Continuous-variable Quantum Information Research Articles

Quantum squeezing in a nonlinear mechanical oscillator

Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.

Generation of stationary entanglement and quantum discord in an optomechanical system through three-level atoms

In this paper, we investigate the stationary entanglement and quantum discord between the cavity and mechanical oscillator mode of an optomechanical system whose cavity contains three-level atoms. We examine how sharing entanglement and correlations would be affected by increasing the level of atoms injected into the cavity. In particular, using the appropriate preference of injected atoms to the cavity and optical cavity detuning, we found the impact of atoms and couplings on the degree of steady-state entanglement and quantum discord. Consequently, the stationary entanglement and quantum discord together rise to a certain range of normalized detuning and atom injection levels. Furthermore, both entanglement and Gaussian quantum discord are enhanced when three-level atoms are present, and the maximum entanglement manifests closest to the ringing case. Moreover, we are aware that the system’s physical parameters affect the generation of stationary entanglement and quantum correlation. Therefore, these results may provide a platform for a valuable asset in the practical realization of continuous variable entanglement and quantum information processing.

Deterministic generation of highly squeezed GKP states in ultracold atoms

We demonstrate a method for encoding Gottesman–Kitaev–Preskill (GKP) error-correcting qubits with single ultracold atoms trapped in individual sites of a deep optical lattice. Using quantum optimal control protocols, we demonstrate the generation of GKP qubit states with 10 dB squeezing, which is the current minimum allowable squeezing level for use in surface code error correction. States are encoded in the vibrational levels of the individual lattice sites and generated via phase modulation of the lattice potential. Finally, we provide a feasible experimental protocol for the realization of these states. Our protocol opens up possibilities for generating large arrays of atomic GKP states for continuous-variable quantum information.

Efficient bosonic nonlinear phase gates

Continuous-variable (CV) quantum information processing harnesses versatile experimental tools that leverage the power of infinite-dimensional oscillators controlled by a single qubit. Increasingly available elementary Rabi gates have been proposed as a resource for implementing universal CV gates, but the requirement of many weak, non-commuting gates is a bottleneck in scaling up such an approach. In this study, we propose a resource-efficient technique using Fourier expansion to implement arbitrary non-linear phase gates in a single oscillator. This method reduces the number of sequentially required gates exponentially. These gates represented by cubic, quartic, and other arbitrary nonlinear potentials have applications in CV quantum information processing with infinite-dimensional oscillators controlled by a single qubit. Our method outperforms previous approaches and enables the experimental realization of a wide range of applications, including the development of bosonic quantum sensors, simulations, and computation using trapped ions and superconducting circuits.

Continuous Variable Quantum Teleportation in a Dissipative Environment: Comparison of Non‐Gaussian Operations Before and After Noisy Channel

AbstractThis article explores the relative advantages in continuous‐variable quantum teleportation when non‐Gaussian operations, namely, photon subtraction, addition, and catalysis, are performed before and after interaction with a noisy channel. The resource state for teleporting unknown coherent and squeezed vacuum states is generated using two distinct strategies: i) Implementation of non‐Gaussian operations on two mode squeezed vacuum (TMSV) state before interaction with a noisy channel, ii) Implementation of non‐Gaussian operations after interaction of TMSV state with a noisy channel. The results show that non‐Gaussian operations can enhance teleportation fidelity in a dissipative environment. However, the most advantageous non‐Gaussian operation and appropriate strategy depend on the state and channel parameters. The results suggest that employing such strategies can be advantageous in other non‐Gaussian continuous variable quantum information (QIP) processing tasks in a dissipative environment.

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Entanglement dynamics via periodic modulations in an optomechanical system with embedded double quantum dots

In our theoretical study, we explore the dynamic behavior and entanglement properties of a hybrid optomechanical system containing double quantum dots (QDs). The system is driven by a laser with amplitude modulation and we consider the modulation of the resonance frequency of the two QDs. Through the application of modulation techniques, we can achieve the targeted mean field value and effectively control the entanglement between various degrees of freedom. This innovative approach shows great potential for the development of efficient quantum memories suitable for continuous variable quantum information processing.

Relative entropy via distribution of observables

We obtain formulas for Petz–Rényi and Umegaki relative entropy from the idea of distribution of a positive self-adjoint operator. Classical results on Rényi and Kullback–Leibler divergences are applied to obtain new results and new proofs for some known results about Petz–Rényi and Umegaki relative entropy. Most important among these, is a necessary and sufficient condition for the finiteness of the Petz–Rényi [Formula: see text]-relative entropy. All of the results presented here are valid in both finite and infinite dimensions. In particular, these results are valid for states in Fock spaces and thus are applicable to continuous variable quantum information theory.

Quantum correlation in a nano-electro-optomechanical system enhanced by an optical parametric amplifier and Coulomb-type interaction

In this paper, we investigated the quantum correlation of nano-electro-optomechanical system enhanced by an optical parametric amplifier (OPA) and Coulomb-type interaction. In particular, we consider a hybrid system consisting of a cavity and two charged mechanical oscillators with an OPA, where the optical cavity mode is coupled with a charged mechanical oscillator via radiation pressure, and the two charged mechanical oscillators are coupled through a Coulomb interaction. We use logarithmic negativity to quantify quantum entanglement, and quantum discord to measure the quantumness correlation between the two mechanical oscillators. We characterize quantum steering using the steerability between the two mechanical oscillators. Our results show that the presence of OPA and strong Coulomb coupling enhances the quantum correlations between the two mechanical oscillators. In addition, Coulomb interactions are more prominent in quantum correlations. Besides, in the presence of OPA, the maximum amount of quantum entanglement, quantum steering, and quantum discord were achieved between the two mechanical oscillators is greater than in the absence of OPA. Moreover, a proper phase choice of the optical field driving the OPA enhances quantum correlations under suitable conditions. We obtain quantum entanglement confines quantum steering and quantum discord beyond entanglement. Furthermore, quantum entanglement, quantum steering, and quantum discord decrease rapidly with increasing temperature as a result of decoherence. In addition, quantum discord persists at higher temperature values, although the quantum entanglement between the systems also vanishes completely. Our proposed scheme enhances quantum correlation and proves robust against fluctuations in the bath environment. We believe that the present scheme of quantum correlation provides a promising platform for the realization of continuous variable quantum information processing.

Bipartite and tripartite continuous variable entanglement in a circular array of coupled optical waveguides

Integrated optical systems have evolved into suitable platforms in the field of photonic quantum technologies. New technologies open up new possibilities for multimode quantum operations. Here we study how circularly coupled waveguide arrays generate bipartite and tripartite continuous-variable (CV) entanglement. We focus on the single-mode squeezed state as input to the circular array of the waveguide system. Our findings suggest that the circularly coupled arrays can be used to generate entangled sources in CV quantum technologies. So the generation of entanglement makes the circular arrays more critical for further investigation and in the applications of photonic CV quantum-information processing.

Two-mode squeezing over deployed fiber coexisting with conventional communications.

Squeezed light is a crucial resource for continuous-variable (CV) quantum information science. Distributed multi-mode squeezing is critical for enabling CV quantum networks and distributed quantum sensing. To date, multi-mode squeezing measured by homodyne detection has been limited to single-room experiments without coexisting classical signals, i.e., on "dark" fiber. Here, after distribution through separate fiber spools (5 km), -0.9 ± 0.1-dB coexistent two-mode squeezing is measured. Moreover, after distribution through separate deployed campus fibers (about 250 m and 1.2 km), -0.5 ± 0.1-dB coexistent two-mode squeezing is measured. Prior to distribution, the squeezed modes are each frequency multiplexed with several classical signals-including the local oscillator and conventional network signals-demonstrating that the squeezed modes do not need dedicated dark fiber. After distribution, joint two-mode squeezing is measured and recorded for post-processing using triggered homodyne detection in separate locations. This demonstration enables future applications in quantum networks and quantum sensing that rely on distributed multi-mode squeezing.

Frequency-domain engineering of bright squeezed vacuum for continuous-variable quantum information.

Multimode bright squeezed vacuum is a non-classical state of light hosting a macroscopic photon number while offering promising capacity for encoding quantum information in its spectral degree of freedom. Here, we employ an accurate model for parametric down-conversion in the high-gain regime and use nonlinear holography to design quantum correlations of bright squeezed vacuum in the frequency domain. We propose the design of quantum correlations over two-dimensional lattice geometries that are all-optically controlled, paving the way toward continuous-variable cluster state generation on an ultrafast timescale. Specifically, we investigate the generation of a square cluster state in the frequency domain and calculate its covariance matrix and the quantum nullifier uncertainties, that exhibit squeezing below the vacuum noise level.

Schrödinger cat states of a 16-microgram mechanical oscillator

According to quantum mechanics, a physical system can be in any linear superposition of its possible states. Although the validity of this principle is routinely validated for microscopic systems, it is still unclear why we do not observe macroscopic objects to be in superpositions of states that can be distinguished by some classical property. Here we demonstrate the preparation of a mechanical resonator in Schrödinger cat states of motion, where the ∼1017 constituent atoms are in a superposition of two opposite-phase oscillations. We control the size and phase of the superpositions and investigate their decoherence dynamics. Our results offer the possibility of exploring the boundary between the quantum and classical worlds and may find applications in continuous-variable quantum information processing and metrology with mechanical resonators.

Non-Gaussian quantum state generation by multi-photon subtraction at the telecommunication wavelength.

In the field of continuous-variable quantum information processing, non-Gaussian states with negative values of the Wigner function are crucial for the development of a fault-tolerant universal quantum computer. While several non-Gaussian states have been generated experimentally, none have been created using ultrashort optical wave packets, which are necessary for high-speed quantum computation, in the telecommunication wavelength band where mature optical communication technology is available. In this paper, we present the generation of non-Gaussian states on wave packets with a short 8-ps duration in the 1545.32 nm telecommunication wavelength band using photon subtraction up to three photons. We used a low-loss, quasi-single spatial mode waveguide optical parametric amplifier, a superconducting transition edge sensor, and a phase-locked pulsed homodyne measurement system to observe negative values of the Wigner function without loss correction up to three-photon subtraction. These results can be extended to the generation of more complicated non-Gaussian states and are a key technology in the pursuit of high-speed optical quantum computation.

Toward a multi-core ultra-fast optical quantum processor: 43-GHz bandwidth real-time amplitude measurement of 5-dB squeezed light using modularized optical parametric amplifier with 5G technology

Continuous-variable optical quantum information processing, where quantum information is encoded in a traveling wave of light called a flying qubit, is a candidate for a practical quantum computer with high clock frequencies. Homodyne detectors for quadrature-phase amplitude measurements have been the major factor limiting the clock frequency. Here, we developed a real-time amplitude measurement method using a modular optical parametric amplifier (OPA) and a broadband balanced photodiode that is commercially used for coherent wavelength-division multiplexing telecommunication of the fifth-generation mobile communication systems (5G). The OPA amplifies one quadrature-phase component of the quantum-level signal to a loss-tolerant macroscopic level and suppresses the loss after the OPA from 92.4% to only 0.4%. This method was applied to a broadband squeezed vacuum measurement with a center wavelength of 1545.32 nm. In the time-domain measurement, the squeezing level of 5.1 ± 0.1 dB without loss correction was obtained by a real-time oscilloscope with a sampling rate of 160 GHz and an analog bandwidth of 63 GHz. The frequency-domain analysis also shows that a squeezing level of 5.2 ± 0.5 dB is obtained from DC to 43 GHz, which is limited by the balanced detector. This indicates that the proposed method can be easily broadened by using a broader bandwidth measurement instrument. By applying this method, not only can optical quantum computers with high clock frequencies be realized but also multi-core systems can be realized.

Ultra-Large-Scale Deterministic Entanglement Containing 2×20 400 Optical Modes Based on Time-Delayed Quantum Interferometer.

Quantum entanglement is an indispensable resource for implementing quantum information processing. The scale of quantum entanglement directly determines its quantum information processing capability. Therefore, it is of great importance to generate ultra-large-scale (ULS) quantum entanglement for the development of quantum information science and technology. Many efforts have been made to increase the scale of quantum entanglement. Recently, time-domain multiplexing has been introduced into continuous-variable (CV) quantum systems to greatly enlarge the scale of quantum entanglement. In this Letter, based on a time-delayed quantum interferometer, we theoretically propose and experimentally demonstrate a scheme for generating an ULS CV deterministic entanglement containing 2×20 400 optical modes. In addition, such ULS entanglement contains 81 596 squeezed modes. Our results provide a new platform for implementing ULS CV quantum information processing.

Entanglement of mechanical modes in a doubly resonant optomechanical cavity of a correlated emission laser

We explore the extent of the induced entanglement of the mechanical modes that can be attributed to the transfer of coherence from two-mode cavity radiation in a doubly resonant optomechanical cavity. It is expected that this scheme can support a generation of mechanical oscillations with a robust degree of entanglement combined with significant controllability. The entanglement is found to be sensitive to the specific choices of the frequencies of the bichromatic drive laser. It also turns out that the degree of entanglement would be enhanced with increasing rates of injection of the atoms but with decreasing initial lengths of a doubly resonant cavity and atomic decay rates. In addition, the entanglement is found to behave qualitatively in the same way for the measures of entanglement we have applied. Since the scheme we considered can possibly be implemented with current technology and allows the quantum features of cavity radiation to be accessible for application, we anticipate that it can be utilized in the realization of continuous-variable quantum information processing.

The Synthetic Hilbert Space of Laser-Driven Free-Electrons

Recent advances in laser interactions with coherent free electrons have enabled to shape the electron's quantum state. Each electron becomes a superposition of energy levels on an infinite quantized ladder, shown to contain up to thousands of energy levels. We propose to utilize the quantum nature of such laser-driven free electrons as a "synthetic Hilbert space" in which we construct and control qudits (quantum digits). The question that motivates our work is what qudit states can be accessed using electron-laser interactions, and whether it is possible to implement any arbitrary quantum gate. We find how to encode and manipulate free-electron qudit states, focusing on dimensions which are powers of 2, where the qudit represents multiple qubits implemented on the same single electron – algebraically separated, but physically joined. As an example, we prove the possibility to fully control a 4-dimenisonal qudit, and reveal the steps required for full control over any arbitrary dimension. Our work enriches the range of applications of free electrons in microscopy and spectroscopy, offering a new platform for continuous-variable quantum information.

Stabilization improvement of the squeezed optical fields using a high signal-to-noise ratio bootstrap photodetector.

High-precision cavity locking is crucial for squeezing optical fields. Here, a bootstrapped low-noise photodetector is utilized in the generation process of the squeezed state of light. This process is based on a combination of a modified trans-impedance amplifier (TIA) circuit and a two-stage bootstrap amplifier circuit. This not only achieves high-precision and long-term stable locking of the optical cavity, but it also improves the degree to which the light field is squeezed. The experiment results show that the detector has a high signal-to-noise ratio (SNR) of 26.7 dB at the analysis frequency of 3 MHz when measuring the shot noise with an injection optical power of 800 µW, and the equivalent optical power noise level is lower than 2.4 pW/Hz in the frequency range of 1-30 MHz. Moreover, the squeezing degree of the quadrature amplitude squeezed state light field can be improved by more than 34.9% when the detector is used for optical cavity locking. The photodetector is useful in continuous variable (CV) quantum information research.

Multiparty quantum anonymous voting with discrete modulated coherent states and an optical frequency comb.

A key challenge for quantum information science is to realize large-scale, precisely controllable, practical systems for multiparty secure communications. Recently, Guidry etal. [Nat. Photonics16, 52 (2022)10.1038/s41566-021-00901-z] have investigated the quantum optics of a Kerr-based optical frequency comb (OFC), which lays out the way for OFC acting as a quantum resource to realize a low-cost and stable multiparty continuous-variable quantum information processing. In this work, we propose a distributed quantum anonymous voting (DQAV) protocol based on discrete modulated coherent states, in which a Kerr-based OFC serves as the resource to generate multi-frequency quantum signals for multiparty voting. We consider both the single-selection and multiple-selection ballot scenarios, and design the phase compensation method for the OFC-based protocol. Voting security is ensured by the basic laws of quantum mechanics, while voting anonymity is achieved by the random assignment of different frequency sources and the homogeneity of the quantum operations taken on the same voting choice. Numerical analysis calculates the secure voting distance over the thermal-lossy channel, showing the advancement of the proposed protocol under multiparty and multivalued voting tasks.