Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering processes.

Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)] showed that shared nonlocal boxes with a CHSH (Clauser, Horne, Shimony, and Holt) probability greater than $\frac{3+\sqrt{6}}{6}$ yield trivial communication complexity. There still exists a gap with the maximum CHSH probability $\frac{2+\sqrt{2}}{4}$ achievable by quantum mechanics. It is an interesting open question to determine the exact threshold for the trivial communication complexity. Brassard et al.'s idea is based on recursive bias amplification by the three-input majority function. It was not obvious if another choice of function exhibits stronger bias amplification. We show that the three-input majority function is the unique optimal function, so that one cannot improve the threshold $\frac{3+\sqrt{6}}{6}$ by Brassard et al.'s bias amplification. In this work, protocols for computing the function used for the bias amplification are restricted to be nonadaptive protocols or a particular adaptive protocol inspired by Pawłowski et al.'s protocol for information causality [Nature (London) 461, 1101 (2009)]. We first show an adaptive protocol inspired by Pawłowski et al.'s protocol, and then show that the adaptive protocol improves upon nonadaptive protocols. Finally, we show that the three-input majority function is the unique optimal function for the bias amplification if we apply the adaptive protocol to each step of the bias amplification.

We consider two protocols for the measurement of the temporal correlation functions of a dichotomic variable $Q$ appearing in Leggett-Garg-type inequalities. The protocols measure solely whether $Q$ has the same or a different sign at the end of a given time interval, thereby measuring no more than is required for determination of the correlation function. They are inspired, in part, by a decoherent histories analysis of the two-time histories of $Q$, which yields a number of useful insights, although the protocols are ultimately expressed in macrorealistic form independent of quantum theory. The first type involves an ancilla coupled to the system with two sequential controlled-not (cnot) gates, and the two-time histories of the system (whose probabilities yield the correlation function) are determined in a single final time measurement of the ancilla. It is noninvasive for special choices of initial system states and partially invasive for more general choices. Modified Leggett-Garg-type inequalities which accommodate the partial invasiveness are discussed. The quantum picture of the protocol shows that for certain choices of the primary system initial state, the final state is unaffected by the two cnot gate interactions, hence the protocol is undetectable with respect to final system-state measurements, although it is still invasive at intermediate times. This invasiveness can be reduced with different choices of ancilla states and the protocol is then similar in flavor to a weak measurement. The second type of protocol is based on the fact that the behavior of $Q$ over a time interval can be determined from knowledge of the dynamics together with a measurement of certain initial (or final) data. Its quantum version corresponds to the known fact that when sets of histories are decoherent, their probabilities may be expressed in terms of a record projector, hence the two-time histories in which $Q$ has the same or a different sign can be determined by a single projective measurement. The resulting protocol resembles the decay-type protocol proposed by Huelga and collaborators (which is noninvasive but requires a stationarity assumption).

Steady-state manifolds of open quantum systems, such as decoherence-free subspaces and noiseless subsystems, are of great practical importance to the end of quantum information processing. Yet, it is a difficult problem to find steady-state manifolds of open quantum systems, especially of non-Markovian systems. In this paper, we propose an approach to find the steady-state manifolds, which is generally applicable to both Markovian and non-Markovian systems. Our approach is based on an arbitrarily given steady state, and by following the standard steps of the approach, the steady-state manifold on the support subspace of the given state can be obtained. Our work reduces the problem of finding a manifold of steady states to that of finding only one steady state, which is indeed an interesting progress towards completely solving the difficult problem. Besides, in deriving our approach, we introduce the notions of the modified noise algebra and its commutant, and prove two theorems on the structure of steady-state manifolds of general open systems, which themselves are interesting findings too.

The second law of thermodynamics states that the entropy of a closed system is nondecreasing. Discussing the second law in the quantum world poses different challenges and provides different opportunities, involving fundamental quantum-information-theoretic questions and interesting quantum-engineered devices. In quantum mechanics, systems with an evolution described by a so-called unital quantum channel evolve with a nondecreasing entropy. Here, we seek the opposite, a system described by a nonunital and, furthermore, energy-conserving channel that describes a system whose entropy decreases with time. We propose a setup involving a mesoscopic four-lead scatterer augmented by a microenvironment in the form of a spin that realizes this goal. Within this nonunital and energy-conserving quantum channel, the microenvironment acts with two noncommuting operations on the system in an autonomous way. We find that the process corresponds to a partial exchange or swap between the system and environment quantum states, with the system's entropy decreasing if the environment's state is more pure. This entropy-decreasing process is naturally expressed through the action of a quantum Maxwell demon and we propose a quantum-thermodynamic engine with four qubits that extracts work from a single heat reservoir when provided with a reservoir of pure qubits. The special feature of this engine, which derives from the energy conservation in the nonunital quantum channel, is its separation into two cycles, a working cycle and an entropy cycle, allowing us to run this engine with no local waste heat.

Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-reservoir systems, namely the single-site Bose-Hubbard model coupled to two reservoirs at different temperatures. Using Redfield equations in a Born-Markov approximation, we compute nonequilibrium average particle number, energy, and currents beyond linear response regime, both time dynamics and steady state, and investigate its dependence on various tunable parameters analytically. We find interesting scaling laws in high-temperature regimes that are independent of choice of bath spectral functions. We also demonstrate that the system shows very interesting particle and energy current rectification properties which can be controlled via the relative strength of interaction and temperatures, as well as via the degree of asymmetry in system-bath coupling. Specifically, we find inversion of direction of energy rectification as a function of the relative strength of the interaction strength and the temperatures. We also show that, in the limit of low-temperature and high interaction strength, our results are consistent with the nonequilibrium spin-Boson model. Our results are experimentally relevant not only to hybrid quantum systems but also in other areas such as molecular junctions.

Temporal Bell inequalities, or Leggett-Garg inequalities (LGIs), are studied for continuous-variable systems placed in a squeezed state. The importance of those systems lies in their broad applicability, which allows the description of many different physical settings in various branches of physics, ranging from cosmology to condensed matter physics and from optics to quantum information theory. Leggett-Garg inequality violations are explored and systematically mapped in squeezing parameter space. Configurations for which LGI violation occurs are found, but it is shown that no violation can be obtained if all squeezing angles vanish, contrary to what happens for the spatial Bell inequalities. We also assess the effect of decoherence on the detectability of such violations. Our study opens up the possibility of new experimental designs for the observation of LGI violation.

For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each party. We show that for two symmetric multiqubit states and local unitary transformations this is the case; the maximal overlap can be reached by applying the same unitary matrix everywhere. For local invertible operations (stochastic local operations assisted by classical communication equivalence), however, we present counterexamples, demonstrating that considering the same operation everywhere is not enough.

We test a general method to detect lower bounds of the quantum channel capacity for two-qubit correlated channels. We consider in particular correlated dephasing, depolarizing, and amplitude damping channels. We show that the method is easily implementable, it does not require a priori knowledge about the channels, and it is very efficient, since it does not rely on full quantum process tomography.

We present a proof-of-principle experiment demonstrating measurement of the collectibility, a nonlinear entanglement witness proposed by Ł. Rudnicki et al. [Phys. Rev. Lett. 107, 150502 (2011)]. This entanglement witness works for both mixed and pure two-qubit states. In the latter case it can be used to measure entanglement in terms of the negativity. We measured the collectibility for three distinct classes of photonic polarization-encoded two-qubit states, i.e., maximally entangled, separable, and maximally mixed states. We demonstrate that the measurement procedure is feasible and robust against typical experimental shortcomings such as imperfect two-photon indistinguishability.

In a hybrid pumping alkali-metal vapor cell filled with both K and Rb atoms, the K atom spins are optically pumped by the laser and the Rb atom spins are polarized by the K spins through spin exchange. We discovered that the ac Stark shift of the Rb atom spins, caused by the far-off-resonant pumping laser tuned to the K absorption lines, was mixed together with the ac Stark shift of the K atom spins through fast spin exchange. This mixing is studied and we demonstrate a K-Rb-${}^{21}\mathrm{Ne}$ comagnetometer in which the ac Stark shift of the Rb atom spins is eliminated by compensating for the Rb ac Stark shift with the K ac Stark shift. An ac Stark shift elimination method has been developed.

We derive the scattering length of composite bosons (cobosons) within the framework of the composite-boson many-body formalism that uses correlated-pair states as a basis instead of free-fermion states. The integral equation constructed from this physically relevant basis makes transparent the role of fermion exchange in the coboson-coboson effective scattering. Three potentials used for Cooper pairs, fermionic-atom dimers, and semiconductor excitons are considered. While the $s$-wave scattering length for the BCS-like potential is just equal to its Born value, the other two are substantially smaller. For fermionic-atom dimers and semiconductor excitons, our results, calculated within a restricted correlated-pair basis, are in good agreement with those obtained from procedures numerically more demanding. We also propose model coboson-coboson scatterings that are separable and thus easily workable and that produce scattering lengths which match quantitatively well with the numerically obtained values for all fermion mass ratios. These separable model scatterings can facilitate future works on many-body effects in coboson gases.

We study dissociative electron attachment (DEA) to the ClF and ${\mathrm{F}}_2$ molecules. We formulate a method for calculation of partial resonance widths and calculate the angular distributions of the products in the ClF case using the local and nonlocal versions of the complex potential theory of DEA. They show the dominance of the $p$ wave except in a narrow energy region close to zero energy. Comparison of the local and nonlocal DEA cross sections show that the former are smaller than the latter by a factor of 2 in the energy region important for calculation of thermal rate coefficients. This result is confirmed by comparison of the local and nonlocal calculations for ${\mathrm{F}}_2$. Only at low energies below 30 meV the local cross sections exceed nonlocal due to the $1/E$ divergence of the local results. On the other hand, the thermal rate coefficients generated from the local cross sections agree better with experiment than those calculated from the nonlocal cross sections. The most likely reason for this disagreement is the overestimated resonance width in the region of internuclear distances close to the point of crossing between the neutral and anion potential-energy curves.

We generalize the quantum adiabatic theorem to the non-Hermitian system and build a strict adiabaticity condition to make the adiabatic evolution nonlossy when taking into account the effect of the adiabatic phase. According to the strict adiabaticity condition, the nonadiabatic couplings and the effect of the imaginary part of adiabatic phase should be eliminated as much as possible. Also, the non-Hermitian Hamiltonian reverse-engineering method is proposed for adiabatically driving an artificial quantum state. A concrete two-level system is adopted to show the usefulness of the reverse-engineering method. We obtain the desired target state by adjusting extra rotating magnetic fields at a predefined time. Furthermore, the numerical simulation shows that certain noise and dissipation in the systems are no longer undesirable but play a positive role in the scheme. Therefore, the scheme is quite useful for quantum information processing in some dissipative systems.

We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system well within experimentally measured lifetimes, in contrast to previous research, which either focused on interactions near Förster resonances or on few-atom systems. We build a spin-$\frac{1}{2}$ from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, which we demonstrate can be used to characterize the Rydberg-dressed interactions. Furthermore, the dynamics can differ significantly from that observed in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results also apply to bare (undressed) Rydberg states as a special case, for which we quantitatively reproduce recent ultrafast experiments without fitting.

The predissociation of the ${\mathrm{N}}_2{}^{+}$ molecular ion in the $C {}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic state through the nonadiabatic coupling with the $B {}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic state is studied by solving the Schrödinger equation. The predissociation rates are calculated using Fermi's golden rule and compared with experimental results. We characterize the dynamics by calculating the nuclear probability density $\rho (R,t)$, the nuclear flux density $j(R,t)$, and the two-electron flux density $\mathbf{j}({\mathbf{r}}_1,{\mathbf{r}}_2,t)$. It is found that at the early dynamics, $t\le 100$ fs, Fermi's golden rule breaks down, while a strong correlation between the electronic and nuclear dynamics is observed. Fourier analyses of the probability and flux densities are also presented and yield insight in their frequency dependency.

The transverse spatial distribution of weakly interacting Bose gas in a narrow channel is found. The corresponding analytical solution of the Gross-Pitaevskii equation has the form of a cnoidal wave. The possible physical realization of the model is a system of cold atoms or quasiparticles, e.g., excitons, cavity photons, exciton polaritons. The obtained formula is used for the numerical calculation of the spectrum of excitations and the critical velocity of the condensate. These numerical results do not coincide with the Bogoliubov spectrum, and we show that the strongly inhomogeneous condensate density leads to larger values of the critical velocity. We also make numerical estimation of the critical velocity for various types of considered particles or quasiparticles.

We report on the production of ${}^{39}\mathrm{K}$ matter-wave bright solitons, i.e., one-dimensional matter waves that propagate without dispersion thanks to attractive interactions. The volume of the soliton is studied as a function of the scattering length through three-body losses, revealing peak densities as high as $\sim 5\times {10}^{20}{\mathrm{m}}^{-3}$. Our solitons, close to the collapse threshold, are strongly bound and will find applications in fundamental physics and atom interferometry.

We study the impurity problem in a gas of ${}^{173}\mathrm{Yb}$ atoms near the recently discovered orbital Feshbach resonance. In an orbital Feshbach resonance, atoms in the electronic ground state ${}^{1}S_0$ interact with those in the long-lived excited ${}^{3}P_0$ state with magnetically tunable interactions. We consider an impurity atom with a given hyperfine spin in the ${}^{3}P_0$ state interacting with a single-component Fermi sea of atoms in the ground ${}^{1}S_0$ manifold. Close to the orbital Feshbach resonance, the impurity can induce collective particle-hole excitations out of the Fermi sea, which can be regarded as the polaron state. As the magnetic field decreases, a molecular state becomes the ground state of the system. We show that a polaron to molecule transition exists in ${}^{173}\mathrm{Yb}$ atoms close to the orbital Feshbach resonance. Furthermore, due to the spin-exchange nature of the orbital Feshbach resonance, the formation of both the polaron and the molecule involve spin-flipping processes with interesting density distributions among the relevant hyperfine spin states. We show that the polaron to molecule transition can be detected using Raman spectroscopy.

Ultracold atoms in optical lattices provide one of the most promising platforms for analog quantum simulations of complex quantum many-body systems. Large-size systems can now routinely be reached and are already used to probe a large variety of different physical situations, ranging from quantum phase transitions to artificial gauge theories. At the same time, measurement techniques are still limited and full tomography for these systems seems out of reach. Motivated by this observation, we present a method to directly detect and quantify to what extent a quantum state deviates from a local Gaussian description, based on available noise correlation measurements from in situ and time-of-flight measurements. This is an indicator of the significance of strong correlations in ground and thermal states, as Gaussian states are precisely the ground and thermal states of noninteracting models. We connect our findings, augmented by numerical tensor network simulations, to notions of equilibration, disordered systems, and the suppression of transport in Anderson insulators.