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In recent years, neural-network quantum states have emerged as powerful tools for the study of quantum many-body systems. Electronic structure calculations are one such canonical many-body problem that have attracted sustained research efforts spanning multiple decades, whilst only recently being attempted with neural-network quantum states. However, the complex non-local interactions and high sample complexity are substantial challenges that call for bespoke solutions. Here, we parameterize the electronic wavefunction with an autoregressive neural network that permits highly efficient and scalable sampling, whilst also embedding physical priors reflecting the structure of molecular systems without sacrificing expressibility. This allows us to perform electronic structure calculations on molecules with up to 30 spin orbitals—at least an order of magnitude more Slater determinants than previous applications of conventional neural-network quantum states—and we find that our ansatz can outperform the de facto gold-standard coupled-cluster methods even in the presence of strong quantum correlations. With a highly expressive neural network for which sampling is no longer a computational bottleneck, we conclude that the barriers to further scaling are not associated with the wavefunction ansatz itself, but rather are inherent to any variational Monte Carlo approach. To perform electronic structure calculations in quantum chemistry systems, methods are needed that are both accurate and scalable as the size of the molecule of interest increases. Barrett and colleagues employ an autoregressive neural-network ansatz that allows them to study larger molecules than previously attempted with neural-network quantum state approaches.

The ability to prepare arbitrary quantum states within a certain Hilbert space is the holy grail of quantum information technology. It is particularly important for light, as this is the only physical system that can communicate quantum information over long distances. We propose and experimentally verify a scheme to produce arbitrary single-mode states of a travelling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel. The measurement consists of bringing the idler field into interference with two ancilla coherent states, followed by two single-photon detectors, which, in coincidence, herald the preparation event. By varying the amplitudes and phases of the ancillae, we can prepare any arbitrary superposition of zero-, one- and two-photon states. Tailoring of arbitrary single-mode states of travelling light up to the two-photon level is proposed and demonstrated. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel.

Entanglement distillation, the purpose of which is to probabilistically increase the strength and purity of quantum entanglement, is a primary element of many quantum communication and computation protocols. It is particularly necessary in quantum repeaters in order to counter the degradation of entanglement that inevitably occurs due to losses in communication lines. Here, we distil the Einstein–Podolsky–Rosen state of light, the workhorse of continuous-variable entanglement, using noiseless amplification. The advantage of our technique is that it permits recovering a macroscopic level of entanglement, however low the initial entanglement or however high the loss may be. Experimentally, we recover the original entanglement level after one of the Einstein–Podolsky–Rosen modes has experienced a loss factor of 20. The level of entanglement in our distilled state is higher than that achievable by direct transmission of any state through a similar loss channel. This is a key step towards realizing practical continuous-variable quantum communication protocols. A protocol to recover states of optical continuous-variable entanglement is developed based on approximate heralded noiseless amplification. The degraded entanglement is completely recovered no matter how significant these losses are.

Schrodinger’s cat paradox embodies the open question of whether quantum effects can survive at macroscopic scales. A quantum optics experiment explores this question by creating entanglement between a microscopic and a macroscopic system. Schrödinger’s famous thought experiment 1 involves a (macroscopic) cat whose quantum state becomes entangled with that of a (microscopic) decaying nucleus. The creation of such micro–macro entanglement is being pursued in several fields, including atomic ensembles 2 , superconducting circuits 3 , electro-mechanical 4 and opto-mechanical 5 systems. Here we experimentally demonstrate the micro–macro entanglement of light. The macro system involves over a hundred million photons, whereas the micro system is at the single-photon level. We show that microscopic quantum fluctuations (in field quadrature measurements) on one side are correlated with macroscopic fluctuations (in the photon number statistics) on the other side. Further, we demonstrate entanglement by bringing the macroscopic state back to the single-photon level and performing full quantum state tomography of the final state. Although Schrödinger’s thought experiment was originally intended to convey the absurdity of applying quantum mechanics to macroscopic objects, this experiment and related ones suggest that it may apply on all scales.

Highly entangled quantum states, shared by remote parties, are vital for quantum communications and metrology. Particularly promising are the N00N states—entangled N -photon wavepackets delocalized between two different locations—which outperform coherent states in measurement sensitivity. However, these states are notoriously vulnerable to losses, making them difficult to both share them between remote locations and recombine in order to exploit interference effects. Here we address this challenge by utilizing the reverse Hong–Ou–Mandel effect to prepare a high-fidelity two-photon N00N state shared between two parties connected by a lossy optical medium. We measure the prepared state by two-mode homodyne tomography, thereby demonstrating that the enhanced phase sensitivity can be exploited without recombining the two parts of the N00N state. Finally, we demonstrate the application of our method to remotely prepare superpositions of coherent states, known as Schrödinger’s cat states. N00N states are promising for quantum communications and metrology, but are vulnerable to losses. Here the authors develop a technique for preparing high-fidelity two-photon N00N states in a loss-free fashion, and demonstrate enhanced phase sensitivity without requiring recombination.

Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude coherent states. We furthermore demonstrate the application of this state as a resource for the interfacing of quantum information between these encodings. In particular, we show teleportation of a polarization qubit onto a freely propagating continuous-variable qubit. Interfacing quantum information between discrete and continuous would allow exploiting the best of both worlds, but it has been shown only for single-rail encoding. Here, the authors extend this to the more practical dual-rail encoding, realizing teleportation between a polarization qubit and a CV qubit.

The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.

A widely tested approach to overcoming the diffraction limit in microscopy without disturbing the sample relies on substituting widefield sample illumination with a structured light beam. This gives rise to confocal, image scanning, and structured illumination microscopy methods. On the other hand, as shown recently by Tsang and others, subdiffractional resolution at the detection end of the microscope can be achieved by replacing the intensity measurement in the image plane with spatial mode demultiplexing. In this work, we study the combined action of Tsang’s method with image scanning. We experimentally demonstrate superior lateral resolution and enhanced image quality compared to either method alone. This result paves the way for integrating spatial demultiplexing into existing microscopes, contributing to further pushing the boundaries of optical resolution. Improving imaging resolution and quality by combining Tsang’s spatial mode demultiplexing with scanning a focused illumination beam over the sample.

We show that, under certain circumstances, an optical field in a two-mode squeezed vacuum (TMSV) state can propagate through a lossy atomic medium without degradation or evolution. Moreover, the losses give rise to that state when a different state is initially injected into the medium. Such a situation emerges in a Λ-type atomic system, in which both optical transitions are driven by strong laser fields that are two-photon resonant with the respective signal modes. Then the interactions of the two signal modes with the ground-state atomic coherence interfere destructively, thereby ensuring the preservation of the TMSV with a particular squeezing parameter. This mechanism permits unified interpretation of recent experimental results and predicts new phenomena.

We report a technique for experimental characterization of an M-mode quantum optical process, generalizing the single-mode coherent-state quantum-process tomography method [1, 2]. By measuring the effect of the process on multi-mode coherent states via balanced homodyne tomography, we obtain the process tensor in the Fock basis. This rank- tensor, which predicts the effect of the process on an arbitrary density matrix, is iteratively reconstructed directly from the experimental data via the maximum-likelihood method. We demonstrate the capabilities of our method using the example of a beam splitter, reconstructing its process tensor within the subspace spanned by the first three Fock states. In spite of using purely classical probe states, we recover quantum properties of this optical element, in particular the Hong-Ou-Mandel effect.