In a network, a channel introduces correlations to the parties that aim to establish a communication protocol. We present a framework of nonlocal network coding by exploiting a Bell scenario and show the usefulness of nonlocal and quantum resources in network coding. Two-sender and two-receiver interference channels are considered, for which network coding is characterized by two-input and four-outcome Bell scenarios. It is shown that nonsignaling correlations lead to strictly higher channel capacities than quantum correlations in general. This also holds true for quantum and local correlations: network coding with quantum resources shows a strictly higher channel capacity than local ones. It turns out, however, that more nonlocality does not necessarily imply a higher channel capacity. The framework can be generally applied to network communication protocols.

Certifying that quantum devices behave as intended is crucial for quantum information science. Here, methods are developed for certification of both state preparation devices and measurement devices based on prepare-and-measure experiments with independent devices. The experimenter assumes the independence of the devices and knowledge of the Hilbert space dimension. Thus no precise characterization of any part of the experiment is required. The certification is based on a randomized version of unambiguous state discrimination and targets the class of state ensembles corresponding to quantum $t$ designs of any size and any dimension. These quantum designs are sets of states over which the average of any $t$-degree polynomial equals its average over all pure states, and they accommodate many of the most useful discrete structures in quantum information processing. Furthermore, it is shown that the same experiments also certify the detection efficiency of the measurement devices, as well as their nonprojective nature. The presented methods can readily be implemented in experiments.

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters $K$ and $d$ of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most $d$ with at most $K$ qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any $(K,d)$-clustered quantum circuit on a $d$-qubit machine in time roughly $2^{O(K)}$, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems—such as large molecules—that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the ${\mathrm{BeH}}_2$ molecule while running on a physical quantum device with half the number of required qubits.

In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to four ions using radial modes. The ions are individually addressed by two tightly focused beams steered using microelectromechanical system mirrors. We deduce a gate fidelity of 99.49(7)% in a two-ion chain and 99.30(6)% in a four-ion chain by applying a sequence of up to 21 two-qubit gates and measuring the final state fidelity. We characterize the residual errors and discuss methods to further improve the gate fidelity towards values that are compatible with fault-tolerant quantum computation.

This Letter presents a neural estimator for entropy production (NEEP), that estimates entropy production (EP) from trajectories of relevant variables without detailed information on the system dynamics. For steady state, we rigorously prove that the estimator, which can be built up from different choices of deep neural networks, provides stochastic EP by optimizing the objective function proposed here. We verify the NEEP with the stochastic processes of the bead spring and discrete flashing ratchet models and also demonstrate that our method is applicable to high-dimensional data and can provide coarse-grained EP for Markov systems with unobservable states.

Zel’dovich proposed that electromagnetic (EM) waves with angular momentum reflected from a rotating metallic, lossy cylinder will be amplified. However, we are still lacking a direct experimental EM-wave verification of this fifty-year-old prediction due to the challenging conditions in which the phenomenon manifests itself: the mechanical rotation frequency of the cylinder must be comparable with the EM oscillation frequency. Here, we propose an experimental approach that solves this issue and is predicted to lead to a measurable Zel’dovich amplification with existing superconducting circuit technology. We design a superconducting circuit with low frequency EM modes that couple through free space to a magnetically levitated and spinning microsphere placed at the center of the circuit. We theoretically estimate the circuit EM mode gain and show that rotation of the microsphere can lead to experimentally observable amplification, thus paving the way for the first EM-field experimental demonstration of Zel’dovich amplification.

Multipartite entanglement (ME) is the fundamental ingredient for building quantum networks. The scale of ME determines its quantum information carrying and processing capability. Most of the current efforts for boosting the scale of ME focus on increasing the number of entangled nodes. However, the number of channels for broadcasting ME is also an important index for characterizing its scale. In this Letter, we experimentally exploit orbital angular momentum multiplexing and the spatial pump shaping technique to simultaneously and deterministically generate 11 channels of individually accessible and mutually orthogonal continuous variable (CV) spatially separated hexapartite entangled states over 66 optical modes in a single quantum system. These results suggest that our method can greatly expand the scale of ME and provide a new perspective and platform to construct a CV quantum network.

Quantum entanglement is fragile to thermal fluctuations, which raises the question whether finite temperature phase transitions support long-range entanglement similar to their zero temperature counterparts. Here we use quantum Monte Carlo simulations to study the third Renyi negativity, a generalization of entanglement negativity, as a proxy of mixed-state entanglement in the 2D transverse field Ising model across its finite temperature phase transition. We find that the area-law coefficient of the Renyi negativity is singular across the transition, while its subleading constant is zero within the statistical error. This indicates that the entanglement is short-range at the critical point despite a divergent correlation length. Renyi negativity in several exactly solvable models also shows qualitative similarities to that in the 2D transverse field Ising model.

We demonstrate the power of 2D tensor networks for obtaining large deviation functions of dynamical observables in a classical nonequilibrium setting. Using these methods, we analyze the previously unstudied dynamical phase behavior of the fully 2D asymmetric simple exclusion process with biases in both the $x$ and $y$ directions. We identify a dynamical phase transition, from a jammed to a flowing phase, and characterize the phases and the transition, with an estimate of the critical point and exponents.

The thermodynamic uncertainty relation (TUR) describes a trade-off relation between nonequilibrium currents and entropy production and serves as a fundamental principle of nonequilibrium thermodynamics. However, currently known TURs presuppose either specific initial states or an infinite-time average, which severely limits the range of applicability. Here we derive a finite-time TUR valid for arbitrary initial states from the Cramér-Rao inequality. We find that the variance of an accumulated current is bounded from below by the instantaneous current at the final time, which suggests that “the boundary is constrained by the bulk”. We apply our results to feedback-controlled processes and successfully explain a recent experiment which reports a violation of a modified TUR with feedback control. We also derive a TUR that is linear in the total entropy production and valid for discrete-time Markov chains with nonsteady initial states. The obtained bound exponentially improves the existing bounds in a discrete-time regime.

Coherent superposition and entanglement are two fundamental aspects of nonclassicality. Here we provide a quantitative connection between the two on the level of operations by showing that the dynamical coherence of an operation upper bounds the dynamical entanglement that can be generated from it with the help of additional incoherent operations. In case a particular choice of monotones based on the relative entropy is used for the quantification of these dynamical resources, this bound can be achieved. In addition, we show that an analog to the entanglement potential exists on the level of operations and serves as a valid quantifier for dynamical coherence.

The Jaynes-Cummings model is a cornerstone of light-matter interactions. While finite, the model provides an illustrative example of renormalization in perturbation theory. We show, however, that exact renormalization reveals a rich nonperturbative structure, and that the model provides a physical example of a theory with a chaotic coupling trajectory and multivalued $\beta$ function. We also construct an exact Wilsonian-like renormalization group flow for the effective scattering matrix, and show how multivalued features arise in the flow. Our results shed light on nonperturbative aspects of renormalization and on the structure of the Jaynes-Cummings model itself.

We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled nonlinear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.

Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the phase of an electromagnetic field and single-shot measurements of this phase are necessary. While there are measurements able to estimate the phase of light in a single shot with small uncertainties, demonstrations of near-optimal single-shot measurements for an unknown phase of a coherent state remain elusive. Here, we propose and demonstrate strategies for single-shot measurements for ab initio phase estimation of coherent states that surpass the sensitivity limit of heterodyne measurement and approach the Cramer-Rao lower bound for coherent states. These single-shot estimation strategies are based on real-time optimization of coherent displacement operations, single photon counting with photon number resolution, and fast feedback. We show that our demonstration of these optimized estimation strategies surpasses the heterodyne limit for a wide range of optical powers without correcting for detection efficiency with a moderate number of adaptive measurement steps. This is, to our knowledge, the most sensitive single-shot measurement of an unknown phase encoded in optical coherent states.

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-$1/2$ particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.

We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff $⟨{\dot{S}}_e⟩\mathcal{T}\ge k_B$ between the entropy flow $⟨{\dot{S}}_e⟩$ into the reservoirs and the mean time $\mathcal{T}$ to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.

In this work, we address the question of how a closed quantum system thermalizes in the presence of a random external potential. By investigating the quench dynamics of the isolated quantum spherical $p$-spin model, a paradigmatic model of a mean-field glass, we aim to shed new light on this complex problem. Employing a closed-time Schwinger-Keldysh path integral formalism, we first initialize the system in a random, infinite-temperature configuration and allow it to equilibrate in contact with a thermal bath before switching off the bath and performing a quench. We find evidence that increasing the strength of either the interactions or the quantum fluctuations can act to lower the effective temperature of the isolated system and stabilize glassy behavior.