Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into a few copies of nearly pure states of high quality via local operations and classical communication. Especially in the multiparticle case, the task of entanglement purification is complicated, as many inequivalent forms of pure state entanglement exist and purification protocols need to be tailored for different target states. In this paper we present optimized protocols for the purification of hypergraph states, which form a family of multiqubit states that are relevant from several perspectives. We start by reformulating an existing purification protocol in a graphical language. This allows for systematical optimization and we present improvements in three directions. First, one can optimize the sequences of the protocol with respect to the ordering of the parties. Second, one can use adaptive schemes, where the measurement results obtained within the protocol are used to modify the protocols. Finally, one can improve the protocol with respect to the efficiency, requiring fewer copies of noisy states to reach a certain target state.

Currently, there is great interest in laser cooling of barium monofluoride (BaF) molecules for precision tests of fundamental symmetries. We use high-resolution absorption spectroscopy to characterize several as yet imprecisely known transition frequencies required to realize such cooling. We extract an improved set of molecular constants for the bosonic ${}^{138}\mathrm{Ba}{}^{19}\mathrm{F}$ and ${}^{136}\mathrm{Ba}{}^{19}\mathrm{F}$ isotopologues, confirm the existence of a significant hyperfine splitting in the excited state of the laser cooling cycle, and investigate the effects of this splitting on the achievable cooling forces. As a direct application of our spectroscopic insights, we experimentally demonstrate nearly background-free fluorescence imaging of a BaF molecular beam in a glass cell vacuum chamber. We expect such high-fidelity detection to be useful for various types of precision measurement scenarios.

We calculate the hyperfine structure of ${}^{229}\mathrm{Th}$ and its ions (Th iv, Th iii, Th ii, Th i) to reveal the dependence of the nuclear clock frequency on the hyperfine interaction (HFI). We calculate first- and second-order HFI shifts and demonstrate that due to the differences in the hyperfine structure for different ions and for the ground and isomeric nuclear states the nuclear frequencies in Th iv, Th iii, Th ii, and Th i are also different. The first-order shift of frequency is large for a particular hyperfine component, but it vanishes after averaging over all hyperfine states. The second-order shift is small but it does not vanish after averaging. It is 3 to 6 orders of magnitude smaller than the shift of the nuclear frequencies due to the Coulomb electron-nucleus interaction considered in our previous work (V. A. Dzuba and V. V. Flambaum, arXiv:2309.11176.). However, it is 6 to 8 orders of magnitude larger than the projected accuracy of the nuclear clock $\left({10}^{-19}\right)$.

Dynamic tuning of optical cavities is highly desired in many photonic systems. Here, we show that Fabry-Pérot (FP) cavities can be actively controlled by the Casimir force. The optical FP cavities consist of a gold nanoplate approaching to an electrical-connecting multilayer substrate in a liquid environment. The gold nanoplate can be stably suspended due to the balance of repulsive and attractive Casimir forces. Moreover, the suspension distance is modulated strongly by the electric gating or temperature of the system. As a result, we could shift the resonant wavelengths of the cavities with tens of nanometers at optical frequencies. Finally, we analyze the influence of Brownian motion on the equilibrium distances. Due to the high $Q$ factor of the FP cavities, our proposed system offers a remarkable platform to experimentally investigate the thermal Casimir effect at submicrometer separations.

We consider a closed quantum system subjected to stochastic Poissonian resetting with rate $r$ to its initial state. Resetting drives the system to a nonequilibrium stationary state (NESS) with a mixed density matrix which has both classical and quantum correlations. We provide a general framework to study these NESS correlations for a closed quantum system with a general Hamiltonian $H$. We then apply this framework to a simple model of a pair of ferromagnetically coupled spins, starting from state $\mid \downarrow \downarrow \rangle$ and resetting to the same state with rate $r$. We compute exactly the NESS density matrix of the full system. This then provides access to three basic observables, namely, (i) the von Neumann entropy of a subsystem, (ii) the fidelity between the NESS and the initial density matrix, and (iii) the concurrence in the NESS (that provides a measure of the quantum entanglement in a mixed state), as a function of the two parameters: the resetting rate and the interaction strength. One of our main conclusions is that a nonzero resetting rate and a nonzero interaction strength generate quantum entanglement in the NESS (quantified by a nonzero concurrence) and moreover this concurrence can be maximized by appropriately choosing the two parameters. Our results show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of an interacting quantum system.

In this study we investigate how correlations of a multipartite quantum system affect its thermodynamics when subsystems of which interact with a thermal reservoir in a cascaded manner. We propose the concept of apparent temperature for an individual subsystem, which is determined by one-way correlations of the subsystem with its preceding subsystems and governs the direction of heat flow between the subsystem and reservoir. We demonstrate the possibility of reversing heat flow between the subsystem and reservoir conditioned on the apparent temperature and derive the conditions for achieving this reversal. We also examine the entropy production of this thermodynamic process and observe a tradeoff between contributions from one-way and global correlations to entropy production. Our results provide insight into the roles of one-way multipartite correlations on thermodynamic properties and expand the ways of applications of quantum resources in the area of thermodynamics.

Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates and make quantum algorithms fundamentally different from their classical counterparts. Based on this unique principle of quantum computing, we develop an algorithmic toolbox, quantum phase processing, that can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator. The quantum phase processing circuit is constructed simply, consisting of single-qubit rotations and controlled unitaries, typically using only one ancilla qubit. Besides the capability of phase transformation, quantum phase processing in particular can extract the eigeninformation of quantum systems by simply measuring the ancilla qubit, making it naturally compatible with indirect measurement. Quantum phase processing complements another powerful framework known as quantum singular value transformation and leads to more intuitive and efficient quantum algorithms for solving problems that are particularly phase related. As a notable application, we propose a quantum phase estimation algorithm without quantum Fourier transform, which requires the fewest ancilla qubits and matches the best performance so far. We further exploit the power of our method by investigating a plethora of applications in Hamiltonian simulation, entanglement spectroscopy, and quantum entropy estimation, demonstrating improvements or optimality for almost all cases.

A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multibody observables. One strategy to reduce circuit depth in such algorithms involves simultaneous diagonalization of Pauli operators generating unitary evolution operators or observables of interest. We propose an algorithm yielding quantum circuits with depths $O(nlogr)$ diagonalizing $n$-qubit operators generated by $r$ Pauli operators. Moreover, as our algorithm iteratively diagonalizes all operators on at least one qubit per step, it is well suited to maintain low circuit depth even on hardware with limited qubit connectivity. We observe that our algorithm performs favorably in producing quantum circuits diagonalizing randomly generated Hamiltonians as well as molecular Hamiltonians with short depths and low two-qubit gate counts.

Partial information decomposition (PID) takes one step beyond Shannon's theory in decomposing the information two variables, $A$ and $B$, possess about a third variable, $\mathcal{T}$, into distinct parts: unique, shared (or redundant), and synergistic information. Here we show how these concepts can be defined in a quantum setting. We apply a quantum PID to scrambling in quantum many-body systems, for which a quantum-theoretic description has been proven to be productive. Unique information in particular provides a finer description of scrambling than does the so-called tri-information.

We consider a multiparameter quantum metrology problem with bright soliton networks in the presence of weak losses. We introduce the general Heisenberg limit (GHL) ${\sigma }_{\mathit{\chi }}=1/N^k$ that characterizes fundamental limitations for unknown parameter measurement and estimation accuracy ${\sigma }_{\mathit{\chi }}$ within linear ($k=1$) and nonlinear ($k=3$) quantum metrology approaches to solitons. We examine multipartite NOON states specially prepared for the improvement of multiparameter estimation protocols. As a particular example of producing such states, we propose a three-mode soliton Josephson-junction (TMSJJ) model as a three-mode extension for the soliton Josephson-junction bosonic model, which we previously proposed. The energy spectrum of the TMSJJ exhibits sharp phase transition peculiarities for the TMSJJ ground state. The transition occurs from a Gaussian-like (coherent) state to the superposition of entangled Fock states, which rapidly approach the three-mode NOON state. We show that in the presence of weak losses the TMSJJ enables saturation scaling relevant to the optimal state limit close to the GHL. Our findings open prospects for quantum network sensorics with atomtronic circuits.

The slow light propagation effect in electromagnetically induced transparency with a spatial partially coherent coupling field has been studied. We find that the group velocity of the probe beam can be significantly reduced when the spatial coherence of the coupling field decreases. It shows that the group delay of the probe beam can achieve about 10 times that of the fully coherent case. This work shows the effect of spatial coherence of the coupling field in a coherent atomic medium and provides a slow-light mechanism in optical coherence systems.

Exact single photons cannot be generated on demand due to their infinite tails. To quantify how close realizable optical states can be to some target single photon in one dimension, we argue that there are two natural but incompatible ways to specify the target state. Either it can be expressed as a photon with a chosen positive-frequency spectrum, or it can be described as an (unphysical) photon in a chosen positive-time pulse. The results show that for sufficiently short target pulses, the closest realizable states contain substantial multiphoton components. Upper and lower bounds for the maximum fidelity are derived and are expressed as functions of the size of the target state's tail, for negative time or negative frequency, respectively. We also generalize the bounds to arbitrary photon-number states.

In this study, we explore the breaking of time-reversal symmetry in a scalable cavity quantum electrodynamics (QED) lattice. Such a lattice consists of triangular cells of three cavities coupled to a two-level atom. We synthesize artificial magnetic fields to enable the chiral transfer of photons by sinusoidally modulating the cavity frequencies. Considering various configurations with different numbers of cells in the system, we analyze the circulation of photons and investigate the effect of the frequency modulation on the control of the state transfer in the system. We show the breaking and sustaining of time-reversal symmetry in certain system geometries and consider the scalability of the generating synthetic magnetic field in the system. Our study highlights the potential of scalable cavity QED lattices with synthetic magnetic fields as a versatile tool for investigating quantum phenomena and shows the utility of these systems to serve as test beds for the simulation of condensed matter systems in quantum optical settings.

The Rayleigh-Ritz variation principle is a proven way to find ground states and energies for bound quantum systems in the Schrödinger picture. Advances in machine learning and neural networks make it possible to extend it from an analytical search from a subspace of the complete Hilbert space to the a numerical search in the almost complete Hilbert space. In this paper, we extend the Rayleigh-Ritz principle to Nelson's stochastic mechanics formulation of nonrelativistic quantum mechanics and propose an algorithm to find the osmotic velocities $u\left(x\right)$, which contain the information of a quantum systems in this picture. As a proof of concept, we calculated $u\left(x\right)$ for one-dimensional systems, the harmonic oscillator, the double well and the Pöschl-Teller potential. To obtain exited states, we calculate ground states of supersymmetrical partner Hamiltonians for each of these potentials. We will show that this method is more efficient than the stochastic optimal control algorithm that was the usual method to obtain osmotic velocities without going back to the Schrödinger equation.

In traditional scattering theory, the incident projectile is assumed to have an infinite coherence length. However, over the last decade, experimental and theoretical studies of collisions using heavy ion projectiles have shown that this assumption is not always valid. This has led to a growing number of studies that specifically examine the effects of the projectile's coherence length on collision cross sections. These studies have used heavy ion projectiles because they offer a straightforward method to control the projectile's coherence length through its momentum, and using these techniques, it has been demonstrated that the projectile's coherence length alters the cross sections. In contrast, it is widely presumed that the coherence length of an electron projectile is always sufficiently large that any effects on the cross sections can be safely neglected. We show that, contrary to this prevailing opinion, coherence effects are observable for electron projectiles and they can be controlled. We calculate triple differential cross sections (TDCSs) for ionization of ${\mathrm{H}}_2^{+}$ using twisted electron projectiles in the form of Laguerre-Gauss and Bessel electrons. Effects of the projectile's coherence length are observed through the presence or absence of two-slit interference features in the TDCSs. When the electron projectile's coherence length is large, ionization occurs from either nuclear center of the molecule, and two-slit interference features are visible in the TDCSs. In contrast, when the projectile's coherence length is small, ionization occurs from only one nuclear center and the TDCSs resemble those for ionization of atomic hydrogen. We demonstrate that the intrinsic parameters of the vortex projectiles, such as beam waist and opening angle, can be used to control the coherence length of electron projectiles.

We investigate the Casimir-Lifshitz force (CLF) between two identical graphene strip gratings, laid on finite dielectric substrates by using the scattering matrix ($S$-matrix) approach derived from the Fourier modal method with local basis functions (FMM-LBF). We fully take into account the high-order electromagnetic diffractions, the multiple scattering and the exact two-dimensional feature of the graphene strips. We show that the nonadditivity, which is one of the most interesting features of the CLF in general, is significantly high, and can be modulated in situ, without any change in the actual material geometry and this by varying the graphene chemical potential. We discuss the nature of the geometrical effects and show the relevance of the geometric parameter $d/D$ (i.e., the ratio between separation and grating period), which allows to explore the regions of parameters where the additive result is fully acceptable or where the full calculation is needed. This study can open to deeper experimental exploration of the nonadditive features of the CLF with micro or nanoelectromechanical graphene-based systems.

We address extreme-ultraviolet (XUV) initiated high-order harmonic generation (XIHHG) in argon atoms observing a resonant enhancement of the high-energy harmonics when the XUV pulse energy is tuned to the well-known window resonance. We attribute this effect to a three-stage mechanism: excitation of the $3s3p^{6}4p$ window resonance, followed by field-assisted autoionization and strong-field driven recollision. We also verify that the observed effect is robust against intensity-averaging, increasing the possibility that it may be observed experimentally. The resonant XIHHG mechanism represents an important addition to the attosecond toolset, as experimental schemes to identify signatures of correlation have heretofore proved elusive.