Given a specific interacting quantum Hamiltonian in a general spatial dimension, can one access its entanglement properties, such as the entanglement entropy corresponding to the ground state wave function? Even though progress has been made in addressing this question for interacting bosons and quantum spins, as yet there exist no corresponding methods for interacting fermions. Here we show that the entanglement structure of interacting fermionic Hamiltonians has a particularly simple form—the interacting reduced density matrix can be written as a sum of operators that describe free fermions. This decomposition allows one to calculate the Renyi entropies for Hamiltonians which can be simulated via determinantal quantum Monte Carlo calculations, while employing the efficient techniques hitherto available only for free fermions. The method presented works for the ground state, as well as for the thermally averaged reduced density matrix.

We study a two-dimensional fermionic square lattice, which supports the existence of a two-dimensional Weyl semimetal, quantum anomalous Hall effect, and $2\pi$-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and $2\pi$-flux topological semimetal are protected by two distinct novel hidden symmetries, which both correspond to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry.

The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic network. We show that this probability exhibits universal properties. More precisely, the probability to be in the spectrum does not depend on the edge lengths (as long as they are generic) and is also invariant within some classes of graph topologies.

We perform a comprehensive set of experiments that characterize bosonic bunching of up to three photons in interferometers of up to 16 modes. Our experiments verify two rules that govern bosonic bunching. The first rule, obtained recently, predicts the average behavior of the bunching probability and is known as the bosonic birthday paradox. The second rule is new and establishes a $n!$-factor quantum enhancement for the probability that all $n$ bosons bunch in a single output mode, with respect to the case of distinguishable bosons. In addition to its fundamental importance in phenomena such as Bose-Einstein condensation, bosonic bunching can be exploited in applications such as linear optical quantum computing and quantum-enhanced metrology.

The time-dependent work probability distribution function $P(W)$ is investigated analytically for a diffusing particle trapped by an anisotropic harmonic potential and driven by a nonconservative drift force in two dimensions. We find that the exponential tail shape of $P(W)$ characterizing rare-event probabilities undergoes a sequence of dynamic transitions in time. These remarkable locking-unlocking type transitions result from an intricate interplay between a rotational mode induced by the nonconservative force and an anisotropic decaying mode due to the conservative attractive force. We expect that most of the high-dimensional dynamical systems should exhibit similar multiple dynamic transitions.

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained; namely, the specific heat is linearly proportional to temperature, whereas the susceptibility is independent of temperature. In contrast to the phenomenological Tomonaga-Luttinger liquid parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two, and three dimensions.

Several vulnerabilities of single-photon detectors have recently been exploited to compromise the security of quantum-key-distribution (QKD) systems. In this Letter, we report the first proof-of-principle implementation of a new quantum-key-distribution protocol that is immune to any such attack. More precisely, we demonstrated this new approach to QKD in the laboratory over more than 80 km of spooled fiber, as well as across different locations within the city of Calgary. The robustness of our fiber-based implementation, together with the enhanced level of security offered by the protocol, confirms QKD as a realistic technology for safeguarding secrets in transmission. Furthermore, our demonstration establishes the feasibility of controlled two-photon interference in a real-world environment and thereby removes a remaining obstacle to realizing future applications of quantum communication, such as quantum repeaters and, more generally, quantum networks.

Quantum key distribution is proven to offer unconditional security in communication between two remote users with ideal source and detection. Unfortunately, ideal devices never exist in practice and device imperfections have become the targets of various attacks. By developing up-conversion single-photon detectors with high efficiency and low noise, we faithfully demonstrate the measurement-device-independent quantum-key-distribution protocol, which is immune to all hacking strategies on detection. Meanwhile, we employ the decoy-state method to defend attacks on a nonideal source. By assuming a trusted source scenario, our practical system, which generates more than a 25 kbit secure key over a 50 km fiber link, serves as a stepping stone in the quest for unconditionally secure communications with realistic devices.

Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and the quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone. Furthermore, we introduce two experimental schemes, including the spin-resolved Bloch oscillation, to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.

We show that the information collected in the course of a generic quantum tomography experiment can be used for verifying experimenters’ assumptions about the state preparation and measurement. In particular, systematic errors, such as drifts and instabilities inherent in the tomography setup, can be identified without the need for any specific measurements designed to detect such problems. This is done by statistical analysis of available tomography data. As an example, we discuss the detection and characterization of unexpected changes in the signal state preparation during the tomography measurement and argue that minimal tomography schemes, such as symmetric informationally complete measurements, are more difficult to validate than overcomplete schemes. The method is illustrated with the analysis of experimental quantum homodyne tomography.

We propose to encode a quantum bit of information in a superposition of coherent states of an oscillator, with four different phases. Our encoding in a single cavity mode, together with a protection protocol, significantly reduces the error rate due to photon loss. This protection is ensured by an efficient quantum error correction scheme employing the nonlinearity provided by a single physical qubit coupled to the cavity. We describe in detail how to implement these operations in a circuit quantum electrodynamics system. This proposal directly addresses the task of building a hardware-efficient quantum memory and can lead to important shortcuts in quantum computing architectures.

We report on optical detection of a single photostable ${\mathrm{Ce}}^{3+}$ ion in an yttrium aluminium garnet (YAG) crystal and on its magneto-optical properties at room temperature. The spin quantum state of the emitting level of a single cerium ion in YAG can be initialized by a circularly polarized laser pulse. Coherent precession of the electron spin is read out by observing temporal behavior of circularly polarized fluorescence of the ion. This implies direct mapping of the spin quantum state of ${\mathrm{Ce}}^{3+}$ ion onto the polarization state of the emitted photon and represents the quantum interface between a single spin and a single photon.

The dilute Fermi gas at unitarity is scale invariant and its bulk viscosity vanishes. We compute, in the high temperature limit, the leading contribution to the bulk viscosity when the scattering length is not infinite. A measure of scale breaking is provided by the ratio $(P-2/3\mathcal{E})/P$, where $P$ is the pressure and $\mathcal{E}$ is the energy density. At high temperature this ratio scales as $z\lambda /a$, where $z$ is the fugacity, $\lambda$ is the thermal wavelength, and $a$ is the scattering length. We show that the bulk viscosity $\zeta$ scales as the second power of this parameter, $\zeta \sim (z\lambda /a{)}^2{\lambda }^{-3}$.

Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise. However, recent results seem to indicate that any small amount of realistic noise restricts the advantage of quantum strategies to an improvement by at most a multiplicative constant. Here, we identify a relevant scenario in which one can overcome this restriction and attain superclassical precision scaling even in the presence of uncorrelated noise. We show that precision can be significantly enhanced when the noise is concentrated along some spatial direction, while the Hamiltonian governing the evolution which depends on the parameter to be estimated can be engineered to point along a different direction. In the case of perpendicular orientation, we find superclassical scaling and identify a state which achieves the optimum.

We present a novel numerical approach to track the response of a quantum system to an external perturbation that is progressively switched on. The method is applied, within the framework of the density matrix renormalization group technique, to track current-carrying states of interacting fermions in one dimension and in the presence of an Aharonov-Bohm magnetic flux. This protocol allows us to access highly excited states. We also discuss the connection with the entanglement entropy of these excited states.

Generalizations of the microcanonical and canonical ensembles for paths of Markov processes have been proposed recently to describe the statistical properties of nonequilibrium systems driven in steady states. Here, we propose a theory of these ensembles that unifies and generalizes earlier results and show how it is fundamentally related to the large deviation properties of nonequilibrium systems. Using this theory, we provide conditions for the equivalence of nonequilibrium ensembles, generalizing those found for equilibrium systems, construct driven physical processes that generate these ensembles, and rederive in a simple way known and new product rules for their transition rates. A nonequilibrium diffusion model is used to illustrate these results.

We derive a set of algebraic equations, the so-called multipartite separability eigenvalue equations. Based on their solutions, we introduce a universal method for the construction of multipartite entanglement witnesses. We witness multipartite entanglement of ${10}^3$ coupled quantum oscillators, by solving our basic equations analytically. This clearly demonstrates the feasibility of our method for studying ultrahigh orders of multipartite entanglement in complex quantum systems.

We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that, despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.

Pumped heat electricity storage (PHES) has been recently suggested as a potential solution to the large-scale energy storage problem. PHES requires neither underground caverns as compressed air energy storage (CAES) nor kilometer-sized water reservoirs like pumped hydrostorage and can therefore be constructed anywhere in the world. However, since no large PHES system exists yet, and theoretical predictions are scarce, the efficiency of such systems is unknown. Here we formulate a simple thermodynamic model that predicts the efficiency of PHES as a function of the temperature of the thermal energy storage at maximum output power. The resulting equation is free of adjustable parameters and nearly as simple as the well-known Carnot formula. Our theory predicts that for storage temperatures above $400°\mathrm{C}$ PHES has a higher efficiency than existing CAES and that PHES can even compete with the efficiencies predicted for advanced-adiabatic CAES.

To compare the increasing number of optical frequency standards, highly stable optical signals have to be transferred over continental distances. We demonstrate optical-frequency transfer over a 1840-km underground optical fiber link using a single-span stabilization. The low inherent noise introduced by the fiber allows us to reach short term instabilities expressed as the modified Allan deviation of $2\times {10}^{-15}$ for a gate time $\tau$ of 1 s reaching $4\times {10}^{-19}$ in just 100 s. We find no systematic offset between the sent and transferred frequencies within the statistical uncertainty of about $3\times {10}^{-19}$. The spectral noise distribution of our fiber link at low Fourier frequencies leads to a ${\tau }^{-2}$ slope in the modified Allan deviation, which is also derived theoretically.