Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Many believe quantum computers will transcend such limitations although in the current era the size and noise of these devices militates against significant progress. Here we describe a chemically intuitive approach that permits a subdomain of a molecule's electronic structure to be calculated accurately on a quantum device, while the rest of the molecule is described at a lower level of accuracy using density functional theory running on a classical computer. We demonstrate that this approach produces improved results for molecules that cannot be simulated fully on current quantum computers but which can be resolved classically at a cheaper level of approximation. The algorithm is tunable, so that the size of the quantum simulation can be adjusted to run on available quantum resources. Therefore, as quantum devices become larger, this method will enable increasingly large subdomains to be studied accurately.

Bell nonlocality is the key quantum resource in some device-independent quantum information processing. It is of great importance to study the efficient sharing of this resource. Unsharp measurements are widely used in sharing the nonlocality of an entangled state shared among several sequential observers. Recently, the authors in [Phys. Rev. Lett. 129, 230402 (2022)] showed that the Bell nonlocality of two-qubit pure states can be shared even when one only uses projective measurements and local randomness. We demonstrate that projective measurements are also sufficient for sharing the Bell nonlocality of arbitrary high-dimensional pure bipartite states. Our results promote further understanding of the nonlocality sharing of high-dimensional quantum states under projective measurements.

Open quantum systems provide a conceptually simple setting for the exploration of collective behavior stemming from the competition between quantum effects, many-body interactions, and dissipative processes. They may display dynamics distinct from that of closed quantum systems or undergo nonequilibrium phase transitions which are not possible in classical settings. However, studying open quantum many-body dynamics is challenging, in particular, in the presence of critical long-range correlations or long-range interactions. Here, we make progress in this direction and introduce a numerical method for open quantum systems, based on tree tensor networks. Such a structure is expected to improve the encoding of many-body correlations and we adopt an integration scheme suited for long-range interactions and applications to dissipative dynamics. We test the method using a dissipative Ising model with power-law decaying interactions and observe signatures of a first-order phase transition for power-law exponents smaller than 1.

In this paper, we propose a method for identifying the contribution of various sources of noise to the instability of an optical lattice clock. These sources include Dick noise, quantum projection noise, shot noise, and technical noise. By measuring the clock instability at four different sets of parameters, we can determine the frequency fluctuations due to each type of noise separately. Furthermore, we can accurately extract the absolute number of atoms, the photon number detected per atom by the photoelectric detector, and the root mean square fluctuations of the atom number. We demonstrate the effectiveness of our approach through numerical simulations, showcasing the ability to determine these parameters with an uncertainty of less than 10%. Specifically, a remarkable uncertainty of 1% can be achieved when determining the atom number.

This paper proves the equality of the group velocity and the energy velocity for surface electromagnetic waves on the interface between two bianisotropic homogeneous half-infinite nonabsorbing dielectrics. It is also shown that the projection of the energy velocity on the direction of propagation is equal to the phase velocity provided that the material constants do not depend on the frequency. Moreover, this equality holds true locally, i.e., the energy velocity along the direction of propagation coincides with the phase velocity at any distance from the interface. The obtained relations holds true in magneto-optically active media as well. It is assumed that the media are of generic crystallographic symmetry, so, when deriving the desired equalities, no simplifications due to a specific crystallographic symmetry are used.

Resonant mode conversions in partially parity-time ($\mathcal{PT}$)-symmetric multimode waveguides are investigated. First, the symmetry breaking and degeneracy splitting of linear eigenmodes are found numerically and analytically. Moreover, mode conversions in the nonconservative system are demonstrated using longitudinally periodic modulation of the complex refractive index. The results show that, under the resonance condition, conversions between the unbroken modes with the same topological charge can occur, with conversion frequency being presented analytically. Finally, the influence of nonlinear effects on the resonant mode conversions is also discussed. It is found that the mode conversions depend on the dynamic equilibrium of the modes in nonlinear media, resulting in the conversions between the quadrupole modes in self-focusing medium, and the basic modes with ring structure in defocusing medium can be achieved. These results are beneficial for our further understanding of mode conversions in complex waveguides and can be applied to manipulation of the optical beam.

In this paper we provide a detailed theoretical and experimental analysis of the two-photon orbital-angular-momentum-entangled state, generated by a type-I spontaneous parametric down conversion (SPDC) process, when decomposed in terms of the helical Ince-Gauss (HIG) mode basis. By exploiting the unique characteristics of this modal basis we show how the probability detection of the photon pair can be tuned with the ellipticity parameter of the modes. We also show that on the HIG basis the SPDC state has the contribution of two different symmetric Bell states, and it is possible to maximize the probability of each HIG symmetric Bell state separately also by tuning the elipticity of the projected basis. The observed properties are confirmed experimentally by implementing measurements of the HIG modal joint probability of the SPDC two-photon state and Bell-type inequality violation experiments.

An inner (Hermitian) product of two polarization states describes the interference of polarized beams, detection and production of polarized radiation, entanglement of polarized photons, etc. Here we pose the question of expressing the inner product $\gamma \equiv \mathbf{u}{{}_1}^{†}{\mathbf{u}}_2$ of two Jones vectors (polarization states $\mathbf{u}{}_1$ and $\mathbf{u}{}_2$) explicitly in terms of ellipticities (${\epsilon }_1,{\epsilon }_2$) and tilts $({\tau }_1,{\tau }_2$) of the associated polarization ellipses. To that end, we derive a remarkably simple equation, $\gamma =cos({\tau }_2-{\tau }_1)cos({\epsilon }_2-{\epsilon }_1)+isin({\tau }_2-{\tau }_1)sin({\epsilon }_2+{\epsilon }_1)$. The Poincaré sphere interpretation in terms of distance between polarization states is given, and the Pancharatnam phase is set to $arg\left(\gamma \right)$ to show its invariance under the parity operation.

In this paper, we present a scheme to simultaneously blockade two remote magnons by coupling them to an odd-number cavity array. In the system, a two-level atom is contained in the middle cavity and two Yttrium iron garnet (YIG) spheres are placed in the symmetrical cavity to the atom. By eliminating the cavity array, a master equation with the effective coherent and dissipative couplings among the two magnons and the atom is obtained. When the frequency of the atom is outside the cavity photon band, the dissipative couplings disappear, and only coherent couplings survive, but the effective dispersive coupling strength decreases rapidly with the increasing of the distance between two YIG spheres. When the frequency of the atom is inside band, although the induced dissipation cannot be eliminated, the dissipative coupling and the coherent coupling between two YIG spheres can coexist for long distance. We further show that, under the condition of single excitation resonance, the simultaneous blockade of two remote magnons can be obtained, but the thermal noise of the magnon and atom is still required to be depressed. Thus, by coupling a local two-level atom to a cavity array, we can simultaneously blockade two remote magnons, which provides us an effective method to manipulate remote YIG spheres.

Wait-time distributions for the $n\mathrm{th}$ photodetection at a detector illuminated by a stationary light beam are studied. Both unconditional measurements, initiated at an arbitrary instant, and conditional measurements, initiated upon a photodetection, are considered. Simple analytic expressions are presented for several classical and quantum sources of light and are used to quantify and compare photon sequences generated by them. These distributions can be measured in photon-counting experiments and are useful in characterizing and generating photon sequences with prescribed statistics. The effects of nonunit detection efficiency are also discussed, and curves are presented to illustrate the behavior.

We study the non-Markovian dynamics of a two-level giant atom interacting with a one-dimensional semi-infinite waveguide through multiple coupling points, where a perfect mirror is located at the endpoint of the waveguide. The system enters a non-Markovian process when the travel time of the photon between adjacent coupling points is sufficiently large compared to the inverse of the bare relaxation rate of the giant atom. The photon released by the spontaneous emission of the atom transfers between multiple coupling points through the waveguide or is reabsorbed by the atom with the photon emitted via the atom having completed the round trip after reflection of the mirror, which leads to the photon being trapped and forming bound states. We find that three different types of bound states can be formed in the system, containing the static bound states with no inversion of population, the periodic equal amplitude oscillation with two bound states, and the periodic nonequal amplitude oscillation with three bound states. The physical origins of the three bound states' formation are revealed. Moreover, we consider the influences of the dissipation of unwanted modes and dephasing on the bound states. Finally, we extend the system to a more general case involving many giant atoms coupled into a one-dimensional semi-infinite waveguide. The obtained set of delay differential equations for the giant atoms might open a way to better understand the non-Markovian dynamics of many giant atoms coupled to a semi-infinite waveguide.

Many applications of quantum optics demand delicate quantum properties of light carefully tailored to accomplish a specific task. To this end, numerical simulations of quantum light sources are vital for designing, characterizing, and optimizing quantum photonic technology. Here, I show that exploiting information hidden in zero-photon measurement outcomes provides an exponential speedup for time-integrated photon-counting simulations, realizing eight orders of magnitude reduction in the time to compute six-photon detection probabilities while achieving 10 orders of magnitude higher precision compared to the state of the art. This enables simulations of large photonic experiments with an unprecedented level of physical detail. It can accelerate the design of sources to generate photonic resource states for quantum sensing and measurement-based quantum computing while capturing realistic imperfections. It also establishes a general theoretical framework to study dynamic interactions between stationary qubits mediated by measurements of flying qubits, which can be used to model distributed quantum computing and quantum communication.

Consider an open quantum system which interacts with its environment. Assuming that the experimenter has access only to the system, an interesting question is whether it is possible to detect initial correlations between the system and the environment by performing measurements only on the system. Various methods have been proposed to detect correlations by local measurements on the system. After reviewing these methods, we will show that initial correlations between the system and the environment are always detectable. In particular, we will show that one can always find a unitary evolution, for the whole system-environment, such that the trace distance method, proposed to witness correlations locally, succeeds. We also find the condition for existence of the optimal unitary evolution, for which the entire correlation is locally detectable. Next, we address the case where the system and the environment interact through a time-independent Hamiltonian. For this case we will see that if the initial correlation can be detected locally at some time $t$, then it can be detected for almost all the other times too. On the other hand, we see that one can find cases for which initial correlations between the system and the environment always remain undetectable even though the unitary evolution, generated by the Hamiltonian, is not factorized.

We propose a method to simulate adiabatically driven two-level quantum systems and detect the Berry phase induced in the cyclic evolution by observing the classical orbit motion of a charged particle under a time-varying magnetic field. Analogy between the dynamics of these two species of systems is revealed and the correspondence relationship is established by virtue of their equations of motion, i.e., the von Neumman equation of the quantum binary system and the Newton-Lorentz equation of the charged particle. In particular, we show how the complex phase information of the quantum system, say, the Berry phase shift acquired by its wave function during the loop evolution, can be visually captured by examining the spatial motion of the classical particle.

This paper explores the phenomenon of avoided level crossings in quantum annealing, a promising framework for quantum computing that may provide a quantum advantage for certain tasks. Quantum annealing (QA) involves letting a quantum system evolve according to the Schrödinger equation, with the goal of obtaining the optimal solution to an optimization problem through measurements of the final state. However, the continuous nature of quantum annealing makes analytical analysis challenging, particularly with regard to the instantaneous eigenenergies. The adiabatic theorem provides a theoretical result for the annealing time required to obtain the optimal solution with high probability, which is inversely proportional to the square of the minimum spectral gap. Avoided level crossings can create exponentially closing gaps, which can lead to exponentially long running times for optimization problems. In this paper, we use a perturbative expansion to derive a condition for the occurrence of an avoided level crossing during the annealing process. We then apply this condition to the MaxCut problem on bipartite graphs. We show that no exponentially small gaps arise for regular bipartite graphs, implying that QA can efficiently solve MaxCut in that case. On the other hand, we show that irregularities in the vertex degrees can lead to the satisfaction of the avoided level crossing occurrence condition. We provide numerical evidence to support this theoretical development, and discuss the relation between the presence of exponentially closing gaps and the failure of quantum annealing.

Quantum key distribution (QKD) stands as a pioneering method for establishing information-theoretically secure communication channels by utilizing the principles of quantum mechanics. In the security proof of QKD, the phase error rate serves as a critical indicator of information leakage and directly influences the security of the shared key bits between communicating parties, Alice and Bob. In estimating the upper bound of the phase error rate, phase randomization and subsequent postselection mechanisms serve pivotal roles across numerous QKD protocols. However, the nonzero interval of phase postselection will introduce intrinsic errors, leading to an overestimation of phase error rate. Here we make a precise phase-error-rate analysis for QKD protocols with phase postselection, which eliminates error rate associated with nonzero interval and helps us to accurately bound the amount of information an eavesdropper may obtain. We further apply our analysis in sending-or-not-sending twin-field quantum key distribution (SNS-TFQKD) and mode-pairing quantum key distribution (MP-QKD). The simulation results confirm that our precise phase error analysis can noticeably improve the key rate performance especially over long distances in practice. Note that our method does not require alterations to the existing experimental hardware or protocol steps. It can be readily applied within current SNS-TF-QKD and MP-QKD for higher key rate generation.

Leptoquark models may explain deviations from the standard model observed in decay processes involving heavy quarks at high-energy colliders. Such models give rise to low-energy parity- and time-reversal-violating phenomena in atoms and molecules. One of the leading effects among these phenomena is the nucleon-electron tensor-pseudotensor interaction when the low-energy experimental probe uses a quantum state of an atom or molecule predominantly characterized by closed electron shells. In the present paper the molecular interaction constant for the nucleon-electron tensor-pseudotensor interaction in the thallium-fluoride molecule—used as such a sensitive probe by the CeNTREX collaboration [O. Grasdijk et al., Quantum Sci. Technol. 6, 044007 (2021)]—is calculated employing highly correlated relativistic many-body theory. Accounting for up to quintuple excitations in the wave-function expansion the final result is $W_T\left(\mathrm{Tl}\right)=-6.25\pm 0.31$ $({10}^{-13}{\langle \mathrm{\Sigma }\rangle }_A \text{a.u.})$ Interelectron correlation effects on the tensor-pseudotensor interaction are studied rigorously in a molecule.

Following up on a previous paper on two-color photoionization of $\mathrm{Ar}\left(3p\right)$ [D. Bharti et al., Phys. Rev. A 103, 022834 (2021)], we present measurements and calculations for a modified three-sideband (3-SB) version of the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) configuration applied to $\mathrm{He}\left(1s\right)$. The 3-SB RABBITT approach allows us to explore interference effects between pathways involving different orders of transitions within the continuum. The relative differences in the retrieved oscillation phases of the three sidebands provide insights into the continuum-continuum transitions. The ground state of helium has zero orbital angular momentum, which simplifies the analysis of oscillation phases and their angle dependence within the three sidebands. We find qualitative agreement between our experimental results and the theoretical predictions for many cases but also observe some significant quantitative discrepancies.