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On mathematical and physical approaches to constructing a quantum cluster state in continuous variables, or is it possible to construct a cluster from different modes?

We consider the problems of constructing a cluster state from a set of orthogonal modes. It is shown that the commonly used unitary transformation is not reduced in this case to a set of standard operations of linear optics performed over fields in a squeezed state, but should be supplemented by a more complicated operation of a noise-free transformation of the quantum signal profile. At the same time, if it is possible to form a cluster whose node amplitudes have different time profiles, this property does not interfere with the performance of calculations on the cluster. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum key distribution and beyond: introduction

This feature issue presents a collection of recent theoretical and experimental developments in the field of quantum key distribution (QKD) and its extension to other quantum cryptography protocols and devices. It encompasses work on a variety of QKD protocols, including continuous-variable, measurement-device independent, and twin-field QKD, as well as other newly proposed protocols, in platforms ranging from optical fiber through to wireless indoor and satellite links. It covers examples of hacking strategies and their countermeasures as well as applications of machine learning techniques in designing quantum networks. It also includes new developments in efficient superconducting photon-number resolving detectors as well as fast quantum random number generators. Distinctively, this feature issue demonstrates how different expertise in science and engineering can come together to produce an outcome that hopefully takes us one step closer to the wide-scale deployment of quantum communications technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Error-Detectable Bosonic Entangling Gates with a Noisy Ancilla

Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between encoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a “Bloch sphere” of bosonic operators, we construct ZZ L ⁡(θ) and exponential-swap(θ) gates for the binomial, four-legged cat, dual-rail, and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beam splitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the 0.01% level with today’s hardware, limited only by second-order hardware errors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Variable Bragg x-ray beam splitters

Beam splitters are utilized in a variety of advanced x-ray instruments and are essential for extending quantum optics techniques to x rays. A new fabrication method has produced thinned Bragg diffracting silicon devices with variable reflectivity and transmission coefficients and negligible absorption losses. Diffraction measurements confirm that silicon continues to exhibit perfect crystal diffraction even for thicknesses below two microns. Devices are machined from standard wafers, with the thinned regions contained within the robust frame of an unperturbed crystal for ease of handling.

Powers, L. T. (ORCID:000900047481248X)↗

Graph states of atomic ensembles engineered by photon-mediated entanglement

Abstract Graph states are a broad family of entangled quantum states, each defined by a graph composed of edges representing the correlations between subsystems. Such states constitute versatile resources for quantum computation and quantum-enhanced measurement. Their generation and engineering require a high level of control over entanglement. Here we report on the generation of continuous-variable graph states of atomic spin ensembles, which form the nodes of the graph. We program the entanglement structure encoded in the graph edges by combining global photon-mediated interactions in an optical cavity with local spin rotations. By tuning the entanglement between two subsystems, we either localize correlations within each subsystem or enable Einstein–Podolsky–Rosen steering—a strong form of entanglement that enables the extraction of precise information from one subsystem through measurements on the other. We further engineer a four-mode square graph state, highlighting the flexibility of our approach. Our method is scalable to larger and more complex graphs, laying groundwork for measurement-based quantum computation and advanced protocols in quantum metrology.

74 ATOMIC AND MOLECULAR PHYSICS↗

Hybrid Entanglement Distribution between Remote Microwave Quantum Computers Empowered by Machine Learning

Superconducting microwave circuits with Josephson junctions, the major platform for quantum computing, can only reach the full capability when connected. This requires an efficient protocol to distribute microwave entanglement. While quantum computers typically use discrete-variable (DV) methods for information encoding, the entire continuous-variable (CV) degree of freedom in electromagnetic fields must be utilized to achieve the highest entanglement distribution rate. Here, we propose a hybrid protocol to resolve the incompatibility between DV microwave quantum computers and CV quantum communications. CV microwave entanglement is distributed using optical swapping of optical-microwave entanglement pairs. To interface with DV microwave quantum computers, we further design a hybrid circuit to simultaneously convert and distill high-quality DV entanglement from noisy CV entanglement. The hybrid circuit is trained with machine-learning algorithms, ensuring high entanglement fidelity and generation rate. In conclusion, our work not only provides a practical method to realize efficient quantum links for superconducting microwave quantum computers, but also opens avenues to bridge the gap between DV and CV quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Boson sampling with Gaussian input states: Toward efficient scaling and certification

A universal quantum computer of large scale is not available yet, however, intermediate models of quantum computation would still permit demonstrations of a quantum computational advantage over classical computing and could challenge the Extended Church-Turing Thesis. One of these models based on single photons interacting via linear optics is called Boson Sampling. Although Boson Sampling was demonstrated and the threshold to claim quantum computational advantage was achieved, the question of how to scale up Boson Sampling experiments remains. To make progress with this problem, here we present a practically achievable pathway to scale Boson Sampling experiments by combining continuous-variable quantum information and temporal encoding. Here, we propose the combination of switchable dual-homodyne and single-photon detections, the temporal loop technique, and scattershot-based Boson Sampling. We detail the required assumptions for concluding computational hardness for this configuration. Furthermore, this particular combination of techniques moves towards an efficient scaling and certification of Boson Sampling, all in a single experimental setup.

79 ASTRONOMY AND ASTROPHYSICS↗

Passive continuous variable quantum key distribution scheme using a thermal source

A passive continuous variable quantum key distribution scheme, where Alice splits the output of a thermal source into two beams, measures one locally and transmits the other mode to Bob after applying attenuation. A secure key can be established based on measurements of the two beams without the use of a random number generator or an optical modulator.

Qi, Bing↗

Quantum key distribution using a thermal source

A passive continuous-variable quantum key distribution scheme, where Alice splits the output of a thermal source into two spatial modes, measures one locally and transmits the other mode to Bob after applying attenuation. A secure key can be established based on measurements of the two modes without the use of a random number generator or an optical modulator.

97 MATHEMATICS AND COMPUTING↗

Quantum secret sharing using weak coherent states

Secret sharing allows a trusted party (the dealer) to distribute a secret to a group of players, who can only access the secret cooperatively. Quantum secret sharing (QSS) protocols could provide unconditional security based on fundamental laws in physics. While the general security proof has been established recently in an entanglement-based QSS protocol, the tolerable channel loss is unfortunately rather small. Here we propose a continuous variable QSS protocol using conventional laser sources and homodyne detectors. In this protocol, a Gaussian-modulated coherent state (GMCS) prepared by one player passes through the secure stations of the other players sequentially, and each of the other players injects a locally prepared, independent GMCS into the circulating optical mode. Finally, the dealer measures both the amplitude and the phase quadratures of the receiving optical mode using double homodyne detectors. Collectively, the players can use their encoded random numbers to estimate the measurement results of the dealer and further generate a shared key. We prove the unconditional security of the proposed protocol against both eavesdroppers and dishonest players in the presence of high channel loss, and discuss various practical issues.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Polarization-agnostic continuous-variable quantum key distribution

Here, we introduce a polarization-agnostic method for Gaussian-modulated coherent-state (GCMS) continuous-variable quantum key distribution (CVQKD). Due to the random and continuous nature of the GCMS protocol, Alice, the transmitter, can encode two distinct quadratures in each of two orthogonal polarization modes, such that Bob, the receiver, measures valid GCMS quadratures in a single polarization mode even when polarization changes occur during transmission. This method does not require polarization correction in the optical domain, does not require monitoring both polarization modes, reduces loss by eliminating optical components, and avoids the noise injected by polarization correction algorithms.

Williams, Brian P. [Oak Ridge National Laboratory ↗

Heisenberg-scaling measurement protocol for analytic functions with quantum sensor networks

Here we generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean-squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and we conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Field test of continuous-variable quantum key distribution with a true local oscillator

A continuous-variable quantum key distribution (CV QKD) using a true local (located at the receiver) oscillator (LO) has been proposed to remove any possibility of side-channel attacks associated with transmission of the LO as well as reduce the cross-pulse contamination. Here we report an implementation of true LO-CV QKD using “off-the-shelf” components and conduct QKD experiments using the fiber optical network at Oak Ridge National Laboratory. A phase reference and quantum signal are time multiplexed and then wavelength division multiplexed with the classical communications that “coexist” with each other on a single optical network fiber. Importantly, this is the first demonstration of CV QKD with a receiver-based true LO over a deployed fiber network, a crucial step for its application in real-world situations.

97 MATHEMATICS AND COMPUTING↗

Heralded Multiplexed High-Efficiency Cascaded Source of Dual-Rail Entangled Photon Pairs Using Spontaneous Parametric Down-Conversion

Deterministic sources of high-fidelity entangled qubit pairs encoded in the dual-rail photonic basis, i.e., presence of a single photon in one of two orthogonal modes, are a key enabling technology of many applications of quantum information processing, including high-rate, high-fidelity quantum communications over long distances. The most popular and mature sources of such photonic entanglement, e.g., those that leverage spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing, generate an entangled (so-called continuous-variable) quantum state that contains contributions from high-order photon terms that lie outside the span of the dual-rail basis, which is detrimental to most applications. One often uses low pump power to mitigate the effects of those high-order terms. However, that reduces the pair generation rate, and the source becomes inherently probabilistic. We investigate a cascaded source that performs a linear-optical entanglement swap between two SPDC sources, to generate a heralded photonic entangled state that has a higher fidelity (to the ideal Bell state) compared to a free-running SPDC source. Furthermore, with the Bell swap providing a heralding trigger, we show how to build a multiplexed source, which despite reasonable switching losses and detector loss and noise, yields a fidelity versus success probability trade-off of a high-efficiency source of high-fidelity dual-rail photonic entanglement. We find, however, that there is a threshold of 1.5 dB of loss per switch, beyond which multiplexing hurts the fidelity versus success probability trade-off.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Concatenated dual displacement code for continuous-variable quantum error correction

The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.

quantum error correction↗

Microwave and Optical Entanglement for Quantum Transduction with Electro-Optomechanics

Quantum transduction refers to the coherent conversion between microwave and optical states, which can be achieved by quantum teleportation if given high-fidelity microwave-optical entanglement, namely entanglement-based quantum transduction. Reliable microwave-optical entanglement can be generated using various platforms. Here, in this paper we base the discussion on a piezo-optomechanical system and make the teleportation induced conversion scheme more concrete in the framework of quantum channel theory. By comparing the quantum capacity between the entanglement-based conversion channel and the traditional direct quantum transduction channel, we show that the entanglement-based scheme indeed admits a positive transduction rate when the direct quantum transduction has zero quantum capacity. Given two piezo-optomechanical systems, we also investigate the generation of microwave-microwave entanglement from entanglement swapping within continuous-variable and discrete-variable settings, showing the potentials of directly connecting microwave quantum processors by microwave-microwave quantum teleportation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗