Quantum measurements are inherently probabilistic and quantum theory often forbids precisely predicting the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, the problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. By constructing a close connection between observables and graph theory, we derive uncertainty relations valid for any set of dichotomic observables. For arbitrary observables, we obtain an upper bound on the sum of the square of their expectation values. We furthermore show how this bound behaves when the observables are imprecisely calibrated. As applications, our results can be straightforwardly used to formulate entropic uncertainty relations, separability criteria, and entanglement witnesses.

A measurement of the time between quantum jumps implies the capability to measure the next jump. During the time between jumps the quantum system is not evolving in a closed or unitary manner. While the wave function maintains phase coherence it evolves according to a non-Hermitian effective Hamiltonian. So under null measurement the timing of the next quantum jump can change by very many orders of magnitude when compared to rates obtained by multiplying lifetimes with occupation probabilities obtained via unitary transformation. The theory developed in 1987 for atomic fluorescence is here extended to transitions in transmon qubits. These systems differ from atoms in that they are read out with a harmonic cavity whose resonance is determined by the state of the qubit. We extend our analysis of atomic fluorescence to this infinite level system by treating the cavity as a quantum system. We find that next photon statistics is highly nonexponential and when implemented will enable faster readout, such as on timescales shorter than the decay time of the cavity. Commonly used heterodyne measurements are applied on timescales longer than the cavity lifetime. The overlap between the next photon theory and the theory of heterodyne measurement which are described according to the stochastic Schrödinger equation is elucidated. In the limit of large dispersion the intrinsic error for next jump detection, at short time, tends to zero. Whereas for short-time dyne detection the error remains finite for all values of dispersion.

Bipartite entangled states whose violations of the Clauser-Horne-Shimony-Holt Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs exist [Brown and Colbeck, Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider their analogs for tripartite systems: a tripartite entangled state is shared among Alice, Bob, and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie, who measures again with other measurements, and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies can share genuine nonlocality of the Greenberger-Horne-Zeilinger state via the violation of the Svetlichny inequality with Alice and Bob [S. Saha et al., Quantum Inf. Process. 18, 42 (2019); Zhang and Fei, Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of the Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with a single Alice and single Bob.

The geometric (Berry-Pancharatnam) phase originates from the intrinsic geometry of the space of quantum states and can be observed in different situations, such as a cyclic evolution of a quantum system. Here, we utilize the geometric phase to obtain a surprising insight: It is possible to create nonlocal correlations in a fixed interferometer with independent photon inputs by varying the photons' internal states. In particular, we consider a cyclic interferometer that is fixed, i.e., that has no variable internal phase shifts or subsequent measurement settings. Instead, the measurement choices of the different parties correspond to the internal states of the input photons which influence the observed correlations via a collective $N$-photon geometric phase, constituting a different approach for the generation of nonlocality with respect to the usual paradigm. We observe a trade-off between the geometric phases and the visibility of the many-photon interference, impeding the generation of nonlocality. However, by making use of the dynamical quantum Zeno effect, we show that nonlocality can be created in the fixed cyclic interferometer using 12 (or more) independent photons.

The problem of elastic scattering of a nonrelativistic electron Airy beam on a hydrogen atom in the ground $1s$ state is considered in the Born approximation. It is demonstrated that the angular dependence of the scattering probability density is, in general, azimuthally asymmetric. When the position of the atom happens to coincide with a minimum of the probability density of the Airy beam, the asymmetric pattern is represented by four separated peaks. We show that this behavior is very sensitive to the precision with which the relative position of the atom and the minima is defined and study how uncertainty in the position can affect observation of the azimuthal asymmetry. Finally, we consider a spatially localized target and discuss the difficulties of observing the asymmetry for targets with sizes exceeding a critical value determined by the beam parameters and by the position of the target center.

Using high-temperature virial expansion, we study the quench dynamics of the thermal Bose gases near wide, narrow, and intermediate Feshbach resonances. Our results show that the shallow bound state near Feshbach resonances leads to oscillation of ${\widehat{n}}_{\mathbf{k}}$. Near the wide Feshbach resonance, the long-time momentum distribution ${\widehat{n}}_{\mathbf{k}}$ oscillates when the scattering length $a_s$ is quenched to large but with finite positive values. The oscillation frequency is determined by the bound-state energy. When $a_s$ is quenched to infinity or negative value, the oscillation vanishes. Near the narrow Feshbach resonance, when the background scattering length $a_{\mathrm{bg}}$ is larger than de Broglie wave length $\lambda$, there is an oscillation, and the frequency is determined by the energy of the shallow bound state in the open channel. When $a_{\mathrm{bg}}<0$ or $0<a_{\mathrm{bg}}\ll \lambda$, there is no shallow bound state in the open channel, and hence no oscillation. We check our conclusion using some realistic systems, and the results are consistent with our conclusion.

Recently, we computed third-order corrections to the ground-state energy of an arbitrarily polarized diluted gas of spin-$\frac{1}{2}$ fermions interacting through a spin-independent repulsive two-body potential. Here we extend this result to the gas of spin-$s$ fermions [a system whose Hamiltonian has an accidental $\text{SU}(2s+1)$ symmetry] with arbitrary densities of fermions having different spin projections. The corrections are computed semianalytically using the effective-field-theory approach and are parametrized by the $s$- and $p$-wave scattering lengths $a_0$ and $a_1$ and the $s$-wave effective radius $r_0$, measurable in the low-energy fermion-fermion elastic scattering. The result is used to study the impact the higher-order corrections can have on the characteristics of the phase transition (at zero temperature) to the ordered phase (on the emergence of the itinerant ferromagnetism).

We investigate how the Rayleigh-Plateau instability of a filament made of a ${}^{41}\mathrm{K}\text{−}{}^{87}\mathrm{Rb}$ self-bound mixture may lead to an array of identical quantum droplets, with typical breaking times which are shorter than the lifetime of the mixture. If the filament is laterally confined, as it happens in a toroidal trap, and atoms of one species are in excess with respect to the optimal equilibrium ratio, the droplets are immersed into a superfluid background made by the excess species which provides global phase coherence to the system, suggesting that the droplet array in the unbalanced system may display supersolid character. This possibility is investigated by computing the nonclassical translational inertia coefficient. The filament may be a reasonable representation of a self-bound mixture subject to toroidal confinement when the bigger circle radius of the torus is much larger than the filament radius.

Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential “flattening” of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter-tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data that lacks special structure.

In recent years, in quantum information theory, there has been a remarkable development in the general theoretical framework for studying symmetry in dynamics. This development, called resource theory of asymmetry, is expected to have a wide range of applications, from accurate time measurements to black-hole physics. Despite its importance, the foundation of resource theory of asymmetry still has room for expansion. An important problem is in quantifying the amount of resource. When the symmetry prescribed U(1) or $\mathbb{R}$, i.e., with a single conserved quantity, the quantum Fisher information is known as a resource measure that has suitable properties and a clear physical meaning related to quantum fluctuation of the conserved quantity. However, it is not clear what is the resource measure with such suitable properties when a general symmetry prevails for which there are multiple conserved quantities. The purpose of this paper is to fill this gap. Specifically, we show that the quantum Fisher information matrix is a resource measure whenever a connected linear Lie group describes the symmetry. We also consider the physical meaning of this matrix and see which properties that the quantum Fisher information has when the symmetry is described by U(1) or $\mathbb{R}$ can be inherited by the quantum Fisher information matrix.

The lifetime of the galliumlike ${\mathrm{Mo}}^{11+}$ ion $4s^{2}4p{}^{2}P_{3/2}$ metastable level was measured at an electron-beam ion trap. The lifetime was inferred from the temporal behavior of its associated $4s^{2}4p{}^{2}P_{3/2}-{}^{2}P_{1/2}$ transition. Particular effort was devoted to reducing the systematic errors and the obtained lifetime value was $4.813\left(9\right){(}_{-5}^{+2})$ (stat)(syst) ms. Most of the predictions without the electron anomalous magnetic moment correction are consistent with our measurement results. However, all the available, theoretical, effect-corrected results show an unexpected discrepancy with the measured results.

We experimentally study three-body energy exchange during Rydberg excitation near a two-body Förster resonance. By varying the excitation pulse duration or Rabi frequency, we coherently control the excitation of three-atom entangled states. We prove coherence using an optical rotary echo technique and compare with a model for excitation in a three-atom basis. Our results suggest a robust way to implement a three-body entangling operation.

In Khairulin et al. [Sci. Rep. 12, 6204 (2022)] we proposed a method for amplifying a train of sub-femtosecond pulses of circularly or elliptically polarized extreme ultraviolet radiation, composed by high-order harmonics of an infrared (IR) laser field, in a neonlike active medium of a plasma-based x-ray laser, additionally irradiated with a replica of a fundamental frequency laser field used to generate harmonics. Here we present the analytical theory and numerical study of an amplification process of an individual harmonic with either preservation of its polarization state or ellipticity enhancement. We also analyze in detail the spectral-temporal and polarization properties of a sub-femtosecond pulse train formed by a set of elliptically or circularly polarized harmonics during the propagation through the medium. We discuss also the possibility of an experimental implementation of the suggested technique in an active medium of an x-ray laser based on neonlike ${\mathrm{Ti}}^{12+}$ ions irradiated by an IR laser field with a wavelength of 3.2 µm.

We propose a general experimental scheme based on binary trees of partially polarizing beam splitters (PPBSs) for realizing sequential unsharp measurements of photon polarization. The sharpnesses and the bases of the particular photon polarization measurements can be chosen arbitrarily by using corresponding PPBSs and phase plates in the setup. In the limit of low sharpnesses the scheme can realize sequential weak measurements, too. We develop a general formalism for describing sequential unsharp measurements of photon polarization in which the particular unsharp measurements are characterized by appropriate measurement operators. We show that a straightforward experimental realization of this model is the proposed scheme. In this formalism the output polarization states after the sequential measurement and any correlation functions characterizing the measurement results can be easily calculated. Our model can be used for analyzing the consequences of applying postselection and reselection in the measurement. We derive the anomalous mean value for an unsharp polarization measurement with postselection and the anomalous second-order correlation function for the sequential unsharp measurement of photon polarization with reselection. We show that these anomalies can be easily measured using the proposed scheme.

There has been a problem of gauge ambiguities with the Rabi Hamiltonian due to the fact that it can be derived from two formally different but physically equivalent fundamental Hamiltonians. This problem has recently been resolved for models with a single quantized electromagnetic mode. In this paper, we mathematically and numerically verify this for multimode models. With this established, we combine the numerical methods, matrix product states (MPS) and numerical mode decomposition (NMD), for analyzing cavity QED systems. The MPS method is used to efficiently represent and time evolve a quantum state. However, since the coupling structure of the Rabi Hamiltonian is incompatible with MPS, it is numerically transformed into an equivalent Hamiltonian that has a chain coupling structure, which allows efficient application of MPS. The technique of NMD is used to extract the numerical electromagnetic modes of an arbitrary environment. As a proof of concept, this combined approach is demonstrated by analyzing one-dimensional cavity QED systems in various settings.

Transformations which convert between fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of nonlocal games and satisfiability problems. Drawing on ideas from entanglement-assisted quantum error-correcting codes and quantum convolutional codes, we prove the obtainable lower bound for the number of qubits needed to represent such Pauli operations which are equivalent to the initial ones and provide a procedure for determining such a set of minimal register Pauli operations.

Decay rates of the positronium hydride PsH, a bound state of a proton, a positron, and two electrons, are determined for two rare channels, $\text{PsH}\to p^{+}{e}^{-}\gamma$ and $\text{PsH}\to p^{+}{e}^{-}$. Previous studies overestimated these rates by factors of about 2 and 700, respectively. We explain the physics underlying these wrong predictions. We confirm a range of static PsH properties, including the nonrelativistic ground-state energy, expectation values of interparticle distances and their powers, and the three- and four-particle coalescence probabilities, using a variational method in the Gaussian basis.