved (PNR) detection is one of the typical non-Gaussian operations in quantum optics. In this paper, we show that, by such an operation, the antibunching light can be generated by performing the beam-splitting PNR measurements of the superbunching squeezed vacuum light to subtract the odd photons. This is because that the squeezed vacuum is superposed by the even-photon Fock states, while its odd-photons subtracted state is just superposed by the odd-photon Fock states and the superposed probability of the single-photon state is significantly high. Hopefully, beam-splitting PNR detection could also be used to implement other desired non-Gaussian operations for engineering various nonclassical light, as the PNR detectors have been well developed in recent years.

Trans-Media Continuous-Variable Quantum Key Distribution via Untrusted Entanglement Source

We propose a continuous-variable quantum key distribution (CVQKD) scheme based on the atmosphere-to-seawater channel. In particular, an untrusted entanglement source (two modes of the compressed vacuum state, TMSV) is deployed on the surface of the seawater, each mode of TMSV is sent to one of the two legitimate parts, respectively. In this way, we can establish a trans-media CVQKD link between the atmosphere and the underwater. Meanwhile, a suitable non-Gaussian operation, namely photon subtraction, is introduced to enhance the performance of the trans-media CVQKD scheme. Security analysis shows that the proposed scheme can establish a trans-media quantum communication system on the atmosphere-to-seawater channel. Moreover, the maximum transmission distance can be further extended by using proper photon subtraction operation. Our scheme provides a guidance for applying CVQKD to trans-media channels.

Nonlinear Squeezing for Measurement-Based Non-Gaussian Operations in Time Domain

Quantum non-Gaussian gate is a missing piece to the realization of continuous-variable universal quantum operations in the optical system. In a measurement-based implementation of the cubic phase gate, a lowest-order non-Gaussian gate, non-Gaussian ancillary states that has a property we call nonlinear squeezing are required. This property, however, has never been experimentally verified. In this paper, we generate a superposition between a vacuum state and a single photon state whose nonlinear squeezing are maximized by the optimization of the superposition coefficients. The nonlinear squeezing is observed via real-time quadrature measurements, meaning that the generated states are compatible with the real-time feedforward and are suitable as the ancillary states for the cubic phase gate in time domain. Moreover, by increasing the number of the photons, it is expected that nonlinear squeezing can be further improved. The idea presented here can be readily extended to the higher-order phase gates [P. Marek et al., Phys. Rev. A 97, 022329 (2018)]. As such, this work presents an important step to extend the CV quantum information processing from Gaussian regime to non-Gaussian regime.

Continuous-variable quantum key distribution based on photon addition operation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11664017 and 11964013) and the Training Program for Academic and Technical Leaders of Major Disciplines in Jiangxi Province, China (Grant No. 20204BCJL22053).

It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution (CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source. It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.

Performance improvement of unidimensional continuous-variable quantum key distribution using zero-photon quantum catalysis

Compared with symmetric Gaussian-modulated coherent state protocol, the unidimensional continuous-variable quantum key distribution (UCVQKD) only modulates one of the quadratures in phase space of coherent state, thereby simplifying its implementation. Although UCVQKD does reduce the system’s complexity, its performance is reduced. In this work, we suggest an improved approach for UCVQKD using zero-photon quantum catalysis (ZPQC) technology. By taking advantage of this non-Gaussian operation, both secret key rate and maximal transmission distance of UCVQKD can be enhanced. Moreover, compared with another well-studied non-Gaussian operation, i.e., photon subtraction, ZPQC has higher success possibility, so that it would be beneficial for improving the amount of information acquired by legitimate users. Numerical simulation shows that the performance of UCVQKD can be improved by properly applying ZPQC. In particular, we find out that the performance of ZPQC-based UCVQKD outperforms that of photon subtraction-based UCVQKD, thereby providing an alternative way to better improve UCVQKD system. Furthermore, by taking finite-size effect into account, we derive more practical secure bound of ZPQC-based UCVQKD.

Enhanced Uplink Quantum Communication With Satellites via Downlink Channels

In developing the global Quantum Internet, quantum communication with low-Earth-orbit satellites will play a pivotal role. Such communication will need to be two way: effective not only in the satellite-to-ground (downlink) channel but also in the ground-to-satellite channel (uplink). Given that losses on this latter channel are significantly larger relative to the former, techniques that can exploit the superior downlink to enhance quantum communication in the uplink should be explored. In this work we do just that - exploring how continuous variable entanglement in the form of two-mode squeezed vacuum (TMSV) states can be used to significantly enhance the fidelity of ground-to-satellite quantum-state transfer relative to direct uplink-transfer. More specifically, through detailed phase-screen simulations of beam evolution through turbulent atmospheres in both the downlink and uplink channels, we demonstrate how a TMSV teleportation channel created by the satellite can be used to dramatically improve the fidelity of uplink coherent-state transfer relative to direct transfer. We then show how this, in turn, leads to the uplink-transmission of a higher alphabet of coherent states. Additionally, we show how non-Gaussian operations acting on the received component of the TMSV state at the ground station can lead to even further enhancement. Since TMSV states can be readily produced in situ on a satellite platform and form a reliable teleportation channel for most quantum states, our work suggests future satellites forming part of the emerging Quantum Internet should be designed with uplink-communication via TMSV teleportation in mind.

Enhancing quantum entanglement of the two-mode squeezed vacuum state via multiphoton catalysis

Multiphoton catalysis is a non-Gaussian operation which has aroused interest recently in quantum information processing. There are two schemes of multiphoton catalysis in the current literature: one uses a beam splitter, while the other uses an optical parametric amplifier. We derive the catalysis operator in the Fock basis for each scheme and find a close relationship between them. We propose to enhance quantum entanglement of the two-mode squeezed vacuum state by performing two-mode multiphoton catalysis independently using two beam splitters. We calculate the optimal entanglement, which is maximized over two independent transmissivities, for the catalyzed states with various pairs of catalysis photon numbers, and find that in each case entanglement is enhanced only when the squeezing parameter is below a certain threshold. We also find that the optimal entanglement is nonzero in the limit of low squeezing, and deduce the analytical forms of the limiting catalyzed state and its entanglement in each case from numerical coefficients.

Enhancing the Unidimensional Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction

Unidimensional continuous-variable quantum key distribution (CV-QKD) protocol with Gaussian modulation is simpler in implementation and lower in costs than its two-dimensional counterpart, but its secure transmission distance is not as far as the latter. In this paper, we give a solution that using the photon subtraction, which is one of non-Gaussian operations, to improve the performance of the unidimensional CV-QKD protocol. Security analysis and numerical simulation indicate that the photon subtraction operation can significantly improve the secure transmission distance of the unidimensional CV-QKD protocol.