We demonstrate that linear combinations of subregion entropies with canceling boundary terms, commonly used to calculate the topological entanglement entropy, may suffer from spurious nontopological contributions even in models with zero correlation length. These spurious contributions are due to a specific kind of long-range string order, and persist throughout certain subsystem symmetry-protected phases. We introduce an entropic quantity that measures the presence of such order, and hence should serve as an order parameter for the aforementioned phases.

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law, $1/r^\alpha$. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when $\alpha>3D$ (where $D$ is the number of dimensions).

Simulating quantum algorithms with classical resources generally requires exponential resources. However, heuristic classical approaches are often very efficient in approximately simulating special circuit structures, for example with limited entanglement, or based on one-dimensional geometries. Here we introduce a classical approach to the simulation of general quantum circuits based on neural-network quantum states (NQS) representations. Considering a set of universal quantum gates, we derive rules for exactly applying single-qubit and two-qubit Z rotations to NQS, whereas we provide a learning scheme to approximate the action of Hadamard gates. Results are shown for the Hadamard and Fourier transform of entangled initial states for systems sizes and total circuit depths exceeding what can be currently simulated with state-of-the-art brute-force techniques. The overall accuracy obtained by the neural-network states based on Restricted Boltzmann machines is satisfactory, and offers a classical route to simulating highly-entangled circuits. In the test cases considered, we find that our classical simulations are comparable to quantum simulations affected by an incoherent noise level in the hardware of about $10^{-3}$ per gate.

Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We use bit threads to prove the monogamy of mutual information (MMI) property of holographic entanglement entropies. This is accomplished using the concept of a so-called multicommodity flow, adapted from the network setting, and tools from the theory of convex optimization. Based on the bit thread picture, we conjecture a general ansatz for a holographic state, involving only bipartite and perfect-tensor type entanglement, for any decomposition of the boundary into four regions. We also give new proofs of analogous theorems on networks.

We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is composed of decoupled 1D SPTs with global symmetries. We propose a natural definition for strong equivalence of such phases, in terms of a linearly-symmetric local unitary transformation, under which a weak subsystem SPT is equivalent to the trivial phase. This leads to a number of distinct equivalence classes of strong subsystem SPTs, which we show are in one-to-one correspondence with elements of the group $\mathcal{C}[G_s] = \mathcal{H}^{2}[G_s^2,U(1)]/(\mathcal{H}^{2}[G_s,U(1)])^3$, where $G_s$ is the finite abelian onsite symmetry group. We also show that strong subsystem SPTs by our classification necessarily exhibit a spurious topological entanglement entropy on a cylinder.

We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). In particular, we provide a novel proof of MMI, using bit threads directly. To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. We conjecture that our method applies in a wide class of configurations, including ones with non-trivial topology, causal structure, and time dependence. The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity.

Quantum heat engine with ideal gas has been well studied, yet the role of interaction was seldom explored. We construct a quantum Otto heat engine with N repulsive Bosonic particles in a 1D hard wall box. With the advantage of exact solution using Bethe Ansatz, we obtain not only the exact numerical result of efficiency in all interacting strength c, but also analytical results for strong interaction. We find the efficiency \eta recovers to the one of non-interacting case $\eta_{\mathrm{non}}=1-(L_{1}/L_{2})^{2}$ for strong interaction with asympotic behavior $\eta\sim\eta_{\mathrm{non}}-4(N-1)L_{1}\left(L_{2}-L_{1}\right)/(cL_{2}^{3})$. Here, $L_{1}$ and $L_{2}$ are two trap sizes during the cycle. Such recovery reflects the duality between 1D strongly repulsive Bosons and free Fermion. We observe and explain the appearance of a minimum efficiency at a particular interacting strength c, and study its dependence on the temperature.

Quantum network has significant applications both practically and fundamentally. A hybrid architecture with photons and stationary nodes is highly promising. So far, experimental realizations are limited to two nodes with two photons. Going beyond state of the art by entangling many photons with many quantum nodes is highly appreciated. Here, we report an experiment realizing hybrid entanglement between three photons and three atomic-ensemble quantum memories. We make use of three similar setups, in each of which one pair of photon-memory entanglement with high overall efficiency is created via cavity enhancement. Through three-photon interference, the three quantum memories get entangled with the three photons. Via measuring the photons and applying feedforward, we heraldedly entangle the three memories. Our work demonstrates the largest size of hybrid memory-photon entanglement, which may be employed as a build block to construct larger and complex quantum network.

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories.

We investigate the properties of a Tonks-Girardeau gas in the presence of a one-dimensional lattice potential. Such a system is known to exhibit a pinning transition when the lattice is commensurate with the particle density, leading to the formation of an insulating state even at infinitesimally small lattice depths. Here we examine the properties of the gas at all lattices depths and, in addition to the static properties, also consider the non-adiabatic dynamics induced by the sudden motion of the lattice potential with a constant speed. Our work provides a continuum counterpart to the work done in discrete lattice models.

We present a hybrid system consisting of a superconducting coplanar waveguide resonator coupled to a nanomechanical string and a transmon qubit acting as nonlinear circuit element. We perform spectroscopy for both the transmon qubit and the nanomechanical string. Measuring the ac-Stark shift on the transmon qubit as well as the electromechanically induced absorption on the string allows us to determine the average photon number in the microwave resonator in both the low and high power regimes. In this way, we measure photon numbers that are up to nine orders of magnitude apart. We find a quantitative agreement between the calibration of photon numbers in the microwave resonator using the two methods. Our experiments demonstrate the successful combination of superconducting circuit quantum electrodynamics and nano-electromechanics on a single chip.

We report on the detection of extremely narrow Feshbach resonances by employing a Mott-insulating state for cesium atoms in a three-dimensional optical lattice. The Mott insulator protects the atomic ensemble from high background three-body losses in a magnetic field region where a broad Efimov resonance otherwise dominates the atom loss in bulk samples. Our technique reveals three ultra-narrow and previously unobserved Feshbach resonances in this region with widths below $\approx 10\,\mu$G, measured via Landau-Zener-type molecule formation and confirmed by theoretical predictions. For comparatively broader resonances we find a lattice-induced substructure in the respective atom-loss feature due to the interplay of tunneling and strong particle interactions. Our results provide a powerful tool to identify and characterize narrow scattering resonances, particularly in systems with complex Feshbach spectra. The observed ultra-narrow Feshbach resonances could be interesting candidates for precision measurements.

Both the electron transport-based qubits, implemented through double quantum dots, and the sources of indistinguishable single-photons like self-assembled quantum dots are strong candidates for the implementation of quantum technologies, such as quantum computers and quantum repeaters. Here, we demonstrate a reliable way of coupling these two types of qubits, uncovering the possibility of controlling and reading out the population of the double quantum dot via optical excitation. It is also showed that, in spite of the decoherence mechanisms affecting the qubits, the entanglement between them is achievable and, consequently, the implementation of the suggested system in quantum technologies is feasible.

In this paper a commercial 28-nm FDSOI CMOS technology is characterized and modeled from room temperature down to 4.2 K. Here we explain the influence of incomplete ionization and interface traps on this technology starting from the fundamental device physics. We then illustrate how these phenomena can be accounted for in circuit device-models. We find that the design-oriented simplified EKV model can accurately predict the impact of the temperature reduction on the transfer characteristics, back-gate sensitivity, and transconductance efficiency. The presented results aim at extending industry-standard compact models to cryogenic temperatures for the design of cryo- CMOS circuits implemented in a 28 nm FDSOI technology.

We investigate orbital alignment dynamics within the valence shell of atoms in coherently excited $j=3/2,1/2$ fine-structure manifolds generated by short-pulse photodetachment of F$^-$, Cl$^-$ and Br$^-$ anions. Using Keldysh-type theory, we calculate the density matrix of the residual atoms generated by few-cycle pulses, whose elements determine the populations and coherence among the electronic states. Our calculations demonstrate that the degree of atomic coherence can be represented by a near universal function of the ratio between the pulse duration $\tilde{\tau}_p$ and the beat period $\tau_{j'j}$ of the atomic system, which allows one to characterize the coherence generated in atomic states.

We present a detailed analysis of a robust and fast laser cooling scheme [J. Cerrillo et al.,Phys. Rev. Lett. 104, 043003 (2010)] on a three-level system. A special laser configuration, applicable to trapped ions, atoms, or cantilevers, designs a double-path quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon interactions. As a consequence, cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very flexible under constraints of the physical parameters such as laser intensity, detuning, or optical access, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes. Its suitability as a cooling scheme for several ions in a trap and three-dimensional cooling is shown.

Non-classical states of light find applications in enhancing the performance of optical interferometric experiments, with notable example of gravitational wave-detectors. Still, the presence of decoherence hinders significantly the performance of quantum-enhanced protocols. In this review, we summarize the developments of quantum metrology with particular focus on optical interferometry and derive fundamental bounds on achievable quantum-enhanced precision in optical interferometry taking into account the most relevant decoherence processes including: phase diffusion, losses and imperfect interferometric visibility. We introduce all the necessary tools of quantum optics as well as quantum estimation theory required to derive the bounds. We also discuss the practical attainability of the bounds derived and stress in particular that the techniques of quantum-enhanced interferometry which are being implemented in modern gravitational wave detectors are close to the optimal ones.

We describe how physical universes that are composed of gauge and gravitationally interacting bosonic and fermionic quantum fields arise from the generic discrete distribution of many quantifiable properties of arbitrary static entities. Alternate presentations of the smooth coarse-graining (fit) for this discrete distribution compose probability-related evolving wave function of the fields' dynamical modes. Their gauge modes, being symmetry transformations, and constrained modes require no additional material structure. We prove that evolution of any origin for which the quantum superposition principle is absolute cannot be governed by specific laws. In contrast, locally supersymmetric quantum fields that emerge as described from the basic discrete distribution evolve by unchanging and closed physical laws. The emergent quantum evolution is many-world; yet its Everett's branches whose norm diminishes below a positive threshold cease to exist. Then some experiments that for the standard Everett view would seem safe are instead fatal for the participants. The Born rule arises dynamically in emergent systems with extended regular past. It and, consequently, quasi-deterministic macroscopic evolution emerge in systems that allow cosmological inflation but not in typical random ones. This resolves the Boltzmann brain problem. We explain how inflation creates new physical degrees of freedom around the Planck scale. Quantum entanglement for the emergent fields is trivial because their wave function, up to its representation, is material.

We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated with precision scaling as $1/T$, where $T$ is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum Master equation, implying at most $1/\sqrt{T}$ scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction like protocol must satisfy in order to regain the $1/T$ precision scaling in case the above mentioned algebraic condition is not satisfied. Furthermore, we apply the developed methods to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of non-linear metrological models.

A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the $(1+1)-$dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operators---differently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.