Many promising approaches to fault-tolerant quantum computation require repeated quantum nondemolition (QND) readout of binary observables such as quantum bits (qubits). A commonly used figure of merit for readout performance is the error rate for binary assignment in a single repetition. However, it is known that this figure of merit is insufficient. Indeed, real-world readout outcomes are typically analog instead of binary. Binary assignment therefore discards important information on the level of confidence in the analog outcomes. Here, a generalized figure of merit that fully captures the information contained in the analog readout outcomes is suggested. This figure of merit is the Chernoff information associated with the statistics of the analog readout outcomes in one repetition. Unlike the single-repetition error rate, the Chernoff information uniquely determines the asymptotic cumulative error rate for arbitrary readout noise. As a result, non-Gaussian readout noise common in experiments can be described by effective Gaussian noise with the same Chernoff information. Importantly, it is shown that such a universal description persists for the small number of repetitions and non-QND imperfections relevant to real experiments. Finally, the Chernoff information is used to rigorously quantify the amount of information discarded by analog-to-binary conversion. These results provide a unified framework for qubit readout and should facilitate optimization and engineering of near-term quantum devices across all platforms.

The basic idea behind Rayleigh's criterion on resolving two incoherent optical point sources is that the overlap between the spatial modes from different sources would reduce the estimation precision for the locations of the sources, dubbed Rayleigh's curse. We generalize the concept of Rayleigh's curse to the abstract problems of quantum parameter estimation with incoherent sources. To manifest the effect of Rayleigh's curse on quantum parameter estimation, we define the curse matrix in terms of quantum Fisher information and introduce the global and local immunity to the curse accordingly. We further derive the expression for the curse matrix and give the necessary and sufficient condition on the immunity to Rayleigh's curse. For estimating the one-dimensional location parameters with a common initial state, we demonstrate that the global immunity to the curse on quantum Fisher information is impossible for more than two sources.

We present computer simulations about the spatial and temporal evolution of a 1-MeV proton microbeam transmitted through an insulating macrocapillary with the length of 45 mm and with the inner diameter of 800 μm. The axis of the capillary was tilted to 1° relative to the axis of the incident beam, which ensured geometrical nontransparency. The simulation is based on the combination of stochastic (Monte Carlo) and deterministic methods. It involves (1) random sampling of the initial conditions, according to distributions generated by the widely used and freely available computer software packages, srim and wintrax, (2) the numerical solution of the governing equations for following the classical trajectory of the projectiles, and (3) the description of the field-driven charge migration on the surface and in the bulk of the insulator material. We found that our simulation describes reasonably all of our previous experimental observations, indicating the functionality and reliability of the applied model. In addition, we found that at different phases of the beam transmission, different atomic processes result in the evolution of the beam distribution. First, in a scattering phase, the multiple small angle atomic scattering dominates in the beam transmission, resulting in an outgoing beam into a wide angular range and in a wide energy window. Later, in a mixed phase, scattering and guiding happens simultaneously, with a continuously increasing contribution of guiding. Finally, in the phase of the stabilized, guided transmission, a quadrupolelike focusing effect is observed, i.e., the transmitted beam is concentrated into a small spot, and the transmitted protons keep their initial kinetic energy.

The present constraint on the space parity $\mathcal{P}$ and time-reflection invariance $\mathcal{T}$ violating the electron electric dipole moment $\left(e\mathrm{EDM}\right)$ is based on the observation of the electron-spin precession in an external electric field using the ThO molecule. We propose an alternative approach: observation of the $\mathcal{P},\mathcal{T}$-odd Faraday effect in an external electric field using the cavity-enhanced polarimetric scheme in combination with a molecular beam crossing the cavity. Our theoretical simulation of the proposed experiment with the PbF and ThO molecular beams shows that the present constraint on the $e\mathrm{EDM}$ in principle can be improved by a few orders of magnitude.

We report the efficient and fast $(\sim 2\mathrm{Hz})$ preparation of randomly loaded one-dimensional (1D) chains of individual ${}^{87}\mathrm{Rb}$ atoms and of dense atomic clouds trapped in optical tweezers using an upgraded experimental platform. This platform is designed for the study of atomic ensembles featuring either ordered or disordered distributions of the atomic positions. It is composed of two high-resolution optical systems perpendicular to each other, enhancing observation and manipulation capabilities. The setup includes a dynamically controllable telescope, which we use to vary the tweezer beam waist. A $\mathrm{\Lambda }$-enhanced gray molasses on the D1 line enhances the loading of the traps from a magneto-optical trap. Using these tools, we prepare chains of up to $\sim 100$ atoms separated by $\sim 1\mu \mathrm{m}$ by retroreflecting the tweezer light, hence producing a 1D optical lattice with strong transverse confinement. Dense atomic clouds with peak densities up to $n_0\sim {10}^{15}$ $\mathrm{atoms}/{\mathrm{cm}}^3$ are obtained by compression of an initial cloud. This high density results in interatomic distances smaller than $\lambda /\left(2\pi \right)$ for the D2 optical transitions, making it ideal to study light-induced interactions in dense samples.

We study ultracold color fermions with three internal states, red, green, and blue, with $\mathrm{SU}\left(3\right)$ symmetry in optical lattices, when color-orbit coupling and color-flip fields are present. This system corresponds to a generalization of two internal state fermions with $\mathrm{SU}\left(2\right)$ symmetry in the presence of spin-orbit coupling and spin-flipping Zeeman fields. We investigate the eigenspectrum and Chern numbers to describe different topological phases that emerge in the phase diagrams of color-orbit coupled fermions in optical lattices. We obtain the phases as a function of artificial magnetic, color-orbit, and color-flip fields that can be independently controlled. For fixed artificial magnetic flux ratio, we identify topological quantum phases and phase transitions in the phase diagrams of chemical potential versus color-flip fields or color-orbit coupling, where the chirality and number of midgap edge states changes. The topologically nontrivial phases are classified in three groups: The first group has total nonzero chirality and exhibits only the quantum charge Hall effect; the second group has total nonzero chirality and exhibits both quantum charge and quantum color Hall effects; and the third group has total zero chirality but exhibits the quantum color Hall effect. These phases are generalizations of the quantum Hall and quantum spin Hall phases for charged spin-$1/2$ fermions. Lastly, we also describe the color density of states and a staircase structure in the total and color filling factors versus chemical potential for fixed color-orbit coupling, color-flip field, and magnetic flux ratio. We show the existence of incompressible states at rational filling factors precisely given by a gap labelling theorem that relates the filling factors to the magnetic flux ratio and topological quantum numbers.

Communal pairing in superconductors introduces variational freedom for Cooper pairs to share fermions. Temporal oscillations of the superconducting gap entropically drive communal pairing through the order by disorder phenomenology, stabilizing a finite momentum space width of the superconducting gap that increases with interaction strength, creating a smooth evolution from the weakly interacting BCS state to the strongly interacting Bose-Einstein condensate state.

We demonstrate an atomic Faraday dichroic beam splitter suitable for spatially separating signal and idler fields from pump degenerate four-wave mixing in an atomic source. By rotating the plane of polarization of one mode ${90}^{\circ }$ with respect to the other, a subsequent polarizing beam splitter separates the two frequencies, which differ by only 13.6 GHz, and achieves a suppression of $(-26.3\pm 0.1)$ and $(-21.2\pm 0.1)$ dB in the two outputs, with a corresponding transmission of 97% and 99%, respectively. This technique avoids the necessity of using spatial separation of four-wave mixing modes and thus opens the door for enhancing the process efficiency in waveguide experiments. As a proof of principle, we generate light via four-wave mixing in ${}^{87}\mathrm{Rb}$ loaded into a hollow-core photonic crystal fiber and interface it with the atomic Faraday dichroic beam splitter.

Large clouds of cold atoms prepared in a magneto-optical trap are known to present spatiotemporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears similarities with trapped plasmas where the role of the Coulomb interaction is played by the exchange of scattered photons, and astrophysical objects, such as stars whose size is dependent on radiative forces. We present in this paper a study of the phase space of such instabilities and reveal different dynamical regimes. Three-dimensional simulations of the highly nonlinear atomic dynamics permit a detailed analysis of the experimental observations.

Observations and studies of what we call magnetic induced transitions have arguably re-opened a whole new area of atomic spectroscopy. There are transitions from upper levels that are sensitive to externally applied magnetic fields, such as those in tokamaks and the solar corona. So far only two types of ionic systems have been confirmed as leading to magnetic induced transitions, namely Ne-like Ar and Fe, and Cl-like Fe. We here propose a homologous system to Cl-like ions, namely Br-like ions, as a new candidate. These transitions are fed by close degeneracy between levels of relative short and long lifetimes, respectively. A similar close degeneracy as in Cl-like Fe is present in Br-like Sr and will give rise to an observable magnetic induced transition. We have predicted the magnetic induced transition rate for the ${}^4{D}_{7/2}$ level in Sr iv as a function of magnetic field strengths.

In this paper, we present a proof of principle of the formation of pure maximally entangled states from the Greenberger-Horne-Zeilinger (GHZ) class, in the experimental context of charged quantum dots. Each qubit must be identified as a pair of quantum dots, sharing an excess electron, coupled by tunneling. The electron-electron interaction is accounted for and is responsible for the coupling between the qubits. The interplay between coherent tunneling events and many-body interaction gives rise to the formation of highly entangled states. We begin by treating the problem of encoding three qubits in a system with three pairs of quantum dots, and the numerical analysis of the exact quantum dynamics to find the conditions for the generation of the GHZ states. An effective two-level model sheds light on the role of a high-order tunneling process behind the dynamics. The action of the main decoherence process, the charge dephasing, is quantified in the process. We then evaluate the physical requirements for the dynamical generation of GHZ states in an $N$-qubit scenario, and its challenges.

We present a detailed description of the diagrammatic technique for a semianalytical description of large-scale quantum repeater networks devised recently by V. V. Kuzmin et al. [npj Quantum Inf. 5, 115 (2019)]. The technique takes into account all essential experimental imperfections, including continuous dissipative Liouville dynamics of the network quantum memories and the classical communication delays. The results obtained with the semianalytic method match the exact Monte Carlo simulations while the required computational resources scale only linearly with the network size, thus allowing for precise comparison and optimization of large-scale quantum networks subjected to relevant realistic imperfections. We illustrate the potential of the method by optimizing the secret key rate in one- and two-dimensional quantum networks for a range of network sizes and memory coherence times. The presented approach opens new possibilities for the development and efficient optimization of future quantum networks.

A quantum battery is a temporary energy-storage system. We construct a quantum battery model of an $N$-spin chain with nearest-neighbor hopping interaction and investigate the quantum battery's charging process. We obtain the maximum energy in the quantum battery charged by a coherent cavity driving field or a thermal heat bath. We confirm that for a finite-length spin chain, thermal charging results in a nonzero ergotropy, contradicting a previous result: An incoherent heat source cannot charge a single-spin quantum battery. The nearest-neighbor hopping interaction induces energy-band splitting, enhancing the energy storage and the ergotropy of the quantum battery. We find a critical point in the energy and ergotropy resulting from the ground-state quantum phase transition after which the energy significantly enhances. Finally, we also find that disorder increases the energy of the quantum battery.

The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a particular choice of system-detector coupling, the Zeno effect is avoided and the system can be described effectively by a non-Hermitian effective Hamiltonian. As a specific example we consider the evolution of a quantum particle on a one-dimensional lattice that is subjected to position measurements at a specific site. By solving the corresponding non-Hermitian wave-function evolution equation, we present analytic closed-form results on the survival probability and the first arrival time distribution. Finally we discuss the limit of vanishing lattice spacing and show that this leads to a continuum description where the particle evolves via the free Schrödinger equation with complex Robin boundary conditions at the detector site. Several interesting physical results for this dynamics are presented.

We study the role of driving in an initial maximally entangled state evolving under the presence of a structured environment in a weak and strong regime. We focus on the enhancement and degradation of maximal concurrence when the system is driven on and out of resonance for a general evolution, as well as the effect of adding a transverse coupling among the particles of the model. We further investigate the role of driving in the acquisition of a geometric phase for the maximally entangled state. As the model studied herein can be used to model experimental situations such as hybrid quantum classical systems feasible with current technologies, this knowledge can aid the search for physical setups that best retain quantum properties under dissipative dynamics.

We combine the dynamics of open quantum systems with interferometry and interference, introducing the concept of an open system interferometer. By considering a single photon in a Mach-Zehnder interferometer, where the polarization (open system) and frequency (environment) of the photon interact, we theoretically show that inside the interferometer, pathwise polarization dephasing dynamics is Markovian while the joint dynamics displays non-Markovian features. Outside the interferometer and due to interference, the open system displays rich dynamical features with distinct alternatives: only one path displays non-Markovian memory effects, both paths individually display them, or no memory effects appear at all. The scheme allows one to (1) probe the optical path difference inside the interferometer by studying pathwise non-Markovianity outside the interferometer, and (2) introduce pathwise dissipative features for the open system dynamics even though the system-environment interaction itself contains only dephasing. Due to the path dependencies, our results are tightly connected to quantum erasure. In general, our results open up alternative ways to control open system dynamics and for fundamental studies of quantum physics.

One can think of some physical evolutions as being the emergent-effective result of a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide a simple procedure to coarse-grain color-blind quantum cellular automata that follow the so-called Goldilocks rules. The procedure consists in (i) space-time grouping the quantum cellular automaton (QCA) in cells of size $N$; (ii) projecting the states of a cell onto its borders, connecting them with the fine dynamics; (iii) describing the overall dynamics by the border states, that we call signals; and (iv) constructing the coarse-grained dynamics for different sizes $N$ of the cells. A by-product of this simple toy model is a general discrete analogous of the Stokes law. Moreover we prove that in the space-time limit, the automaton converges to a Dirac free Hamiltonian. The QCA we introduce here can be implemented by present-day quantum platforms, such as Rydberg arrays, trapped ions, and superconducting qubits. We hope our study can pave the way to a richer understanding of those systems with limited resolution.

We present an alternative approach to unveil a different kind of entanglement in bipartite quantum states whose diagonal zero patterns in suitable matrix representations admit a nice description in terms of triangle-free graphs. Upon application of a local averaging operation, the separability of such states transforms into a simple matrix positivity condition, the violation of which implies the presence of entanglement. We completely characterize the class of triangle-free graphs, which allows for nontrivial entanglement detection using the above test. Moreover, we develop a recipe to construct a plethora of unique classes of positive partial transpose (PPT) entangled states in arbitrary dimensions. Finally, we link the task of entanglement detection in general states to the well-known graph-theoretic problem of finding triangle-free-induced subgraphs in a given graph.

Recently, a theoretical method and corresponding experiment have shown that the information about entanglement in the state of the qubit photon pair can be retrieved by measuring only one of the photons, even though the state is mixed. In this paper, we investigate this process with the high-dimensional photon pair and more information about the state. We present a method that enables us to determine the state of the photon pair fully. Our method measures only one of the photons while dropping the other one. Importantly, no adjustment of the transformation is required in our method. Moreover, our method is robust to photon loss so that the state can be perfectly determined as long as the photon is not all lost.

A generic qubit unitary operator affected by depolarizing noise is duplicated and inserted in a quantum switch process, realizing a superposition of causal orders. The characterization of the resulting switched quantum channel is worked out for its action on the joint state of the probe-control qubit pair. The switched channel is then specifically investigated for the important metrological task of phase estimation on the noisy unitary operator, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional techniques of estimation where the noisy unitary is directly probed in a one-stage or two-stage cascade with definite order or several uses of them with two or more qubits. In the switched channel with indefinite order, specific properties are reported, meaningful for estimation and not present with conventional techniques. It is shown that the control qubit, although it never directly interacts with the unitary, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. Also, measurement of the control qubit maintains the possibility of efficient estimation in difficult conditions where conventional estimation becomes less efficient, as for instance with ill-configured input probes, or in blind situations when the axis of the unitary is unknown. Effective estimation by measuring the control qubit remains possible even when the input probe tends to align with the axis of the unitary, or with a fully depolarized input probe, while in these conditions conventional estimation becomes inoperative. Measurement of the probe qubit of the switched channel is also analyzed and shown to add useful capabilities for phase estimation. The results contribute to the ongoing identification and analysis of the properties and capabilities of switched quantum channels with indefinite order for information processing and uncover new possibilities for quantum estimation and qubit metrology.