Quantum error correcting codes with finite-dimensional Hilbert spaces have yielded new insights on bulk reconstruction in AdS/CFT. In this paper, we give an explicit construction of a quantum error correcting code where the code and physical Hilbert spaces are infinite-dimensional. We define a von Neumann algebra of type II$_1$ acting on the code Hilbert space and show how it is mapped to a von Neumann algebra of type II$_1$ acting on the physical Hilbert space. This toy model demonstrates the equivalence of entanglement wedge reconstruction and the exact equality of bulk and boundary relative entropies in infinite-dimensional Hilbert spaces.

Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of motion' (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized \emph{strong zero modes}, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.

Concomitant with the rapid development of quantum technologies, challenging demands arise concerning the certification and characterization of devices. The promises of the field can only be achieved if stringent levels of precision of components can be reached and their functioning guaranteed. This Expert Recommendation provides a brief overview of the known characterization methods of certification, benchmarking, and tomographic recovery of quantum states and processes, as well as their applications in quantum computing, simulation, and communication.

The Karolyhazy uncertainty relation is the statement that if a device is used to measure a length $l$, there will be a minimum uncertainty $\delta l$ in the measurement, given by $(\delta l)^3 \sim L_P^2\; l$. This is a consequence of combining the principles of quantum mechanics and general relativity. In this note we show how this relation arises in our approach to quantum gravity, in a bottom-up fashion, from the matrix dynamics of atoms of space-time-matter. We use this relation to define a space-time-matter foam at the Planck scale, and to argue that our theory is holographic. By coarse graining over time scales larger than Planck time, one obtains the laws of quantum gravity. Quantum gravity is not a Planck scale phenomenon; rather it comes into play whenever no classical space-time background is available to describe a quantum system. Space-time and classical general relativity arise from spontaneous localisation in a highly entangled quantum gravitational system. The Karolyhazy relation continues to hold in the emergent theory. An experimental confirmation of this relation will constitute a definitive test of the quantum nature of gravity.

We study the robustness of the paradigmatic Resonating Valence Bond (RVB) spin liquid and its orthogonal version, the quantum dimer model, on the kagome lattice. The non-orthogonality of singlets in the RVB model and the induced finite length scale not only makes it difficult to analyze, but can also significantly affect its physics, such as its resilience to perturbations. Surprisingly, we find that this is not the case: The robustness of the RVB spin liquid is not affected by the finite correlation length, which demonstrates that the dimer model forms a viable model for studying RVB physics under perturbations. A microscopic analysis, based on tensor networks, allows us to trace this robustness back to two universal mechanisms: First, the dominant correlations in the RVB are spinon correlations, making the state robust against doping with visons. Second, reflection symmetry stabilizes the spin liquid against doping with spinons, by forbidding mixing of the initially dominant correlations with the correlations which lead to the breakdown of topological order.

A non-Hermitian topological insulator with real spectrum is interesting in the theory of non-Hermitian extension of topological systems. We find an experimentally realizable example of a two dimensional non-Hermitian topological insulator with real spectrum. We consider two-dimensional Su-Schrieffer-Heeger (SSH) model with gain and loss. We introduce non-Hermitian polarization vector to explore topological phase and show that topological edge states in the band gap exist in the system.

Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.

Karl Popper published, in 1968, a paper that allegedly found a flaw in a very influential article of Birkhoff and von Neumann, which pioneered the field of "quantum logic". Nevertheless, nobody rebutted Popper's criticism in print for several years. This has been called in the historiographical literature an "unsolved historical issue". Although Popper's proposal turned out to be merely based on misinterpretations, and was eventually abandoned by the author himself, this paper aims at providing a resolution to such historical open issues. I show that (i) Popper's paper was just the tip of an iceberg of a much vaster campaign conducted by Popper against quantum logic (which encompassed several more unpublished papers that I retrieved); and (ii) that Popper's paper stimulated a heated debate that remained however confined within private correspondence.

The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is `squeezed'.

We start by surveying the history of the idea of a fundamental conservation law and briefly examine the role conservation laws play in different classical contexts. In such contexts we find conservation laws to be useful, but often not essential. Next we consider the quantum setting, where the conceptual problems of the standard formalism obstruct a rigorous analysis of the issue. We then analyze the fate of energy conservation within the various viable paths to address such conceptual problems; in all cases we find no satisfactory way to define a (useful) notion of energy that is generically conserved. Finally, we focus on the implications of this for the semiclassical gravity program and conclude that Einstein's equations cannot be said to always hold.

Different nonlocal quantum correlations of entanglement, steering and Bell nonlocality are defined with the help of local hidden state (LHS) and local hidden variable (LHV) models. Considering their unique roles in quantum information processing, it is of importance to understand the individual nonlocal quantum correlation as well as their relationship. Here, we investigate the effects of amplitude damping decoherence on different nonlocal quantum correlations. In particular, we have theoretically and experimentally shown that the entanglement sudden death phenomenon is distinct from those of steering and Bell nonlocality. In our scenario, we found that all the initial states present sudden death of steering and Bell nonlocality, while only some of the states show entanglement sudden death. These results suggest that the environmental effect can be different for different nonlocal quantum correlations, and thus, it provides distinct operational interpretations of different quantum correlations.

We report on an experiment demonstrating entanglement swapping of time-frequency entangled photons. We perform a frequency-resolved Bell-state measurement on the idler photons from two independent entangled photon pairs, which projects the signal photons onto a two-color Bell state. We verify entanglement in this heralded state using two-photon interference and observing quantum beating without the use of filters, indicating the presence of two-color entanglement. Our method could lend itself to use as a highly-tunable source of frequency-bin entangled single photons.

Quantum sensing exploits fundamental features of quantum system to achieve highly efficient measurement of physical quantities. Here, we propose a strategy to realize a single-qubit pseudo-Hermitian sensor from a dilated two-qubit Hermitian system. The pseudo-Hermitian sensor exhibits divergent susceptibility in dynamical evolution that does not necessarily involve exceptional point. We demonstrate its potential advantages to overcome noises that cannot be averaged out by repetitive measurements. The proposal is feasible with the state-of-art experimental capability in a variety of qubit systems, and represents a step towards the application of non-Hermitian physics in quantum sensing.

High-precision magnetic field measurement is an ubiquitous issue in physics and a critical task in metrology. Generally, magnetic field has DC and AC components and it is hard to extract both DC and AC components simultaneously. The conventional Ramsey interferometry can easily measure DC magnetic fields, while it becomes invalid for AC magnetic fields since the accumulated phases may average to zero. Here, we propose a scheme for simultaneous measurement of DC and AC magnetic fields by combining Ramsey interferometry and rapid periodic pulses. In our scheme, the interrogation stage is divided into two signal accumulation processes linked by a unitary operation. In the first process, only DC component contributes to the accumulated phase. In the second process, by applying multiple rapid periodic $\pi$ pulses, only the AC component gives rise to the accumulated phase. By selecting suitable input state and the unitary operations in interrogation and readout stages, and the DC and AC components can be extracted by population measurements. In particular, if the input state is a GHZ state and two interaction-based operations are applied during the interferometry, the measurement precisions of DC and AC magnetic fields can approach the Heisenberg limit simultaneously. Our scheme provides a feasible way to achieve Heisenberg-limited simultaneous measurement of DC and AC fields.

We discuss the effects of many-body coherence on the quantum speed limit in ultracold atomic gases. Our approach is focused on two related systems, spinless fermions and the bosonic Tonks-Girardeau gas, which possess equivalent density dynamics but very different coherence properties. To illustrate the effect of the coherence on the dynamics we consider squeezing an anharmonic potential which confines the particles and find that the quantum speed limit exhibits subtle, but fundamental, differences between the atomic species. Furthermore, we explore the difference in the driven dynamics by implementing a shortcut to adiabaticity designed to reduce spurious excitations. We show that collisions between the strongly interacting bosons can lead to changes in the coherence which results in larger speed limits.

We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Through a combination of analytics, exact diagonalization and tensor network methods we show the existence of a fast-to-slow transition throughout the spectrum that follows from a localization transition in the ground state. On the slow side, we explicitly construct a large (exponential in size) number of non-thermal states which become exact finite-energy-density eigenstates in the large size limit, and -- through a "super-spin" generalization -- a further large class of area-law states guaranteed to display very slow relaxation. Under slow conditions many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. We discuss implications of our results for slow thermalization and non-ergodicity more generally in systems with constraints.

The minimum parameterization of the wave function is derived for the time-independent many-body problem of identical fermions. It is shown that the exponential scaling with the number of particles plaguing all other correlation methods stems from the expansion of the wave function in one-particle basis sets. It is demonstrated that using a geminal basis, which fulfill a Lie algebra, the parametrization of the exact wave function becomes independent of the number of particles and only scale quadratic with the number of basis functions in the optimized basis. The resulting antisymmetrized geminal power wave function is shown to fulfill the necessary and sufficient conditions for the exact wavefunction, treat all electrons and electron pairs equally, be invariant to all orbital rotations and virtual-virtual and occupied-occupied geminal rotations, be the most compact representation of the exact wave function possible and contain exactly the same amount of information as the two-particle reduced density matrix. These findings may have severe consequences for quantum computing using identical fermions since the amount of information stored in a state is very little. A discussion of how the most compact wave function can be derived in general is also presented. Due to the breaking of the scaling wall for the exact wave function it is expected that even systems of biological relevance can be treated exactly in the near future.

We describe a comagnetometer employing the $f=1$ and $f=2$ ground state hyperfine manifolds of a $^{87}$Rb spinor Bose-Einstein condensate as co-located magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The $f=1$ and $f=2$ transverse magnetizations and azimuth angles are independently measured by non-destructive Faraday rotation probing, and we demonstrate a $44.0(8)\text{dB}$ common-mode rejection in good agreement with theory. We show how spin-dependent interactions can be used to inhibit $2\rightarrow 1$ hyperfine relaxing collisions, extending to $\sim 1\text{s}$ the transverse spin lifetime of the $f=1,2$ mixtures. The technique could be used in high sensitivity searches for new physics on sub-millimeter length scales, precision studies of ultra-cold collision physics, and angle-resolved studies of quantum spin dynamics.

Semiconductor quantum dots embedded in micro-pillar cavities are excellent emitters of single photons when pumped resonantly. Often, the same spatial mode is used to both resonantly excite a quantum dot and to collect the emitted single photons, requiring cross-polarization to reduce the uncoupled scattered laser light. This inherently reduces the source brightness to 50 %. Critically, for some quantum applications the total efficiency from generation to detection must be over 50 %. Here, we demonstrate a resonant-excitation approach to creating single photons that is free of any cross-polarization, and in fact any filtering whatsoever. It potentially increases single-photon rates and collection efficiencies, and simplifies operation. This integrated device allows us to resonantly excite single quantum-dot states in several cavities in the plane of the device using connected waveguides, while the cavity-enhanced single-photon fluorescence is directed vertical (off-chip) in a Gaussian mode. We expect this design to be a prototype for larger chip-scale quantum photonics.

The Bremermann-Bekenstein bound sets a fundamental upper limit on the rate with which information can be processed. However, the original treatment heavily relies on cosmological properties and plausibility arguments. In the present analysis, we derive equivalent statements by relying on only two fundamental results in quantum information theory and quantum dynamics -- Fannes inequality and the quantum speed limit. As main results, we obtain Bremermann-Bekenstein-type bounds for the rate of change of the von Neumann entropy in quantum systems undergoing open system dynamics, and for the rate of change of the Shannon information over some logical basis in unitary quantum evolution.