In private broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among all parties, and to send to each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum [i.e., in quantum private broadcasting (QPB)]. In this work, we give three solutions to $t$-recipient quantum private broadcasting ($t$-QPB) and compare them in terms of key lengths. The first method is the independent encryption with the quantum one-time pad, which requires a key linear in the number of recipients, $t$. We show that the key length can be decreased to be logarithmic in $t$ by using unitary $t$-designs. Our main contribution is to show that this can be improved to a key length that is logarithmic in the dimension of the symmetric subspace, using a concept that we define of symmetric unitary $t$-designs, which may be of independent interest.

The process of the capture of a target electron into the projectile continuum (ECC) is investigated both experimentally and theoretically for collisions of 1.25–6.00 MeV deuterons with multielectron gas targets. Double-differential cross sections (DDCS), $d^2\sigma /d\mathrm{\Omega }dE$, of the ECC cusp-shaped electron peak involving He, Ne, and Ar gas targets were measured at the emission angle of zero degrees with respect to the ion-beam velocity. Corresponding DDCS calculations, obtained using continuum distorted-wave (CDW) and continuum distorted-wave eikonal initial-state (CDW-EIS) theories, were critically compared to the measurements. The role of each atomic subshell of the multielectron Ne and Ar targets is examined employing the CDW-EIS theory with numerical target wave functions, which is found to best agree with the measurements.

We study the non-Markovian dispersive readout of a single-mode bosonic (SMB) quantum system coupled to the open cavity with two non-Markovian environments. Assuming that the SMB quantum system is initially prepared in a thermal equilibrium state, the susceptibility of the measured SMB quantum system to the cavity can be obtained by the nonequilibrium linear response theory, which provides the dispersive frequency shift of the cavity. We analytically derive the transmission and reflection of the cavity in the non-Markovian regime and discuss the non-Markovian dispersive readout of the SMB quantum system, which is in good agreement with that obtained by the Markovian approximation. We show that the effect of non-Markovian dynamics on the system's behavior leads to the decrease of the transmission and shifts of the frequency corresponding to the peak of the transmission in the dispersive regime compared with the Markovian case and the increase of the sum of the transmission and reflection due to the excitation backflowing induced by the couplings of the cavity and two non-Markovian environments, which could be applied to quantum secure direct communication with quantum memory. Finally, we generalize the readout theory to the periodically driven SMB quantum system based on the Floquet theory and quantum network, which contain all influences from the non-Markovian environments. The formalism presented in this paper opens an alternative field of possible applications in quantum information and quantum communication with non-Markovianity by manipulating the spectral densities of the environments.

We introduce an approach to characterize the dynamics of disordered quantum networks. Each quantum element (i.e., each node) of the network experiences the other nodes as an effective environment that can be self-consistently represented by a Feynman-Vernon influence functional. For networks having the topology of locally treelike graphs, these Feynman-Vernon (FV) functionals can be determined by a new version of the cavity or belief propagation (BP) method. Here, we find the fixed point solution of this version of BP for a network of uniform quantum harmonic oscillators. Then, we estimate the effects of the disorder in these networks within the replica symmetry ansatz. We show that over a large time interval, at small disorder, the real part of the FV functional induces decoherence and classicality while at sufficiently large disorder the Feynman-Vernon functional tends to zero and the coherence survives, signaling in a time setting, the onset of an Anderson's transition.

The network structure offers in principle the possibility for novel forms of quantum nonlocal correlations, that are proper to networks and cannot be traced back to standard quantum Bell nonlocality. Here we define a notion of genuine network quantum nonlocality. Our approach is operational and views standard quantum nonlocality as a resource for producing correlations in networks. We show several examples of correlations that are genuine network nonlocal, considering the so-called bilocality network of entanglement swapping. In particular, we present an example of quantum self-testing which relies on the network structure; the considered correlations are nonbilocal, but are local according to the usual definition of Bell locality.

Network nonlocality is the study of the network nonlocal correlations created by several independent entangled states shared in a network. In this paper, we provide two generic strategies to produce nonlocal correlations in large classes of networks without input. In the first one, called token counting (TC), each source distributes a fixed number of tokens and each party counts the number of received tokens. In the second one, called color matching (CM), each source takes a color and a party checks if the color of neighboring sources match. Using graph theoretic tools and Finner's inequality, we show that TC and CM distributions are rigid in wide classes of networks, meaning that there is essentially a unique classical strategy to simulate such correlations. Using this rigidity property, we show that certain quantum TC and CM strategies produce correlations that cannot be produced classicality. This leads us to several examples of network nonlocality without input. These examples involve creation of coherence throughout the whole network, which we claim to be a fingerprint of genuine forms of network nonlocality. This work extends a more compact parallel work [Phys. Rev. Lett. 128, 060401 (2022)] on the same subject and provides all the required technical proofs.

In the Bloch sphere picture, one finds the coefficients for expanding a single-qubit density operator in terms of the identity and Pauli matrices. A generalization to $n$ qubits via tensor products represents a density operator by a real vector of length $4^n$, conceptually similar to a state vector. Here, we study this approach for the purpose of quantum circuit simulation, including noise processes. The tensor structure leads to computationally efficient algorithms for applying circuit gates and performing few-qubit quantum operations. In view of variational circuit optimization, we study “backpropagation” through a quantum circuit and gradient computation based on this representation, and generalize our analysis to the Lindblad equation for modeling the (nonunitary) time evolution of a density operator.

By use of the grasp2018 package we perform multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations with configuration interaction (CI) for the ${}^{1}S_0$ and ${}^{3}P_{0,1}^o$ levels in neutral cadmium and mercury. By supplying the resultant atomic state functions to the ris4 program, we evaluate the mass- and field-shift parameters for the ${}^{1}S_0-{}^{3}P_0^o$ (clock) and ${}^{1}S_0-{}^3{P}_1^o$ (intercombination) lines. We make revised estimates of the nuclear charge parameters ${\lambda }^{A,A^{\prime }}$ and differences in mean-square charge radii $\delta {\langle r^2\rangle }^{A,A^{\prime }}$ for both elements and point out a discrepancy with tabulated data for Cd. In constructing a King plot with the Hg lines we examine the second-order hyperfine interaction for the ${}^{3}P_{0,1}^o$ levels. Isotope shifts for the clock transition have been estimated, from which we predict the unknown clock line frequencies in the bosonic Hg isotopes and all the naturally occurring isotopes of Cd.

We investigate the high harmonic generation from stretched acetylene molecules subjected to intense laser fields employing time-dependent Hartree-Fock methods. It is found that as the C-C and C-H bonds are stretched, the harmonic efficiency increases significantly due to the increased ionization of inner valence $\sigma$ orbitals in the monochromatic field, while the harmonic yield will be limited by the strong depletion of the ground-state population under a certain bond length. Moreover, the harmonic emission is affected by the nonadiabatic electron dynamics from the multiorbital coupling effects. In addition, by introducing a two-color field scheme for different C-H bond configurations with the fixed C-C bond, the aforementioned harmonic efficiency will be further enhanced due to laser-induced strong excitation from inner valence orbitals to initially unoccupied orbitals. The above results would be helpful for further understanding multiorbital dynamics in the harmonic generation from polyatomic molecules.

We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as “chiral damping.” Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase transition with the inclusion of the hopping amplitude modulation. By using the spectral topology and a finite-size scaling analysis in the commensurate case, we show there exists a phase transition of the skin effect with non-Bloch anti-parity-time symmetry breaking. For the incommensurate case, we find richer phases with the coexistence of the non-Hermitian skin effect and the Anderson localization, which are separated by a generalized mobility edge. We reveal the transition of the damping dynamics as a consequence of the phase transition. Furthermore, we propose a possible scheme with ultracold atoms in a dissipative momentum lattice to realize and detect the damping dynamics.

By considering an on-site attraction between a spin-$\uparrow$ and a spin-$\downarrow$ fermion in a multiband tight-binding lattice, here we study the two-body spectrum and derive an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states. In addition to the intraband (or the so-called conventional) contribution that depends only on the single-particle spectrum and the interband (or the so-called geometric) contribution that is controlled by the quantum metric, our generalized relation has an additional interband contribution that depends on the so-called band-resolved quantum metric. All of our analytical expressions are applicable to those multiband lattices that simultaneously exhibit time-reversal symmetry and fulfill the condition on spatially uniform pairing. As a nontrivial illustration we analyze the two-body problem in a kagome lattice with nearest-neighbor hoppings, and we show that the exact relation provides a perfect benchmark.

Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be nonlinear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.

We present a theoretical method to calculate Delbrück scattering amplitudes. Our formalism is based on the exact analytical Dirac-Coulomb Green's function and therefore accounts for the interaction of the virtual electron-positron pair with the nucleus to all orders, including the Coulomb corrections. The numerical convergence of our calculations is accelerated by solving the radial integrals that are involved analytically in the asymptotic region. Numerical results for the collision of photons with energies 102.2 and 255.5 keV with bare neon and lead nuclei are compared with the predictions of the lowest-order Born approximation. We find that our method can produce accurate results within a reasonable computation time and that the Coulomb corrections enhance the absolute value of the Delbrück amplitude by a few percent for the studied photon energies.

We study the role of correlation in mechanisms of energy exchange between an interacting bipartite quantum system and its environment by decomposing the energy of the system to local and correlation-related contributions. When the system Hamiltonian is time independent, no external work is performed. In this case, energy exchange between the system and its environment occurs only due to the change in the state of the system. We investigate the possibility of a special case where the energy exchange with the environment occurs exclusively due to changes in the correlation between the constituent parts of the bipartite system, while their local energies remain constant. We find sufficient conditions for preserving local energies. It is proven that under these conditions and within the Gorini-Kossakowski-Lindblad-Sudarshan dynamics this scenario is not possible for all initial states of the bipartite system. Nevertheless, since the sufficient conditions can be too strong, it is still possible to find special cases for which the local energies remain unchanged during the associated evolution and the whole energy exchange is only due to the change in the correlation energy. We illustrate our results with an example.

Holonomic quantum computation exploits a quantum state's nontrivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through parameter space have been well researched. Discrete holonomies, on the other hand, where the state jumps from point to point in state space, have had little prior investigation. Using a sequence of incomplete projective measurements of the spin operator, we build an explicit approach to universal quantum computation. We show that quantum error correction codes integrate naturally in our scheme, providing a model for measurement-based quantum computation that combines the passive error resilience of holonomic quantum computation and active error correction techniques. In the limit of dense measurements we recover known continuous-path holonomies.

The development of novel neutron optics devices that rely on perfect crystals and nanoscale features are ushering in a new generation of neutron science experiments, from fundamental physics to material characterization of emerging quantum materials. However, the standard theory of dynamical diffraction (DD) that analyzes neutron propagation through perfect crystals does not consider complex geometries, deformations, and/or imperfections, which are now becoming a relevant systematic effect in high-precision interferometric experiments. In this work, we expand upon a quantum information (QI) model of DD that is based on propagating a particle through a lattice of unitary quantum gates. We show that the model output is mathematically equivalent to the spherical wave solution of the Takagi-Taupin equations when in the appropriate limit, and that the model can be extended to the Bragg as well as the Laue-Bragg geometry where it is consistent with experimental data. The presented results demonstrate the universality of the QI model and its potential for modeling scenarios that are beyond the scope of the standard theory of DD.

We investigate the dynamics of a general two-level based anti-parity-time (anti-$\mathcal{PT}$)-symmetric qubit and study its decoherence as well as entanglement entropy properties. We compare our findings with that of the corresponding parity-time ($\mathcal{PT}$)-symmetric and Hermitian qubits. To begin, we consider the time-dependent Dyson map to find the exact analytical dynamics for a general non-Hermitian qubit system weakly coupled with a thermal bath for pure dephasing, before specializing it to the case of a general anti-$\mathcal{PT}$-symmetric qubit. Basing the comparison under the same coupling strength or increasing the non-Hermiticity, we observe that the decoherence function and entanglement entropy of the anti-$\mathcal{PT}$-symmetric qubit decays and grows more slowly, respectively, compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. Similarly, the corresponding variance and area of Fisher information are much higher compared to the $\mathcal{PT}$-symmetric and Hermitian qubits. These results demonstrate that anti-$\mathcal{PT}$-symmetric qubits may be better suited for quantum computing and quantum information processing applications than conventional Hermitian or even $\mathcal{PT}$-symmetric qubits.

The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers [presented in Smart and Mazziotti, Phys. Rev. Lett. 126, 070504 (2021)] in which a contraction of the Schrödinger equation is solved for the two-electron reduced density matrix (2-RDM) to resolve the energy splittings of the ortho-, meta-, and para-isomers of benzyne ${\text{C}}_6{\text{H}}_4$. In contrast to the traditional variational quantum eigensolver, the contracted quantum eigensolver can solve an integration (or contraction) of the many-electron Schrödinger equation onto the two-electron space. The quantum solution of the anti-Hermitian part of the contracted Schrödinger equation provides a scalable approach with few variational parameters that has its foundations in 2-RDM theory. Experimentally, a variety of error-mitigation strategies enable the calculation, including a linear shift in the 2-RDM targeting the iterative nature of the algorithm as well as a projection of the 2-RDM onto the convex set of approximately $N$-representable 2-RDMs defined by the 2-positive $N$-representability conditions. The relative energies exhibit single-digit millihartree errors, capturing a large part of the electron correlation energy, and the computed natural orbital occupations reflect the significant differences in the electron correlation of the isomers.

In a ubiquitous SU(2) dynamics, achieving the simultaneous optimal estimation of multiple parameters is significant but difficult. Using quantum control to optimize this SU(2) coding unitary evolution is one of solutions. We propose a method, characterized by the nested cross products of the coefficient vector $\mathbf{X}$ of SU(2) generators and its partial derivative ${\partial }_{\ell }\mathbf{X}$, to investigate the control-enhanced quantum multiparameter estimation. Our work reveals that quantum control is not always functional in improving the estimation precision, which depends on the characterization of an SU(2) dynamics with respect to the objective parameter. This characterization is quantified by the angle ${\alpha }_{\ell }$ between $\mathbf{X}$ and ${\partial }_{\ell }\mathbf{X}$. For an SU(2) dynamics featured by ${\alpha }_{\ell }=\pi /2$, the promotion of the estimation precision can get the most benefits from the controls. When ${\alpha }_{\ell }$ gradually closes to 0 or $\pi$, the precision promotion contributed to by quantum control correspondingly becomes inconspicuous. Until a dynamics with ${\alpha }_{\ell }=0$ or $\pi$, quantum control completely loses its advantage. In addition, we find a set of conditions restricting the simultaneous optimal estimation of all the parameters, but fortunately, which can be removed by using a maximally entangled two-qubit state as the probe state and adding an ancillary channel into the configuration. Lastly, a spin-$1/2$ system is taken as an example to verify the above-mentioned conclusions. Our proposal sufficiently exhibits the hallmark of control-enhancement in fulfilling the multiparameter estimation mission, and it is applicable to an arbitrary SU(2) parametrization process.