We develop a hierarchical functional derivative (HFD) method to investigate the reduced dynamics of a spin-boson model within the framework of a stochastic decoupling description. Keeping only the lowest-order truncation of the hierarchical functional derivatives, one can recover the second-order Nakajima-Zwanzig quantum master equation. Taking into account the higher-order corrections, our method can be implemented as a highly efficient numerical scheme for a general spin-boson model beyond the usual Markovian, rotating-wave, and weak-coupling approximations.

We propose a protocol using a tunable Xmon qubit chain to construct generalized Su-Schrieffer-Heeger (SSH) models that support various topological phases. We study the time evolution of a single-excitation quantum state in a SSH-type qubit chain and find that such dynamics is linked to the topological winding number. We also investigate the adiabatic transfer of a single-excitation quantum state in a generalized SSH-type qubit chain and show that this process can be connected with the topological Chern number and be used to generate an entanglement-dependent topological pumping. All results have been demonstrated to be robust against qubit coupling imperfections and can be observed in a short Xmon qubit chain. Our study provides a simple method to directly measure topological invariants rooted in momentum space using quantum dynamics in real space.

Coherence measures and their operational interpretations lay the cornerstone of coherence theory. In this paper, we introduce a class of coherence measures with $\alpha$ affinity, say $\alpha$ affinity of coherence for $\alpha \in (0,1)$. Furthermore, we obtain the analytic formulas for these coherence measures and study their corresponding convex roof extension. We provide an operational interpretation for $1/2$ affinity of coherence by showing that it is equal to the error probability to discrimination a set of pure states with the least-square measurement. By employing this relationship we regain the optimal measurement for equiprobable quantum state discrimination. Moreover, we compare these coherence quantifiers and establish a complementarity relation between the $1/2$ affinity of coherence and path distinguishability for some special cases.

Staircases in response functions are associated with physically observable quantities that respond discretely to continuous tuning of a control parameter. A well-known example is the quantization of the Hall conductivity in two-dimensional electron gases at high magnetic fields. Here, we show that such a staircase response also appears in the magnetization of spin-1 atomic ensembles evolving under several spin-squeezing Hamiltonians. We discuss three examples, two mesoscopic and one macroscopic, where the system's magnetization vector responds discretely to continuous tuning of the applied magnetic field or the atom density, thus producing a magnetization staircase. The examples that we consider are directly related to Hamiltonians that have been implemented experimentally in the context of spin and spin-nematic squeezing. Thus, our results can be readily put to experimental test in spin-1 ferromagnetic ${}^{87}\mathrm{Rb}$ and antiferromagnetic ${}^{23}\mathrm{Na}$ condensates.

Many protocols require precise rotation measurement. Here we present a general class of states that surpass the shot-noise limit for measuring rotation around arbitrary axes. We then derive a quantum Cramér-Rao bound for simultaneously estimating all three parameters of a rotation (e.g., the Euler angles) and discuss states that achieve Heisenberg-limited sensitivities for all parameters; the bound is saturated by “anticoherent” states [Zimba, Electron. J. Theor. Phys. 3, 143 (2006)] (we are reluctant to use “anticoherent” to describe the states, but the name has become commonplace over the last decade). Anticoherent states have garnered much attention in recent years, and we elucidate a geometrical technique for finding new examples of such states. Finally, we discuss the potential for divergences in multiparameter estimation due to singularities in spherical coordinate systems. Our results are useful for a variety of quantum metrology and quantum communication applications.

The quantum Cramér-Rao theorem states that the quantum Fisher information bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed to extract information on $\xi$ is regular, i.e., neither its sample space nor its positive-operator valued elements depend on the (true) value of the parameter. A better performance may be achieved by relaxing this assumption. In the case of a general Hamiltonian parameter, i.e., when the parameter enters the system's Hamiltonian in a nonlinear way (making the energy eigenstates and eigenvalues $\xi$ dependent), a family of nonregular measurements, referred to as controlled energy measurements, is naturally available. We perform an analytic optimization of their performance, which enables us to compare the optimal controlled energy measurement with the optimal Braunstein-Caves measurement based on the symmetric logarithmic derivative. As the former may outperform the latter, the ultimate quantum bounds for general Hamiltonian parameters are different than those for phase (shift) parameters. We also discuss in detail a realistic implementation of controlled energy measurements based on the quantum phase estimation algorithm and work out a variety of examples to illustrate our results.

We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains (LMCs), that is, classical Markov chains with added memory. We show that LMCs can simulate the mixing behavior of any quantum walk, under a commonly satisfied invariance condition. This allows us to answer an open question on how the graph topology ultimately bounds a quantum walk's mixing performance, and that of any stochastic local evolution. The results highlight that speedups in mixing and transport phenomena are not necessarily diagnostic of quantum effects, although superdiffusive spreading is more prominent with quantum walks. The general simulating LMC construction may lead to large memory, yet we show that for the main graphs under study (i.e., lattices) this memory can be brought down to the same size employed in the quantum walks proposed in the literature.

The possibility of using squeezed states in the recently suggested unidimensional continuous-variable quantum key distribution based on a single quadrature modulation is addressed. It is shown that squeezing of the signal states expands the physicality bounds of the effective entangled state shared between the trusted parties due to the antisqueezing noise in the unmodulated quadrature. Modulation of the antisqueezed quadrature, on the other hand, effectively shrinks the physicality bounds due to the squeezing in the unmodulated quadrature and also provides noise on the reference side of the protocol, thus limiting the possibility of eavesdropping in noisy channels. This strategy is practical for low-loss (i.e., short-distance) channels, especially if direct reconciliation scheme is applied.

We demonstrate the existence of a finite temperature threshold for a one-dimensional stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have exponentially long lifetimes, as demonstrated by numerical and analytical arguments. We sketch how this algorithm generalizes to higher-dimensional stabilizer codes with stringlike excitations, such as the toric code.

One key parameter in the high-order harmonic generation (HHG) phenomenon is the exact frequency of the generated harmonic field. Its deviation from perfect harmonics of the laser frequency can be explained by considering (i) the single-atom laser-matter interaction and (ii) the spectral changes of the driving laser. In this work, we perform an experimental and theoretical study of the causes that generate spectral changes in the HHG radiation. We measured the driving-laser spectral shift after HHG in a long medium by using a correction factor to take into account the multiple possible HHG initiation distances along the laser path. We separate out the contribution of laser spectral shift from the resultant high-harmonic spectral shift in order to elucidate the microscopic effect of spectral shift in HHG. Therefore, in some cases we are able to identify the dominant electron trajectory from the experimental data. Our investigations lead to valuable conclusions about the atomic dipole phase contribution to a high-harmonic spectral shift. We demonstrate that the significant contribution of a long electron path leads to a high-harmonic shift, which differs from that expected from the driving laser. Moreover, we assess the origin of the high-order harmonics spectral broadening and provide an explanation for the narrowest high-harmonic spectral width in our experiment.

We investigate numerically and analytically the intensity dependence of the fraction of electrons that end up in a Rydberg state after strong-field ionization with linearly polarized light. We find that including the intensity dependent distribution of ionization times and nonadiabatic effects leads to a better understanding of experimental results. Furthermore, we observe using classical trajectory Monte Carlo simulations that the intensity dependence of the Rydberg yield changes with wavelength and that the previously observed power-law dependence breaks down at longer wavelengths. Our work suggests that Rydberg yield measurements can be used as an independent test for nonadiabaticity in strong-field ionization.

We introduce a general scheme of many-particle interferometry in which two identical sources are used and “which-way information” is eliminated by making the paths of one or more particles identical (path identity). The scheme allows us to generate many-particle entangled states. We provide general forms of these states and show that they can be expressed as superpositions of various Dicke states. We illustrate cases in which the scheme produces maximally entangled two-qubit states (Bell states) and maximally three-tangled states (three-particle Greenberger-Horne-Zeilinger-class states). A striking feature of the scheme is that the entangled states can be manipulated without interacting with the entangled particles; for example, it is possible to switch between two distinct Bell states. Furthermore, each entangled state corresponds to a set of many-particle interference patterns. The visibility of these patterns and the amount of entanglement in a quantum state are connected to each other. The scheme also allows us to change the visibility and the amount of entanglement without interacting with the entangled particles and, therefore, has the potential to play an important role in quantum information science.

There has been a body of work deriving the complex Hilbert-space structure of quantum theory from axioms/principles/postulates to deepen our understanding of quantum theory and to reveal ways to go beyond it to resolve foundational issues. Recent progress in incorporating indefinite causal structure into physical theories suggests that a more comprehensive understanding of both quantum theory and the theory beyond it accounts for indefinite causal structure. We formulate a framework of physical theories without assuming definite causal structure and identify postulates that single out the complex Hilbert-space structure. More than one complex Hilbert-space theory is compatible with the postulates, which leaves room for further search for the best among these theories.

In the context of quantum locking of classical correlations protocols, the condition for equality of the amount of unlockable correlations and quantum discord of general classical-quantum states is investigated. Based on this condition, the structure of such general states is obtained. This condition imposes two constraints on the structure of general classical-quantum states. After presenting the interpretation of these constraints, their role in quantum locking protocols is discussed. Finally, the derived structure is generalized to quantum-quantum states and the amount of their unlockable correlations is interpreted in terms of their symmetric discord.

The analytic expressions for the free energy and entropy of the Casimir-Polder interaction between a polarizable and magnetizable atom and a graphene sheet are found in the limiting case of low temperature. In so doing, the response of graphene to electromagnetic fluctuations is described in the framework of the Dirac model by means of the polarization tensor in (2+1)-dimensional space-time. It is shown that the dominant contribution to the low-temperature behavior is given by an explicit dependence of the polarization tensor on temperature as a parameter. We demonstrate that the Lifshitz theory of atom-graphene interaction satisfies the Nernst heat theorem, i.e., is thermodynamically consistent. On this basis possible reasons of thermodynamic inconsistency arising for the Casimir-Polder and Casimir interactions in the case of Drude metals are discussed. The conclusion is made that, although large thermal effect arising in the Casimir interaction between Drude metals at short separations should be considered as an artifact, the giant thermal effect predicted for graphene systems is an important physical phenomenon which awaits its experimental observation.

We study the superfluid phases of a Fermi gas in a multilayer optical lattice system in the presence of out-of-plane Zeeman field, as well as spin-orbit (SO) coupling. We show that the Zeeman field combined with the SO coupling leads to exotic topological pair-density wave (PDW) phases in which different layers possess different superfluid order parameters, even though each layer experiences the same Zeeman field and the SO coupling. We elucidate the mechanism of the emerging PDW phases, and characterize their topological properties by calculating the associated Chern numbers.

A rigorous method of calculating the electromagnetic field, the scattering matrix, and scattering cross sections of an arbitrary finite three-dimensional optical system described by its permittivity distribution is presented. The method is based on the expansion of the Green's function into the resonant states of the system. These can be calculated by any means, including the popular finite-element and finite-difference time-domain methods. However, using the resonant-state expansion with a spherically symmetric analytical basis, such as that of a homogeneous sphere, allows to determine a complete set of the resonant states of the system within a given frequency range. Furthermore, it enables to take full advantage of the expansion of the field outside the system into vector spherical harmonics, resulting in simple analytic expressions. We verify and illustrate the developed approach on an example of a dielectric sphere in vacuum, which has an exact analytic solution known as Mie scattering.

We study the Dicke phase transition in a disordered system of emitters coupled to the plasmonic modes of a graphene monolayer. This system has unique properties associated with the tunable, dissipative, and broadband characters of the graphene surface plasmons, as well as the disorder due to the random spatial distribution and the inhomogeneous linewidth broadening of the emitters. We apply the Keldysh functional-integral approach and identify a normal phase, a superradiant phase, and a spin-glass phase of the system. The conditions for these phases and their experimental signatures are discussed.

It is well established that the collective motion of ion crystals can be used as a quantum bus for multiqubit entanglement. However, as the number of ions increases, it becomes difficult to directly entangle ions far apart and resolve all motional modes of the ion crystal. We introduce a scalable and flexible scheme for efficient entanglement between any pair of ions within a large ion chain, using an evenly distributed 50-ion crystal as an example. By performing amplitude and frequency modulation, we find high-fidelity pulse sequences that primarily drive a transverse motional mode with a wavelength of four ion spacings. We present two $500\mu \mathrm{s}$ pulses that can in theory suppress gate errors due to residual motion to below ${10}^{-4}$, and observe a trade-off between gate power and robustness against unwanted frequency offsets.

We study, from a thermodynamic perspective, the equilibrium states of a qubit interacting with an arbitrary environment of dimension $N\gg 2$. We show that even in the presence of memory about the initial state, in some cases the qubit can be considered in a thermal state characterized by an entanglement Hamiltonian, which encodes the effects of the environment, and an initial-state-dependent entanglement temperature that measures the degree of entanglement generated between the system and its environment. Geometrical aspects of the thermal states are studied and the results are confirmed for the concrete case of the quantum walk on the line.