We address parameter estimation for structured environments and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e., the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature, and the interaction time. Upon investigating the Fisher information of feasible measurements, we arrive at a remarkable simple result: homodyne detection of canonical variables allows one to achieve the ultimate quantum limit to precision under suitable, mild, conditions. Finally, upon exploiting a perturbative approach, we find the invariant sweet spots of the (tunable) characteristic frequency of the probe, able to drive the probe towards the optimal working regime.

Quantum probing consists of suitably exploiting a simple, small, and controllable quantum system to characterize a larger and more complex system. Here, we address the estimation of the cutoff frequency of the Ohmic spectral density of a harmonic reservoir by quantum probes. To this aim, we address the use of single-qubit and two-qubit systems and different kinds of coupling with the bath of oscillators. We assess the estimation precision by the quantum Fisher information of the sole quantum probe as well as the corresponding quantum signal-to-noise ratio. We prove that, for most of the values of the Ohmicity parameter, a simple probe such as a single qubit is already optimal for the precise estimation of the cutoff frequency. Indeed for those values, upon considering a two-qubit probe either in a Bell or in separable state, we do not find improvement to the estimation precision. However, we also showed that there exist few conditions where employing two qubits in a Bell state interacting with a common bath is more suitable for precisely estimating the cutoff frequency.

We present a method to exponentiate nonsparse indefinite low-rank matrices on a quantum computer. Given access to the elements of the matrix, our method allows one to determine the singular values and their associated singular vectors in time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and nonsquare matrices via matrix embedding. Moreover, our method preserves the phase relations between the singular spaces allowing for efficient algorithms that require operating on the entire singular-value decomposition of a matrix. As an example of such an algorithm, we discuss the Procrustes problem of finding a closest isometry to a given matrix.

The distribution of quantum correlations in multipartite systems plays a significant role in several aspects of quantum information theory. While it is well known that these quantum correlations cannot be freely distributed, the way that they are shared in a multipartite system is an open problem even for a small set of qubits. Based on monogamylike relations between entanglement and discord for $n$-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary multipartite pure states.

We propose an effective scheme for realizing a Jaynes-Cummings model with the collective nitrogen-vacancy-center ensemble (NVE) bosonic modes in a hybrid system. Specifically, the controllable transmon qubit can alternatively interact with one of the two NVEs, which results in the production of $N$-particle entangled states. Arbitrary $N$-particle entangled states, NOON states, $N$-dimensional entangled states, and entangled coherent states are demonstrated. Realistic imperfections and decoherence effects are analyzed via numerical simulation. Since no cavity photons or excited levels of the NV center are populated during the whole process, our scheme is insensitive to cavity decay and the spin dephasing effect of the NVE. The idea provides a scalable way to realize NVE-circuit cavity quantum information processing with current technology.

Locality-preserving logical operators in topological codes are naturally fault tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure for finding all locality-preserving logical operators admitted by a large and important class of topological stabilizer codes. In particular, we focus on those equivalent to a stack of a finite number of surface codes of any spatial dimension, where our procedure fully specifies the group of locality-preserving logical operators. We also present examples of how our procedure applies to codes with different boundary conditions, including color codes and toric codes, as well as more general codes such as Abelian quantum double models and codes with fermionic excitations in more than two dimensions.

From an operational perspective, nonclassicality characterizes the exotic behavior in a physical process which cannot be explained with Newtonian physics. There are several widely used measures of nonclassicality, including coherence, discord, and entanglement, each proven to be essential resources in particular situations. There exists evidence of fundamental connections among the three measures. However, the sources of nonclassicality are still regarded differently and such connections are yet to be elucidated. Here, we introduce a general framework of defining a unified nonclassicality with an operational motivation founded on the capability of interferometry. Nonclassicality appears differently as coherence, discord, and entanglement in different scenarios with local measurement, weak basis-independent measurement, and strong basis-independent measurement, respectively. Our results elaborate how these three measures are related and how they can be transformed from each other. Experimental schemes are proposed to test the results.

We have performed quantitative measurements of the variation of the on-resonance absorption coefficients ${\kappa }_0$ of the four hyperfine components of the Cs $D_1$ transition as a function of laser power $P$, for pumping with linearly and with circularly polarized light. Sublevel populations derived from rate equations assuming isotropic population relaxation (at a rate ${\gamma }_1$) yield algebraic ${\kappa }_0\left(P\right)$ dependences that do not reproduce the experimental findings from Cs vapor in a paraffin-coated cell. However, numerical results that consider spin-exchange relaxation (at a rate ${\gamma }_{\mathrm{se}}$) and isotropic relaxation fit the experimental data perfectly well. The fit parameters, viz., the absolute value of ${\kappa }_0$, the optical pumping saturation power $P_{\mathrm{sat}}$, and the ratio ${\gamma }_{\mathrm{se}}/{\gamma }_1$, are well described by the experimental conditions and yield absolute values for ${\gamma }_1$ and ${\gamma }_{\mathrm{se}}$. The latter is consistent with the previously published Cs-Cs spin-exchange relaxation cross section.

We study the dynamics of three-dimensional weakly linked Bose-Einstein condensates using a multimode model with an effective interaction parameter. The system is confined by a ring-shaped four-well trapping potential. By constructing a two-mode Hamiltonian in a reduced highly symmetric phase space, we examine the periodic orbits and calculate their time periods both in the self-trapping and Josephson regimes. The dynamics in the vicinity of the reduced phase space is investigated by means of a Floquet multiplier analysis, finding regions of different linear stability and analyzing their implications on the exact dynamics. The numerical exploration in an extended region of the phase space demonstrates that two-mode tools can also be useful for performing a partition of the space in different regimes. Comparisons with Gross-Pitaevskii simulations confirm these findings and emphasize the importance of properly determining the effective on-site interaction parameter governing the multimode dynamics.

We carry out extensive direct numerical simulations to investigate the interaction of active particles and fields in the two-dimensional Gross-Pitaevskii superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent, spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid helium and Bose-Einstein condensates.

A photon pair can be entangled in many degrees of freedom such as polarization, time bins, and orbital angular momentum (OAM). Among them, the OAM of photons can be entangled in an infinite-dimensional Hilbert space which enhances the channel capacity of sharing information in a network. Twisted photons generated by spontaneous parametric down-conversion offer an opportunity to create this high-dimensional entanglement, but a photon pair generated by this process is typically wideband, which makes it difficult to interface with the quantum memories in a network. Here we propose an annual-ring-type quasi-phase-matching (QPM) crystal for generation of the narrowband high-dimensional entanglement. The structure of the QPM crystal is designed by tracking the geometric divergences of the OAM modes that comprise the entangled state. The dimensionality and the quality of the entanglement can be greatly enhanced with the annual-ring-type QPM crystal.

Steady-state plasmonic lasing is studied theoretically for a system consisting of many dye molecules arranged regularly around a gold nanosphere. A three-level model with realistic molecular dissipation is employed to analyze the performance as a function of the pump field amplitude and number of molecules. Few molecules and moderate pumping produce a single narrow emission peak because the excited molecules transfer energy to a single dipole plasmon mode by amplified spontaneous emission. Under strong pumping, the single peak splits into broader and weaker emission peaks because two molecular excited levels interfere with each other through coherent coupling with the pump field and with the dipole plasmon field. A large number of molecules gives rise to a Poisson-like distribution of plasmon number states with a large mean number characteristic of lasing action. These characteristics of lasing, however, deteriorate under strong pumping because of the molecular interference effect.

We investigate different strategies suitable to generate pure heralded single photons through spontaneous parametric down-conversion, comparing the counterpropagating geometry with more conventional copropagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. We derive general results for the Schmidt number associated to the temporal modes, which provide a quantitative estimate of the purity. An analysis of the correlation of twin photons in the temporal domain provides a more physical view of the mechanisms that permit to eliminate the temporal entanglement of the state and to generate high-purity heralded photons. The efficiency of the various strategies and the individual properties of the heralded photons thereby generated are then compared.

We study theoretically a weak measurement of an observable $A$ and its impact on a subsequent strong measurement of another observable $B$. We assume that both measurements are described by the Gaussian point detectors. It is shown that a decrease of the system-detector interaction during the measurement of $A$ results in an increase of the fluctuations of $A$, while the mean value of $A$ is kept unaltered. The ratio ${\left(\mathrm{\Delta }A\right)}_{\mathrm{weak}\mathrm{measurement}}/{\left(\mathrm{\Delta }A\right)}_{\mathrm{strong}\mathrm{measurement}}$ turns out to be universal, i.e., independent of the physical system, its quantum state, and the quantity measured. Most of our attention is focused on analyzing outcomes of the subsequent strong measurement of the quantity $B$, namely, on the mean value $\overline{B}$ and the variance ${\left(\mathrm{\Delta }B\right)}^2$. We derive explicit analytic corrections for $\overline{B}$ and ${\left(\mathrm{\Delta }B\right)}^2$ arising due to the prior weak measurement of $A$. Importantly, the leading-order impact of the weak measurement of $A$ on $\overline{B}$ and ${\left(\mathrm{\Delta }B\right)}^2$ is encoded in the terms ${}_s\langle \psi |[\widehat{A},[\widehat{A},{\widehat{B}}^k]]{|\psi \rangle }_s$, where $k=1,2$ and ${|\psi \rangle }_s$ is the quantum state vector of our system before the measurements. Our additional contribution consists of deriving Heisenberg-like uncertainty relations for the product ${\left(\mathrm{\Delta }A\right)}_{\mathrm{weak}\mathrm{measurement}}{\left(\mathrm{\Delta }B\right)}_{\mathrm{strong}\mathrm{measurement}}$ and analyzing the case of minimum uncertainty. Finally, our theoretical developments are illustrated numerically via studying the $s$ states of the hydrogen atom, assuming $\widehat{A}=\widehat{r}$ (atomic radius) and $\widehat{B}=\widehat{H}$ (energy).

We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a weighted sum of asymmetry in each mode can be applied as a measure of macroscopic coherence. To exclude the effects of microscopic superpositions, we suggest a method to introduce a cutoff to the weighted sum that will specify the macroscopic portion of the coherence. This cutoff may be interpreted as the fuzziness for a given measurement outcome. Based on the suggested measures, we investigate the quantum macroscopicity for particular concrete examples in $N$-partite spin systems.

Complex decay pathways involving radiative and nonradiative relaxation after deep core-level ionization in argon are disentangled by a unique combination of several synchrotron radiation-based spectroscopic techniques. In particular, by comparing the results obtained from electron-ion coincidence, photon-ion coincidence, and x-ray emission measurements, we are able to distinguish the final ionic states produced in the cascade decay involving $K\alpha$ and $K\beta$ radiative decay and final ionic states produced by nonradiative cascade decay. High-resolution Auger electron spectroscopy is then used as a complementary tool to identify the $LMM$ transitions contributing to the cascade decay. Ab initio calculations are performed to identify the electronic states involved in the $LMM$ decay.

The effect of a decoherence channel, such as a turbulent atmosphere, on the second-order quantum interference in the Hong-Ou-Mandel (HOM) effect is investigated. The investigation includes both theoretical analyses and an experimental implementation of the process. In our experiment, entangled input states are prepared with spontaneous parametric down-conversion. The atmospheric turbulence is modeled as a single-phase screen and simulated with spatial light modulators according to the theory of Kolmogorov. We find both theoretically and experimentally that the HOM dip is unaffected when only one of the photons passes through turbulence. When both photons pass through turbulence, the HOM interference is only slightly affected by the scintillation. The reasons behind these findings and their consequences for HOM-based teleportation are discussed.

We consider a recently proposed entity authentication protocol in which a physical unclonable key is interrogated by random coherent states of light, and the quadratures of the scattered light are analyzed by means of a coarse-grained homodyne detection. We derive a sufficient condition for the protocol to be secure against an emulation attack in which an adversary knows the challenge-response properties of the key and moreover, he can access the challenges during the verification. The security analysis relies on Holevo's bound and Fano's inequality, and suggests that the protocol is secure against the emulation attack for a broad range of physical parameters that are within reach of today's technology.