Fermionic systems differ from bosonic ones in several ways, in particular the time-reversal operator $\mathcal{T}$ is odd, ${\mathcal{T}}^2=-\mathbb{1}$. For $\mathcal{PT}$-symmetric bosonic systems, the no-signaling principle and the quantum brachistochrone problem have been studied to some degree, both of them controversially. In this paper, we apply the basic methods proposed for bosonic systems [Y. Lee et al., Phys. Rev. Lett. 112, 130404 (2014); C. M. Bender et al., Phys. Rev. Lett. 98, 040403 (2007)] to fermionic two- and four-dimensional $\mathcal{PT}$-symmetric Hamiltonians and obtain several surprising results: We find, in contrast to the bosonic case, that the no-signaling principle is upheld for two-dimensional fermionic Hamiltonians; however, the $\mathcal{PT}$ symmetry is broken. In addition, we find that the time required for the evolution from a given initial state, the spin up, to a given final state, the spin down, is a constant, independent of the parameters of the Hamiltonian, under the eigenvalue constraint. That is, it cannot, as in the bosonic case, be optimized. We do, however, also find a dimensional dependence: Four-dimensional $\mathcal{PT}$-symmetric fermionic Hamiltonians considered here again uphold the no-signaling principle, but it is not essential that the $\mathcal{PT}$ symmetry be broken. The symmetry is, however, broken if the measure of entanglement is conserved. In the four-dimensional systems, the evolution time between orthogonal states is dependent on the parameters of the Hamiltonian, with the conclusion that it again can be optimized and approach zero under certain circumstances. However, if we require the conservation of entanglement, the transformation time between these two states becomes the same constant as that found in the two-dimensional case, which coincides with the minimum time for such a transformation to take place in the Hermitian case.

Exact expressions are derived for the intermediate scattering function (ISF) of a quantum particle diffusing in a harmonic potential and linearly coupled to a harmonic bath. The results are valid for arbitrary strength and spectral density of the coupling. The general, exact non-Markovian result is expressed in terms of the classical velocity autocorrelation function, which represents an accumulated phase during a scattering event. The imaginary part of the exponent of the ISF is proportional to the accumulated phase, which is an antisymmetric function of the correlation time $t$. The expressions extend previous results given in the quantum Langevin framework where the classical response of the bath was taken as Markovian. For a special case of non-Markovian friction, where the friction kernel decays exponentially in time rather than instantaneously, we provide exact results relating to unconfined quantum diffusion, and identify general features that allow insight to be exported to more complex examples. The accumulated phase as a function of the $t$ has a universal gradient at the origin, depending only on the mass of the diffusing system particle. At large $t$ the accumulated phase reaches a constant limit that depends only on the classical diffusion coefficient and is therefore independent of the detailed memory properties of the friction kernel. Non-Markovian properties of the friction kernel are encoded in the details of how the accumulated phase switches from its $t\to -\infty$ to its $t\to +\infty$ limit, subject to the constraint of the universal gradient. When memory effects are significant, the transition from one limit to the other becomes nonmonotonic, owing to oscillations in the classical velocity autocorrelation. The result is interpreted in terms of a solvent caging effect, in which slowly fluctuating bath modes create transient wells for the system particle.

We study the spreading of a quantum particle placed in a single site of a lattice or binary tree with the Hamiltonian permitting particle-number changes. We show that the particle-number-changing interactions accelerate the spreading beyond the ballistic expansion limit by inducing off-resonant Rabi oscillations between states of different numbers of particles. We consider the effect of perturbative number-changing couplings on Anderson localization in one-dimensional disordered lattices and show that they lead to decrease of localization. The effect of these couplings is shown to be larger at larger disorder strength, which is a consequence of the disorder-induced broadening of the particle dispersion bands.

It is known that there exist sets of pure orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are nonlocal sets which exhibit nonlocality without entanglement. These nonlocal sets can be completable or uncompletable. In this work both completable and uncompletable small nonlocal sets of multipartite orthogonal product states are constructed. Apart from nonlocality, these sets have other interesting properties. In particular, the completable sets lead to the construction of a class of complete orthogonal product bases with the property that if such a basis is given then no state can be eliminated from that basis by performing orthogonality-preserving measurements. On the other hand, an uncompletable set of the present kind contains several Shifts unextendible product bases (UPBs) that belong to qubit subspaces. Identifying these subspace UPBs, it is possible to obtain a class of high-dimensional multipartite bound entangled states. Finally, it is shown that a two-qubit maximally entangled Bell state shared between any two parties is sufficient as a resource to distinguish the states of any completable set (of the above kind) perfectly by LOCC. This constitutes an example where the amount of entanglement, sufficient to accomplish the aforesaid task, depends neither on the dimension of the individual subsystems nor on the number of parties.

In this paper, we study the local unitary (LU) classification for pairs (triples) of generalized Bell states, based on the local unitary equivalence of two sets. In detail, we first introduce some general unitary operators which give us more local unitary equivalent sets besides Clifford operators. And then we present two necessary conditions for local unitary equivalent sets which can be used to examine the local inequivalence. Following this approach, we completely classify all pairs in the $d\otimes d$ quantum system into ${\prod }_{j=1}^n(k_j+1)-1$ LU-inequivalent pairs when the prime factorization of $d={\prod }_{j=1}^n{p}_j^{k_j}$. Moreover, all triples in the $p^{\alpha }\otimes p^{\alpha }$ quantum system for prime $p$ can be partitioned into $\frac{(\alpha +3)}{6}{p}^{\alpha }+O\left(\alpha p^{\alpha -1}\right)$ LU-inequivalent triples; especially, when $\alpha =2$ and $p>2$, there are exactly $\lfloor \frac{5}{6}{p}^2\rfloor +\lfloor \frac{p-2}{6}+{(-1)}^{\lfloor \frac{p}{3}\rfloor }\frac{p}{3}\rfloor +3$ LU-inequivalent triples.

We study cumulative excitation of Rydberg atoms in blockaded and facilitated regimes. In order to observe the evolution of the system into a steady state, we employ excitation durations extending to longer than the kinetic time scale and the Rydberg-atom lifetime. Despite the presence of strong van der Waals repulsion, the most probable separation between atoms remains fixed due to the continual Rydberg excitation. This indicates that the time scale on which facilitated excitation replenishes the expanding Rydberg-atom cloud is faster than the van der Waals expansion time scale. The cloud expansion velocities are observed to be slower than the terminal velocity of Rydberg-atom pairs prepared at the facilitation radius and subject to binary van der Waals interaction. Atom statistics in the facilitated regime show bimodal Poissonian distributions, an observation we attribute to the statistical nature of the facilitation process. One peak is due to facilitation avalanches that produce many Rydberg atoms and the other reflects cases in which the facilitation does not gain traction.

We investigate theoretically strong-coupling and finite-temperature effects on the $p$-wave contacts, as well as the asymptotic behavior of the momentum distribution in the large-momentum region in a one-component Fermi gas with a tunable $p$-wave interaction. Including $p$-wave pairing fluctuations within a strong-coupling theory, we calculate the $p$-wave contacts above the superfluid transition temperature $T_{\mathrm{c}}$ from the adiabatic energy relations. We show that, while the $p$-wave contact related to the scattering volume monotonically increases with increasing interaction strength, the one related to the effective range depends nonmonotonically on interaction strength and its sign changes in the intermediate-coupling regime. The nonmonotonic interaction dependence of these quantities is shown to originate from the competition between the increase of the cutoff momentum and the decrease of the coupling constant of the $p$-wave interaction with increasing effective range. We also analyze the asymptotic form of the momentum distribution in the large-momentum region. In contrast to the conventional $s$-wave case, we show that the asymptotic behavior cannot be completely described by only the $p$-wave contacts, and the extra terms, which are not related to the thermodynamic properties, appear. Furthermore, in the high-temperature region, we find that the extra terms dominate the subleading term of the large-momentum distribution. We also directly compare our results with the recent experimental measurement by including the effects of a harmonic trap potential within the local density approximation. We show that, while our model qualitatively explains the dependence on the interaction strength of the $p$-wave contacts, there are some quantitative disagreements between our theory and recent experiment; for example, the peak position of the $p$-wave contact related to the effective range. Since the $p$-wave contacts connect the microscopic properties to the thermodynamic properties of the system, our results would be helpful for further understanding many-body properties of this anisotropic interacting Fermi gas in the normal phase.

Recently, sensors with resonances at exceptional points (EPs) have been suggested to have a vastly improved sensitivity due to the extraordinary scaling of the complex frequency splitting of the $n$ initially degenerate modes with the $n\mathrm{th}$ root of the perturbation. We show here that the resulting quantum-limited signal to noise at EPs is proportional to the perturbation, and comparable to other sensors, thus providing the same precision. The complex frequency splitting close to EPs is therefore not suited to estimate the precision of EP sensors. The underlying reason for this counterintuitive result is that the mode fields, described by the eigenvectors, are equal for all modes at the EP, and are strongly changing with the perturbation.

We report on an experimental assessment of the emergence of Quantum Darwinism (QD) from engineered open-system dynamics. We use a photonic hyperentangled source of graph states to address the effects that correlations among the elements of a multiparty environment have on the establishment of objective reality ensuing the quantum-to-classical transition. Besides embodying one of the first experimental efforts toward the characterization of QD, our work illustrates the nontrivial consequences that multipartite entanglement and, in turn, the possibility of having environment-to-system back-action have on the features of the QD framework.

In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [Tsang, Phys. Rev. Lett. 108, 170502 (2012)]. Specializing to the distinction of two candidate hypotheses, we study the achievements of continuous monitoring of the radiation emitted by a quantum system followed by an optimal projective measurement on its conditioned final state. Our study of the radiative decay of a driven two-level system shows an intricate interplay between the maximum information available from photon counting and homodyne detection and the final projective measurement on the emitter. We compare the results with theory predicting a lower bound for the probability to assign a wrong hypothesis by any combined measurement on the system and its radiative environment.

Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum correlation that lies in between entanglement and Bell nonlocality. Its temporal analog, temporal steering, has recently been shown to have applications in quantum information and open quantum systems. Here we show that there exists a hierarchy among the three temporal quantum correlations: temporal inseparability, temporal steering, and macrorealism. Given that the temporal inseparability can be used to define a measure of quantum causality, similarly the quantification of temporal steering can be viewed as a weaker measure of direct cause and can be used to distinguish between direct cause and common cause in a quantum network.

Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimization and execution of the expressed computations. However, the specification format makes it difficult to verify that optimized or executed computations still conform to the initial gate list specifications: showing the computational equivalence between two quantum circuits expressed by different lists of quantum gates is exponentially complex in the worst case. In order to solve this issue, this work presents a derivation of the specification format tailored specifically for fault-tolerant quantum circuits. The circuits are considered a form consisting entirely of single qubit initializations, cnot gates, and single qubit measurements (ICM form). This format allows, under certain assumptions, to efficiently verify optimized (or implemented) computations. Two verification methods based on checking stabilizer circuit structures are presented.

We propose a general scheme for inducing resonant exchange between spins or pseudospins of unmatched levels via periodic driving. The basic idea is illustrated for a system of two heteronuclear atoms, for which analytical results are provided for the effective spin-exchange (SE) interaction strength. It is then applied to the mixture of ${}^{23}\mathrm{Na}$ and ${}^{87}\mathrm{Rb}$ atoms with a radio frequency or microwave field near resonant to the mismatched Zeeman level spacings. SE interaction engineered this way is applicable to ultracold quantum gas mixtures involving spinor Bose-Bose, Bose-Fermi, and Fermi-Fermi atoms.

We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated ab initio studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can account for the antibunching, only the inclusion of the interspecies correlations can lead to the bunching. We show that these correlations effectively create an induced bosonic interaction, which in turn elucidates the occurrence of the bosonic bunching. Finally, we derive a two-site extended Bose-Hubbard model which reveals the low-energy physics of the bosons for the case of much heavier fermions.

We apply the quantum Langevin equations approach to study nonlinear light propagation through one-dimensional interacting open quantum lattice models. We write a large set of quantum Langevin equations of lattice operators obtained after integrating out the light fields and use them to derive nonequilibrium features of the lattice models. We first consider a Heisenberg-type interacting spin-$\frac{1}{2}$ chain with nearest-neighbor coupling. The transient and steady-state transport properties of an incoming monochromatic laser light are calculated for this model. We find how the local features of the spin chain and the chain length dependence of light transport coefficient evolve with an increasing power of the incident light. The steady-state light transmission coefficient at a higher power depends nonmonotonically on the interaction in a finite chain. While the nonlinear light transmission in our studied model seems to be ballistic in the absence of interaction and for a high interaction, it shows an apparent system-size dependence at intermediate interactions. Later, we extend this method to the long-range interaction between spins of the driven-dissipative lattice model and to incorporate various losses typical in many atomic and solid-state systems.

We address SU(1,1) interferometry in the presence of phase diffusion and photon losses and evaluate analytically the corresponding quantum Fisher information. Using this result we determine the thresholds on the noise parameters, as a function of total mean photon number, in order to beat the standard quantum limit to phase sensitivity.

In the present work we study tripartite quantum steering of quantum correlations arising from two local dichotomic measurements on each side in the two types of partially device-independent scenarios: the one-sided device-independent scenario where one of the parties performs untrusted measurements while the other two parties perform trusted measurements and the two-sided device-independent scenario where one of the parties performs trusted measurements while the other two parties perform untrusted measurements. We demonstrate that tripartite steering in the two-sided device-independent scenario is weaker than tripartite steering in the one-sided device-independent scenario by using two families of quantum correlations. That is, these two families of quantum correlations in the two-sided device-independent framework detect tripartite entanglement through tripartite steering for a larger region than that in the one-sided device-independent framework. It is shown that tripartite steering in the two-sided device-independent scenario implies the presence of genuine tripartite entanglement of $2\times 2\times 2$ quantum system, even if the correlation does not exhibit genuine nonlocality or genuine steering.

We investigate high-fidelity fast quantum driving in a generalized nonlinear two-level system with both interparticle interaction and nonlinear energy sweep. We find that fast quantum dynamics depend on the interaction, energy sweep parameter, and energy sweep strength. We show that the driving protocol for a large energy sweep parameter reaches a given final high fidelity in a shorter time. The interparticle interaction can influence the quantum driving dynamics and can even break the quantum speed limit of the linear model. For the attractive interaction, the minimal time decreases monotonically as energy sweep strength increases, while it increases for the repulsive interaction. We also study a critical behavior and obtain analytical expressions of a critical interaction or a critical sweep strength, beyond which the target state cannot be achieved with high fidelity.

We investigate a quantum annealing approach based on real-time quantum dynamics for graph coloring. In this approach, a driving Hamiltonian is chosen so that constraints are naturally satisfied without penalty terms and the dimension of the Hilbert space is considerably reduced. The total Hamiltonian, which consists of driving and problem Hamiltonians, resembles a disordered quantum spin chain. The ground state of the problem Hamiltonian for graph coloring is degenerate. This degeneracy is advantageous and is characteristic of this approach. Real-time quantum simulations in a small system demonstrate interesting results and provide some insight into quantum annealing.