Biological systems are influenced by random processes at all scales, including molecular, demographic, and behavioral fluctuations, as well as by their interactions with a fluctuating environment. We previously established microbial closed ecosystems (CES) as model systems for studying the role of random events and the emergent statistical laws governing population dynamics. Here, we present long-term measurements of population dynamics using replicate digital holographic microscopes that maintain CES under precisely controlled external conditions while automatically measuring abundances of three microbial species via single-cell imaging. With this system, we measure spatiotemporal population dynamics in more than 60 replicate CES over periods of months. In contrast to previous studies, we observe strongly deterministic population dynamics in replicate systems. Furthermore, we show that previously discovered statistical structure in abundance fluctuations across replicate CES is driven by variation in external conditions, such as illumination. In particular, we confirm the existence of stable ecomodes governing the correlations in population abundances of three species. The observation of strongly deterministic dynamics, together with stable structure of correlations in response to external perturbations, points towards a possibility of simple macroscopic laws governing microbial systems despite numerous stochastic events present on microscopic levels.

In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain “anomalous” SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group $G$ is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group $H^4(G,\mathrm{U}(1))$, which also precisely labels the set of 3D SPT phases, with symmetry group $G$. An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [$\mathrm{U}(1{)}_2$] topological order with a reduced symmetry ${\mathbb{Z}}_2\times {\mathbb{Z}}_2\subset \mathrm{SO}(3)$, which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.

Cuprates and iron-based superconductors are two classes of unconventional high-$T_c$ superconductors based on $3d$ transition elements. Recently, two principles, the correspondence principle and the magnetic selective pairing rule, have emerged to unify their high-$T_c$ superconducting mechanisms. These principles strongly regulate electronic structures that can host high-$T_c$ superconductivity. Guided by these principles, here, we propose high-$T_c$ superconducting candidates that are formed by cation-anion trigonal bipyramidal complexes with a $d^7$ filling configuration on the cation ions. Their superconducting states are expected to be dominated by the $d_{xy}\pm i{d}_{x^2-y^2}$ pairing symmetry.

Work and quantum correlations are two fundamental resources in thermodynamics and quantum information theory. In this work, we study how to use correlations among quantum systems to optimally store work. We analyze this question for isolated quantum ensembles, where the work can be naturally divided into two contributions: a local contribution from each system and a global contribution originating from correlations among systems. We focus on the latter and consider quantum systems that are locally thermal, thus from which any extractable work can only come from correlations. We compute the maximum extractable work for general entangled states, separable states, and states with fixed entropy. Our results show that while entanglement gives an advantage for small quantum ensembles, this gain vanishes for a large number of systems.

We introduce a new continuous-variable quantum key distribution (CV-QKD) protocol, self-referenced CV-QKD, that eliminates the need for transmission of a high-power local oscillator between the communicating parties. In this protocol, each signal pulse is accompanied by a reference pulse (or a pair of twin reference pulses), used to align Alice’s and Bob’s measurement bases. The method of phase estimation and compensation based on the reference pulse measurement can be viewed as a quantum analog of intradyne detection used in classical coherent communication, which extracts the phase information from the modulated signal. We present a proof-of-principle, fiber-based experimental demonstration of the protocol and quantify the expected secret key rates by expressing them in terms of experimental parameters. Our analysis of the secret key rate fully takes into account the inherent uncertainty associated with the quantum nature of the reference pulse(s) and quantifies the limit at which the theoretical key rate approaches that of the respective conventional protocol that requires local oscillator transmission. The self-referenced protocol greatly simplifies the hardware required for CV-QKD, especially for potential integrated photonics implementations of transmitters and receivers, with minimum sacrifice of performance. As such, it provides a pathway towards scalable integrated CV-QKD transceivers, a vital step towards large-scale QKD networks.

Continuous-variable quantum key distribution (CV-QKD) protocols based on coherent detection have been studied extensively in both theory and experiment. In all the existing implementations of CV-QKD, both the quantum signal and the local oscillator (LO) are generated from the same laser and propagate through the insecure quantum channel. This arrangement may open security loopholes and limit the potential applications of CV-QKD. In this paper, we propose and demonstrate a pilot-aided feedforward data recovery scheme that enables reliable coherent detection using a “locally” generated LO. Using two independent commercial laser sources and a spool of 25-km optical fiber, we construct a coherent communication system. The variance of the phase noise introduced by the proposed scheme is measured to be 0.04 (${\text{rad}}^2$), which is small enough to enable secure key distribution. This technology also opens the door for other quantum communication protocols, such as the recently proposed measurement-device-independent CV-QKD, where independent light sources are employed by different users.

We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. For arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box device, we show that local operations assisted by one-way classical communication (1W-LOCCs) from the quantum part to the black box cannot create steering. Based on this, we build a resource theory of steering with 1W-LOCCs as the free operations. We introduce the notion of convex steering monotones as the fundamental axiomatic quantifiers of steering. As a convenient example thereof, we present the relative entropy of steering. In addition, we prove that two previously proposed quantifiers, the steerable weight and the robustness of steering, are also convex steering monotones. To end up with for minimal-dimensional systems, we establish, on the one hand, necessary and sufficient conditions for pure-state steering conversions under stochastic 1W-LOCCs and prove, on the other hand, the nonexistence of steering bits, i.e., measure-independent maximally steerable states from which all states can be obtained by means of the free operations. Our findings reveal unexpected aspects of steering and lay the foundations for further research, with potential implications in Bell nonlocality.

Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors. However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads. Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code. With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems. Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than $10^{-3}$ or the per-component noise rate is worse than $10^{-5}$. We identify the performance of switches in the network as the single most influential factor influencing resource scaling.

Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81–0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.

We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-$1/2$ systems. This is achieved by mapping spins to Majorana fermions followed by a $1/N$ expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [ et al., Phys. Rev. Lett. 113, 147205 (2014)].

Transition metal compounds often undergo spin-charge-orbital ordering due to strong electron-electron correlations. In contrast, low-dimensional materials can exhibit a Peierls transition arising from low-energy electron-phonon-coupling-induced structural instabilities. We study the electronic structure of the tunnel framework compound ${\mathrm{K}}_2{\mathrm{Cr}}_8{\mathrm{O}}_{16}$, which exhibits a temperature-dependent ($T$-dependent) paramagnetic-to-ferromagnetic-metal transition at $T_C=180\mathrm{K}$ and transforms into a ferromagnetic insulator below $T_{\mathrm{MI}}=95\mathrm{K}$. We observe clear $T$-dependent dynamic valence (charge) fluctuations from above $T_C$ to $T_{\mathrm{MI}}$, which effectively get pinned to an average nominal valence of ${\mathrm{Cr}}^{+3.75}$ (${\mathrm{Cr}}^{4+}:{\mathrm{Cr}}^{3+}$ states in a $3:1$ ratio) in the ferromagnetic-insulating phase. High-resolution laser photoemission shows a $T$-dependent BCS-type energy gap, with $2G(0)\sim 3.5(k_B{T}_{\mathrm{MI}})\sim 35\mathrm{meV}$. First-principles band-structure calculations, using the experimentally estimated on-site Coulomb energy of $U\sim 4\mathrm{eV}$, establish the necessity of strong correlations and finite structural distortions for driving the metal-insulator transition. In spite of the strong correlations, the nonintegral occupancy (2.25 $d\text{−}\text{electrons}/\mathrm{Cr}$) and the half-metallic ferromagnetism in the $t_{2g}$ up-spin band favor a low-energy Peierls metal-insulator transition.

Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi ${\mathbb{Z}}_3$ states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent $\mathrm{SU}(n)$ cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.

Using pulsed optical excitation and read-out along with single-phonon-counting techniques, we measure the transient backaction, heating, and damping dynamics of a nanoscale silicon optomechanical crystal cavity mounted in a dilution refrigerator at a base temperature of $T_f\approx 11\mathrm{mK}$. In addition to observing a slow (approximately 740-ns) turn-on time for the optical-absorption-induced hot-phonon bath, we measure for the 5.6-GHz “breathing” acoustic mode of the cavity an initial phonon occupancy as low as $⟨n⟩=0.021\pm 0.007$ (mode temperature $T_{\min }\approx 70\mathrm{mK}$) and an intrinsic mechanical decay rate of ${\gamma }_0=328\pm 14\mathrm{Hz}$ ($Q_m\approx 1.7\times {10}^7$). These measurements demonstrate the feasibility of using short pulsed measurements for a variety of quantum optomechanical applications despite the presence of steady-state optical heating.

Nitrogen-vacancy (NV) defect centers in diamond are promising solid-state magnetometers. Single centers allow for high-spatial-resolution field imaging but are limited in their magnetic field sensitivity. Using defect-center ensembles, sensitivity can be scaled with $\sqrt{N}$ when $N$ is the number of defects. In the present work, we use an ensemble of $N\sim {10}^{11}$ defect centers within an effective sensor volume of $8.5\times {10}^{-4}{\mathrm{mm}}^3$ for sensing at room temperature. By carefully eliminating noise sources and using high-quality diamonds with large NV concentrations, we demonstrate, for such sensors, a sensitivity scaling as $1/\sqrt{t}$, where $t$ is the total measurement time. The associated photon-shot-noise-limited magnetic-field sensitivity for ac signals of $f=20\mathrm{kHz}$ is $0.9\mathrm{pT}/\sqrt{\mathrm{Hz}}$. For a total measurement time of 100 s, we reach a standard deviation of about 100 fT. Further improvements using decoupling sequences and material optimization could lead to $\mathrm{fT}/\sqrt{\mathrm{Hz}}$ sensitivity.

Quantum heat engines (QHE) are thermal machines where the working substance is a quantum object. In the extreme case, the working medium can be a single particle or a few-level quantum system. The study of QHE has shown a remarkable similarity with macroscopic thermodynamical results, thus raising the issue of what is quantum in quantum thermodynamics. Our main result is the thermodynamical equivalence of all engine types in the quantum regime of small action with respect to Planck’s constant. They have the same power, the same heat, and the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown that QHE have quantum-thermodynamic signature; i.e., thermodynamic measurements can confirm the presence of quantum effects in the device. We identify generic coherent and stochastic work extraction mechanisms and show that coherence enables power outputs that greatly exceed the power of stochastic (dephased) engines.

Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in fault-tolerant scenarios. Here, I show that for suitable topological codes, a single round of local measurements is enough. This feature is generic and is related to self-correction and confinement phenomena in the corresponding quantum Hamiltonian model. Three-dimensional gauge color codes exhibit this single-shot feature, which also applies to initialization and gauge fixing. Assuming the time for efficient classical computations to be negligible, this yields a topological fault-tolerant quantum computing scheme where all elementary logical operations can be performed in constant time.

Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation, and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for nonpure states or nonideal measurement conditions.

Localized heating of a gas by intense laser pulses leads to interesting acoustic, hydrodynamic, and optical effects with numerous applications in science and technology, including controlled wave guiding and remote atmosphere sensing. Rotational excitation of molecules can serve as the energy source for raising the gas temperature. Here, we study the dynamics of energy transfer from the molecular rotation to heat. By optically imaging a cloud of molecular superrotors, created with an optical centrifuge, we experimentally identify two separate and qualitatively different stages of its evolution. The first nonequilibrium “gyroscopic” stage is characterized by the modified optical properties of the centrifuged gas—its refractive index and optical birefringence, owing to the ultrafast directional molecular rotation, which survives tens of collisions. The loss of rotational directionality is found to overlap with the release of rotational energy to heat, which triggers the second stage of thermal expansion. The crossover between anisotropic rotational and isotropic thermal regimes is in agreement with recent theoretical predictions and our hydrodynamic calculations.

Many NP-hard problems can be seen as the task of finding a ground state of a disordered highly connected Ising spin glass. If solutions are sought by means of quantum annealing, it is often necessary to represent those graphs in the annealer’s hardware by means of the graph-minor embedding technique, generating a final Hamiltonian consisting of coupled chains of ferromagnetically bound spins, whose binding energy is a free parameter. In order to investigate the effect of embedding on problems of interest, the fully connected Sherrington-Kirkpatrick model with random $\pm 1$ couplings is programmed on the D-Wave ${\mathrm{Two}}^{\mathrm{TM}}$ annealer using up to 270 qubits interacting on a Chimera-type graph. We present the best embedding prescriptions for encoding the Sherrington-Kirkpatrick problem in the Chimera graph. The results indicate that the optimal choice of embedding parameters could be associated with the emergence of the spin-glass phase of the embedded problem, whose presence was previously uncertain. This optimal parameter setting allows the performance of the quantum annealer to compete with (and potentially outperform, in the absence of analog control errors) optimized simulated annealing algorithms.

We study the unitary time evolution of antiferromagnetic order in the Hubbard model after a quench starting from the perfect Néel state. In this setup, which is well suited for experiments with cold atoms, one can distinguish fundamentally different pathways for melting of long-range order at weak and strong interaction. In the Mott insulating regime, melting of long-range order occurs due to the ultrafast transfer of energy from charge excitations to the spin background, while local magnetic moments and their exchange coupling persist during the process. The latter can be demonstrated by a local spin-precession experiment. At weak interaction, local moments decay along with the long-range order. The dynamics is governed by residual quasiparticles, which are reflected in oscillations of the off-diagonal components of the momentum distribution. Such oscillations provide an alternative route to study the prethermalization phenomenon and its influence on the dynamics away from the integrable (noninteracting) limit. The Hubbard model is solved within nonequilibrium dynamical mean-field theory, using the density-matrix renormalization group as an impurity solver.