We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, and the lower bounds of concurrence. We show by detailed examples that our separability criteria, entanglement witnesses, and lower bounds can detect and estimate the quantum entanglement better than existing related results.

Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study boson sampling from general, single-mode states using a scheme that can generate any such state by combining Gaussian states and photon number measurements. We derive a formula that can be used to calculate the output photon number probabilities of these states after they travel through a linear interferometer. This extends the Boson sampling protocol to the widest array of possible single-mode states and from this we show that the complexity scaling of all such states is similar and hence there is no complexity advantage of using complex input states over simpler ones.

Recent calculations have suggested that it may be feasible to produce antihydrogen molecular ions in the near future [Zammit et al., Phys. Rev. A 100, 042709 (2019)]. The proposed scheme would laser excite cold antihydrogen $\overline{\text{H}}\left(1s\right)$ atoms held in a magnetic-field minimum trap and the resulting metastable $\overline{\text{H}}\left(2s\right)$ atoms would interact to form the antihydrogen molecular ion, ${\overline{\text{H}}}_2{}^{-}$, by associative ionization. Estimates for the efficiencies of the proposed formation and depletion processes relied on low-energy extrapolations of rate coefficients that were computed at thermal energies. In the present work, we provide quantum calculations of the rate coefficients for associative ionization and for the competing Penning ionization process, which would deplete the population of trapped $\overline{\text{H}}$. In contrast to the low-energy extrapolations, it is found that Penning ionization is the dominant ionization process at all temperatures and the relative efficiency of associative ionization is within a factor of 3 at the low temperatures required by the experimental scheme. Rate constants for single and double excitation transfer are computed as possible loss mechanisms and all rates are found to be small compared to spin-flip decay rates from Stark-induced mixing with $\overline{\text{H}}(2p$) states.

The nonlocal resonance models for nuclear dynamics of low-energy electron-molecule collisions are usually constructed by fitting necessary quantities to the potential energy curves (surfaces) and the eigenphase sums obtained from fixed-nuclei quantum chemistry and scattering calculations. Moreover, the fitting functions have to be chosen in such a way to be able to evaluate the Hilbert transform, which appears in the nonlocal potential, in a closed form. This procedure can be rather elaborate for polyatomic molecules when more than one degree of freedom for nuclear motion is considered. In this paper we propose an alternative, fitting-free way of constructing these models directly from the fixed-nuclei level-shift function that is completely determined by the choice of the discrete state defining the nonlocal resonance model. The Hilbert transform is evaluated numerically using the fast Fourier transform. Using the numerically solvable two-dimensional model of resonant electron-molecule collisions, we demonstrate that the results of nonlocal models constructed using the proposed approach agree with the exact ones up to contributions from background scattering, which can often be neglected for inelastic processes. For completeness, we also compare the results of the proposed method with the usual fitting approach, showing that the proposed fitting-free method of construction of the nonlocal resonance models is more reliable and accurate.

A method combining the Lagrange-mesh and the complex Kohn variational methods is developed for computing the $\mathcal{S}$ matrix of a $2+1$ elastic scattering in the frame of three-body Coulomb systems. Resonance parameters can be obtained from values of the $\mathcal{S}$ matrix at several scattering energies. The method is illustrated with the $S$-wave low-energy scattering of an electron onto hydrogen. The computed phase shifts are at least as accurate as the best literature results. Both the infinite and finite proton mass cases are considered.

We study the propagation of a weak probe field through a dissipative optomechanical system, in which an additional weak mechanical drive is acting directly on a vibrating waveguide. In the presence of a strong coupling field, when the frequency of the mechanical drive precisely matches the frequency difference between the probe and coupling fields, we show that the nearly perfect absorption, complete transmission, and significant amplification of the probe field can be achieved by adjusting the amplitude and phase of the mechanical drive and the power of the coupling field. Moreover, by appropriately choosing the amplitude and phase of the mechanical drive, the group delay of the output probe field is tunable from a large negative value to a large positive value and vice versa. Our study offers an alternative way to control and manipulate the propagation of a weak probe field in a dissipative optomechanical system.

We numerically and experimentally demonstrate the nonlinear continuous modulation of orbital angular momentum (OAM) of a linearly polarized high-order Bessel beam in a biased photorefractive (PR) crystal. According to the simulation results, we identify three nonlinear dynamic regimes depending on the strength of the applied electric field, and we successfully stabilize the OAM via the modulation of a background illumination. As a result, we predict a parabolic trend for the maximal OAM modulation range in the stable regime. In addition, with the comparative analysis between vortex and differently truncated Bessel beams, we report the existence of exploitable plateaus, enabling a more extensive modulation range in the unstable regime. The experimental results are consistent with the simulations, confirming the practical realization of the flexible control of the OAM in both stationary and dynamic regimes. These results contribute to new reconfigurable components in OAM-based communications.

We consider a quantum particle under the dynamical confinement caused by $PT$-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schrödinger equation obeying the time-dependent $PT$-symmetric boundary conditions. The class of the functions, describing time dependence of the wall's position and keeping the system as $PT$-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. It is found that the behavior of the average kinetic energy as a function of time is completely different than that for of Hermitian counterpart of the model, while the average quantum force behaves similarly to that for Hermitian system. Also, geometric phase is calculated for the harmonically oscillating wall regime. The experimental realization of the proposed model is discussed.

In quantum optics, measurement statistics—for example, photocounting statistics—are considered nonclassical if they cannot be reproduced with statistical mixtures of classical radiation fields. We have formulated a necessary and sufficient condition for such nonclassicality. This condition is given by a set of inequalities that tightly bound the convex set of probabilities associated with classical electromagnetic radiation. Analytical forms for full sets and subsets of these inequalities are obtained for important cases of realistic photocounting measurements and unbalanced homodyne detection. As an example, we consider photocounting statistics of phase-squeezed coherent states. Contrary to a common intuition, the analysis developed here reveals distinct nonclassical properties of these statistics that can be experimentally corroborated with minimal resources.

We propose a heralded single-photon source based on injecting a superposition of oppositely squeezed states onto a beam splitter. Our superposition of squeezed states is composed of only even photon number states (the number of photons is equal to $2,6,10,...$) meaning the probability for an emitted single photon given as a heralded single-photon event is higher than what one can achieve from the usual two-mode squeezed state. This enables one to realize an enhanced heralded single-photon source. We discuss how to create this superposition of squeezed states utilizing a single-mode squeezed state and the cross-Kerr nonlinearity. Our proposed method significantly improves the probability of emitting the heralded single photon compared to spontaneous parametric down-conversion.

Quantum state discrimination is one of the most fundamental problems in quantum information theory, with applications ranging from channel coding to metrology and cryptography. In this work, we introduce a variant of this task: local simultaneous state discrimination (LSSD). While previously studied distributed variants of state discrimination allowed some communication between the parties to come up with a joint answer, in LSSD they cannot communicate and have to simultaneously answer correctly. We illustrate by multiple examples that this problem significantly differs from single-party state discrimination, even when the states are completely classical. We show that an additional entangled resource can increase the optimal success probability in LSSD, and stronger-than-quantum no-signaling resources can allow for an even higher success probability. We also show that finding the optimal strategy in (classical) three-party LSSD is NP-hard. Furthermore, we provide an example of symmetric LSSD for which the optimal strategy is not symmetric, and prove a sufficient condition for the existence of an optimal symmetric strategy. While interesting in its own right, the LSSD problem also arises in quantum cryptography. In particular, we explore the connections between the problem of unclonable encryption and LSSD. We give an explicit cloning-indistinguishable attack that succeeds with probability $1/2+\mu /16$ where $\mu$ is related to the largest eigenvalue of the resulting quantum ciphertext states.

In this paper we study the universal V-basis gate sets, which have also been shown to be fault tolerant. Our methods and results can be applied to arbitrary dimensional basis gates, but we explicitly state results for basis gates for SU(2) and SU(4). We also include Cliffords, as done in earlier works. We introduce generating sets in order to represent any unitary implementable by these gate sets and with these we derive a bound on the V count of arbitrary multiqubit unitaries. We analyze the channel representation of the generating set elements, with the help of which we infer that none of these basis gates can be implemented exactly with the other universal fault-tolerant gate sets like Clifford+T, Clifford+CS, Clifford+Toffoli. Also T, CS, and Toffoli cannot be exactly implemented in the V basis. In fact, basis unitaries in dimension four cannot be implemented exactly with those in dimension two. We develop V-count-optimal synthesis algorithms for both approximately and exactly implementable multiqubit unitaries. With the help of these we show that two basis unitaries in dimension four are required to implement each basis unitary in dimension two. The space and time complexities of our provable algorithms are exponential in V count. But for the special case of one-qubit unitaries we achieve a complexity that is linear in V count. Both space and time complexities of our heuristic algorithms are polynomial in V count.

Interest in the Werner-Holevo channel ${\mathrm{\Lambda }}_1\left(\rho \right)=\frac{1}{2}[\mathrm{tr}\left(\rho \right)I-{\rho }^T]$ has been mainly due to its abstract mathematical properties. We show that in three dimensions and with a slight modification, this channel can be realized as the rotation of qutrit states in random directions by random angles. Our modification takes the form ${\mathrm{\Lambda }}_x\left(\rho \right)=(1-x)\rho +x{\mathrm{\Lambda }}_1\left(\rho \right)$. Therefore, and in view of the potential use of qutrits in quantum processing tasks and their realization in many different platforms, the modified Werner-Holevo channel can be used as a very simple and realistic noise model, in the same way that the depolarizing channel is for qubits. We will make a detailed study of this channel and derive its various properties. In particular, we will use the recently proposed flag extension and other techniques to derive analytical expressions and bounds for the different capacities of this channel. The role of symmetry is revealed in these derivations. We also rigorously prove that the channel ${\mathrm{\Lambda }}_x$ is antidegradable and hence has zero quantum capacity, in the region $\frac{4}{7}\le x\le 1.$

For nonreciprocal objects in vacuum, the Casimir interaction can become repulsive. Here, we present a comprehensive study for idealized nonreciprocal materials known as perfect electromagnetic conductors (PEMC). The system consists of two spheres made of different PEMC materials, including the plane-sphere geometry as a particular case. The sign of the Casimir force does not only depend on the distance between the spheres and their geometric parameters but can be controlled by adjusting the temperature. A repulsive Casimir interaction at small distances allows for stable equilibrium configurations of the spheres. A sum rule previously derived for the plane-plane geometry at zero temperature is violated in general, if at least one plane is replaced by a sphere.

It is well known that non-Hermitian, nonreciprocal systems may harbor exponentially localized skin modes. However, in this work, we find that, generically, non-Hermiticity gives rise to abrupt and prominent kinks in the semiclassical wave packet trajectories of quantum gases, despite the absence of sudden physical impulses. This physically stems from a hitherto underappreciated intrinsic nonlocality from non-Hermitian pumping, even if all physical couplings are local, thereby resulting in enigmatic singularities in the band structure that lead to discontinuous band geometry and Berry curvature. Specifically, we focus on the realization of the kinked response in an ultracold atomic setup. For a concrete experimental demonstration, we propose an ultracold atomic setup in a two-dimensional optical lattice with laser-induced loss such that response kinks can be observed without fine-tuning in the physical atomic cloud dynamics. Our results showcase unique nonmonotonic behavior from non-Hermitian pumping beyond the non-Hermitian skin effect and suggest new avenues for investigating non-Hermitian dynamics on ultracold atomic platforms.

We investigate the non-Abelian Thouless pumping in a disorder tunable Lieb chain with degenerate flat bands. The results reveal that quasiperiodic disorder will cause a topological phase transition from the trivial (without non-Abelian Thouless pumping) to the nontrivial (with non-Abelian Thouless pumping) phase. The underlying mechanism is that the monopole originally outside the topological region can be driven into the topological region due to the introduction of quasiperiodic disorder. Moreover, since the corresponding monopole will turn into a nodal line to spread beyond the boundaries of the topological region, the system with large disorder strength will result in the disappearance of non-Abelian Thouless pumping. Furthermore, we numerically simulate the Thouless pumping of non-Abelian systems, and the evolution results of the center-of-mass displacement are consistent with the Chern number. Finally, we discuss the localization properties of the system and find that similar to the work of Zhang et al. [W. Zhang et al., Phys. Rev. Lett. 130, 206401 (2023)], the inverse Anderson transition does not occur in the system with the increase of quasiperiodic strength, while the system still maintains the coexistence of localized and extended states.

We investigate what kind of Markovian quantum master equation (QME) in the Gorini-Kossakowski-Sudarshan-Lindblad form is realized under Poincaré symmetry. The solution of the Markovian QME is given by a quantum dynamical semigroup, for which we introduce invariance under Poincaré transformations. Using the invariance of the dynamical semigroup and applying the unitary representation of the Poincaré group, we derive the Markovian QME for a relativistic massive spin-0 particle. Introducing the field operator of the massive particle and examining its evolution, we find that the field follows a dissipative Klein-Gordon equation. In addition, we show that any two local operators for spacelike separated regions commute with each other. This means that the microcausality condition is satisfied for the dissipative model of the massive particle.