The interaction between the electric dipole moment of a trapped molecular ion and the phonon modes of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without ever optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a cotrapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that virtual phonon exchange can significantly boost the range of the intermolecular dipole-dipole interaction, allowing strong coupling between widely separated molecular ion qubits.

Identifying topological properties is a major challenge because, by definition, topological states do not have a local order parameter. While a generic solution to this challenge is not available yet, a broad class of topological states, namely, symmetry-protected topological (SPT) states, can be identified by distinctive degeneracies in their entanglement spectrum. Here, we propose and realize two complementary protocols to probe these degeneracies based on, respectively, symmetry-resolved entanglement entropies and measurement-based computational algorithms. The two protocols link quantum information processing to the classification of SPT phases of matter. They invoke the creation of a cluster state and are implemented on an IBM quantum computer. The experimental findings are compared to noisy simulations, allowing us to study the stability of topological states to perturbations and noise.

Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities ${\mathcal{F}}_{\rho }>0.98$ for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

Data structure has a dramatic impact on the properties of neural networks, yet its significance in the established theoretical frameworks is poorly understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine operating on data grouped into equally labeled subsets. At variance with the unstructured scenario, entropy is nonmonotonic in the size of the training set, and displays an additional critical point besides the storage capacity. Remarkably, the same behavior occurs in margin classifiers even with randomly labeled data, as is elucidated by identifying the synaptic volume encoding the transition. These findings reveal aspects of expressivity lying beyond the condensed description provided by the storage capacity, and they indicate the path towards more realistic bounds for the generalization error of neural networks.

Quantum networks play a major role in long-distance communication, quantum cryptography, clock synchronization, and distributed quantum computing. Generally, these protocols involve many independent sources sharing entanglement among distant parties that, upon measuring their systems, generate correlations across the network. The question of which correlations a given quantum network can give rise to remains almost uncharted. Here we show that constraints on the observable covariances, previously derived for the classical case, also hold for quantum networks. The network topology yields tests that can be cast as semidefinite programs, thus allowing for the efficient characterization of the correlations in a wide class of quantum networks, as well as systematic derivations of device-independent and experimentally testable witnesses. We obtain such semidefinite tests for fixed measurement settings, as well as parties that independently choose among collections of measurement settings. The applicability of the method is demonstrated for various networks, and compared with previous approaches.

We report the experimental realization of heralded distribution of single-photon path entanglement at telecommunication wavelengths in a repeater-like architecture. The entanglement is established upon detection of a single photon, originating from one of two spontaneous parametric down-conversion photon pair sources, after erasing the photon’s which-path information. In order to certify the entanglement, we use an entanglement witness which does not rely on postselection. We herald entanglement between two locations, separated by a total distance of 2 km of optical fiber, at a rate of 1.6 kHz. This work paves the way towards high-rate and practical quantum repeater architectures.

The entropy production rate associated with broken time-reversal symmetry provides an essential characterization of nanosystems out of equilibrium, from driven colloidal particles to molecular motors. Limited access to the dynamical states is generally expected to hinder the correct estimation of this observable. Here we show how memoryless jump processes can be coarse grained, exactly preserving its average and fluctuations at stationarity. This supports univocal applicability of fluctuation theorems for entropy and allows inference of the genuine thermodynamics together with inaccessible process details.

We experimentally demonstrate that electrically neutral particles, neutrons, can be used to directly visualize the electrostatic field inside a target volume that can be physically isolated or occupied. Electric field images are obtained using a spin-polarized neutron beam with a recently developed polarimetry method for polychromatic beams that permits detection of a small angular change in spin orientation. This Letter may enable a new diagnostic technique sensitive to the structure of electric potential, electric polarization, charge distribution, and dielectric constant by imaging spatially dependent electric fields in objects that cannot be accessed by other probes.

We introduce the resource quantifier of weight of resource for convex quantum resource theories of states and measurements with arbitrary resources. We show that it captures the advantage that a resourceful state (measurement) offers over all possible free states (measurements) in the operational task of exclusion of subchannels (states). Furthermore, we introduce information-theoretic quantities related to exclusion for quantum channels and find a connection between the weight of resource of a measurement and the exclusion-type information of quantum-to-classical channels. Our results apply to the resource theory of entanglement in which the weight of resource is known as the best-separable approximation or Lewenstein-Sanpera decomposition introduced in 1998. Consequently, the results found here provide an operational interpretation to this 21-year-old entanglement quantifier.

A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion (or antidistinguishability) task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements, and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterization of the convex components and corresponding weights of such devices.

Ancilla systems are often indispensable to universal control of a nearly isolated quantum system. However, ancilla systems are typically more vulnerable to environmental noise, which limits the performance of such ancilla-assisted quantum control. To address this challenge of ancilla-induced decoherence, we propose a general framework that integrates quantum control and quantum error correction, so that we can achieve robust quantum gates resilient to ancilla noise. We introduce the path independence criterion for fault-tolerant quantum gates against ancilla errors. As an example, a path-independent gate is provided for superconducting circuits with a hardware-efficient design.

A general attenuator ${\mathrm{\Phi }}_{\lambda ,\sigma }$ is a bosonic quantum channel that acts by combining the input with a fixed environment state $\sigma$ in a beam splitter of transmissivity $\lambda$. If $\sigma$ is a thermal state, the resulting channel is a thermal attenuator, whose quantum capacity vanishes for $\lambda \le 1/2$. We study the quantum capacity of these objects for generic $\sigma$, proving a number of unexpected results. Most notably, we show that for any arbitrary value of $\lambda >0$ there exists a suitable single-mode state $\sigma (\lambda )$ such that the quantum capacity of ${\mathrm{\Phi }}_{\lambda ,\sigma (\lambda )}$ is larger than a universal constant $c>0$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity, provided that the environment state is appropriately controlled. We also find examples of states $\sigma$ such that the quantum capacity of ${\mathrm{\Phi }}_{\lambda ,\sigma }$ is not monotonic in $\lambda$. These findings may have implications for the study of communication lines running across integrated optical circuits, of which general attenuators provide natural models.

We consider the problem of local operations and classical communication (LOCC) discrimination between two bipartite pure states of fermionic systems. We show that, contrary to the case of quantum systems, for fermionic systems it is generally not possible to achieve the ideal state discrimination performances through LOCC measurements. On the other hand, we show that an ancillary system made of two fermionic modes in a maximally entangled state is a sufficient additional resource to attain the ideal performances via LOCC measurements. The stability of the ideal results is studied when the probability of preparation of the two states is perturbed, and a tight bound on the discrimination error is derived.

The NV-NMR spectrometer is a promising candidate for detection of NMR signals at the nanoscale. Field inhomogeneities, however, are a major source of noise that limits spectral resolution in state of the art NV-NMR experiments and constitutes a major bottleneck in the development of nanoscale NMR. Here we propose, a route in which this limitation could be circumvented in NV-NMR spectrometer experiments, by utilizing the nanometric scale and the quantumness of the detector.

We show that the inherently large interatomic interactions of a Bose-Einstein condensate (BEC) can enhance the sensitivity of a high precision cold-atom gravimeter beyond the shot-noise limit (SNL). Through detailed numerical simulation, we demonstrate that our scheme produces spin-squeezed states with variances up to 14 dB below the SNL, and that absolute gravimetry measurement sensitivities between two and five times below the SNL are achievable with BECs between ${10}^4$ and ${10}^6$ in atom number. Our scheme is robust to phase diffusion, imperfect atom counting, and shot-to-shot variations in atom number and laser intensity. Our proposal is immediately achievable in current laboratories, since it needs only a small modification to existing state-of-the-art experiments and does not require additional guiding potentials or optical cavities.

Motivated by recent progress in the experimental development of quantum simulators based on Rydberg atoms, we introduce and investigate the dynamics of a class of ($1+1$)-dimensional quantum cellular automata. These nonequilibrium many-body models, which are quantum generalizations of the Domany-Kinzel cellular automaton, possess two key features: they display stationary behavior and nonequilibrium phase transitions despite being isolated systems. Moreover, they permit the controlled introduction of local quantum correlations, which allows for the impact of quantumness on the dynamics and phase transition to be assessed. We show that projected entangled pair state tensor networks permit a natural and efficient representation of the cellular automaton. Here, the degree of quantumness and complexity of the dynamics is reflected in the difficulty of contracting the tensor network.

Despite the unquestionable empirical success of quantum theory, witnessed by the recent uprising of quantum technologies, the debate on how to reconcile the theory with the macroscopic classical world is still open. Spontaneous collapse models are one of the few testable solutions so far proposed. In particular, the continuous spontaneous localization (CSL) model has become subject of intense experimental research. Experiments looking for the universal force noise predicted by CSL in ultrasensitive mechanical resonators have recently set the strongest unambiguous bounds on CSL. Further improving these experiments by direct reduction of mechanical noise is technically challenging. Here, we implement a recently proposed alternative strategy that aims at enhancing the CSL noise by exploiting a multilayer test mass attached on a high quality factor microcantilever. The test mass is specifically designed to enhance the effect of CSL noise at the characteristic length $r_c={10}^{-7}\mathrm{m}$. The measurements are in good agreement with pure thermal motion for temperatures down to 100 mK. From the absence of excess noise, we infer a new bound on the collapse rate at the characteristic length $r_c={10}^{-7}\mathrm{m}$, which improves over previous mechanical experiments by more than 1 order of magnitude. Our results explicitly challenge a well-motivated region of the CSL parameter space proposed by Adler.