The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state $\rho$ is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we propose a way to circumvent the direct evaluation of such quantities, provided that the employed measures satisfy a self-similarity property. We say that a quantity $\mathcal{E}\left({\rho }^{\otimes N}\right)$ is scalable if it can be described as a function of the variables $\{\mathcal{E}\left({\rho }^{\otimes i_1}\right),\cdots ,\mathcal{E}\left({\rho }^{\otimes i_q}\right);N\}$ for $N>i_j$, while preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of $\mathcal{E}\left({\rho }^{\otimes N}\right)$, which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if $\mathcal{E}\left({\rho }^{\otimes 2^n}\right)$ depends only on $\mathcal{E}\left(\rho \right), \mathcal{E}\left({\rho }^{\otimes 2}\right)$, and $n$, then it is completely determined by Fibonacci polynomials, to leading order. We show that the one-shot distillable (OSD) entanglement is well described as a scalable measure for several families of states. For a particular two-qutrit state $\varrho$, we determine the OSD entanglement for ${\varrho }^{\otimes 96}$ from smaller tensorings, with an accuracy of $97\%$ and no extra computational effort. Finally, we show that superactivation of nonadditivity may occur in this context.

As a variant of the original quantum teleportation, port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a $2M$-qudit state, then it can be expressed as $M$ copies of a two-qudit maximally entangled state, where $M$ is the number of ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of controlled port-based teleportation by combining controlled teleportation with port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present quantities called the control power and the minimal control power for the controlled version on a given tripartite quantum state.

The Yang-Baxter equation (YBE) has created many applications in the integrable models of the statistical mechanics. It is recently shown that the YBE can be further applied in quantum information processing. Conversely, quantum simulation also provides novel approaches for effectively checking the YBE in quantum devices. Here, we adopted the method inspired by the previous work to experimentally perform the simulation of the YBE on a four-qubit nuclear magnetic resonance quantum processor. Whether the YBE is satisfied or not can be preliminarily determined by measuring the ancillary qubit without the assistance of quantum state tomography, and two hand sides of the YBE are concurrently simulated, not in separate forms involved in the existing protocols. The experimental result shows that the discrimination accuracy is over 98.1% when the condition of YBE is satisfied. The global and local entanglements in the YBE system are also studied by the numerical simulation and experiments. It is found that the YBE is not only a tool to yield the global entanglement but also the symptom when the local entanglement is equal to each other.

It is shown, through a mean-field description, that the ground state of weakly interacting Bose particles in a quasi-one-dimensional box trap can be converted into an excited stationary state by an almost adiabatic cyclic operation that involves a quench: A sharp impurity potential is applied, and its strength is varied during the cycle, which induces a nonequilibrium stationary state exhibiting the inversion of population. This process is robust in the sense that the resultant stationary state is almost independent of the details of the cycle, such as the position of the impurity, as long as the cycle is far enough from critical regions. The case of the failure of the population inversion due to the strong interparticle interactions is also examined.

We experimentally realize spin-tensor momentum coupling (STMC) using three ground Zeeman states coupled by three Raman laser beams in an ultracold atomic system of ${}^{40}\mathrm{K}$ Fermi atoms. This type of STMC consists of two bright-state bands as a spin-orbit coupled spin-1/2 system and one dark-state middle band. Using radio-frequency spin-injection spectroscopy, we investigate the energy band of STMC. It is demonstrated that the middle state is a dark state in the STMC system. The experimental realization of STMC open the door for further exploring exotic quantum matter.

Poincaré beams are known to host all three types of Stokes vortices (SVs). We present the optical currents (total transverse energy flow or Poynting vector) in Poincaré beams that contain a bright SV at the center of the beam. Mainly two types of optical flow patterns are observed: circulation at the center and multiple circulation loops around the center. The circulating optical currents are seen only around $S_{12}$ SVs. Open and closed loop-saddle points of the Poynting vector occur in beams containing $S_{23}$ SVs at the center. The number of closed loops in the total transverse flow indicates the magnitude of the ${\sigma }_{23}$ Stokes index. Experimentally obtained energy flow structures in four different Poincaré beams support the theoretical predictions.

Bell's theorem states that no local hidden-variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden-variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett's nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled ${}^{13}\mathrm{C}$ nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than four and seven standard deviations for six and eight measurement settings, respectively. Our experimental results are in full agreement with quantum predictions and violate Leggett's nonlocal hidden-variable inequality with a high level of confidence.

Interaction between a quantum system and its environment can induce stationary coherences—off-diagonal elements in the reduced system density matrix in the energy eigenstate basis—even at equilibrium. This work investigates the “quantumness” of such phenomena by examining the ability of classical and semiclassical models to describe equilibrium stationary coherence in the multilevel spin boson model, a common model for light-harvesting systems. A well justified classical harmonic-oscillator model is found to fail to capture equilibrium coherence. This failure is attributed to the effective weakness of classical system-bath interactions due to the absence of a discrete system energy spectrum and, consequently, of quantized shifts in oscillator coordinates. Semiclassical coherences also vanish for a dimeric model with parameters typical of biological light harvesting, i.e., where both system sites couple to the bath with the same reorganization energy. In contrast, equilibrium coherence persists in a fully quantum description of the same system, suggesting a uniquely quantum-mechanical origin for equilibrium stationary coherence in, e.g., photosynthetic systems. Finally, as a computational tool, a perturbative expansion is introduced that, at third order in $\hslash$, gives qualitatively correct behavior at ambient temperatures for all configurations examined.

This paper shows that it is possible to piggyback classical information on a stream of qubits protected by quantum error-correcting codes. The piggyback channel can be created by introducing intentional errors corresponding to a controlled sequence of syndromes. These syndromes are further protected, when quantum noise is present, by classical error-correcting codes according to a performance-delay trade-off. Classical information can thus be added and extracted at arbitrary epochs without consuming additional quantum resources and without disturbing the quantum stream.

The study of low-temperature hydrogen plasmas is relevant for many technological plasma applications. The theoretical investigation of elementary processes, especially those involving H, D, and T species, is crucial for the modeling of nonequilibrium plasma systems such as those found in fusion plasmas. We report fully quantum time-independent calculations of rate coefficients for the vibrationally inelastic and reactive collisions of T with ${\mathrm{D}}_2(v=0)$ and of D with ${\mathrm{T}}_2(v=0)$. Our calculations are based on the ${\mathrm{H}}_3$ global potential-energy surface of Mielke et al. [S. L. Mielke et al., J. Chem. Phys. 116, 4142 (2002)]. We obtain state-to-state rate coefficients for the formation of DT through $\mathrm{T}+{\mathrm{D}}_2$ and $\mathrm{D}+{\mathrm{T}}_2$ reactions and for the vibrational excitation of ${\mathrm{D}}_2$ by T and of ${\mathrm{T}}_2$ by D for temperatures up to 2500 K. The results are compared to existing ones for other hydrogen isotopes and significant differences are found between the different sets of results, confirming that specific data have to be obtained for all the collisional systems of interest of hydrogen plasmas. We expect that this data will allow a more accurate modeling of hydrogen plasmas of interest for technological applications.

We develop a systematic approach to derive narrowband (NB) and passband (PB) composite sequences which can produce any preselected transition probability with any desired accuracy. The NB composite pulses are derived by successive cancellation of derivative terms in the propagator. The PB pulses are built by combining two $\pi /2$ NB pulses. Both the NB and the PB pulses feature vanishing wings on both sides of the central region around the target transition probability, and the PB pulses offer also a flat (broadband) top around the target probability. The NB sequences are particularly suitable for sensing and metrology applications, whereas the PB sequences can be very useful for qubit control in the case of tightly spaced laser-driven qubits for they ensure both selectivity (suppressed cross talk to neighbors) and robustness (suppressed laser pointing instability). Other possible applications include selective (NB) or both selective and robust (PB) control of close transitions in frequency space.

We analyze zero-temperature universal properties of the simplest Galilean-invariant model of spinless low-dimensional fermions with short-range two-body interactions. In particular, it is shown that after proper renormalization of the coupling constant, even the dilute system possesses a rich phase diagram that includes the superfluid state and the metastable “upper-branch” behavior.

Nuclear-magnetic-resonance gyroscopes that detect rotation as a shift in the precession frequency of nuclear spins have attracted a lot of attention. Under a feedback-generated drive, the precession frequency in the steady state is supposed to be dependent only on the angular momentum and an applied magnetic field. However, nuclei with spins larger than 1/2 experience electric quadrupole interaction with electric-field gradients at the cell walls. This quadrupole interaction shifts the precession frequencies of the nuclear spins, which brings inaccuracy to the rotation measurement as the quadrupole interaction constant $C_q$ is difficult to precisely measure. In this paper, the effects of quadrupole interaction on nuclear-magnetic-resonance gyroscopes are theoretically studied. We find that, when the constant $C_q$ is small compared to the characteristic decay rate of the system, which is the case in most gyroscopes for practical use, as the strength of the feedback-driving field increases, the quadrupole shift monotonically decreases, regardless of the system parameters in including $C_q$. Furthermore, the larger driving amplitude can reduce the quadrupole shift's fluctuation caused by fluctuations of the system parameters, and, thus, it can reduce systematic errors resulted from the quadrupole interaction. In the large-$C_q$ regime, more than one precession frequency exists, and the nuclear spins may precess with a single frequency or multifrequencies depending on initial conditions. In this regime with large driving amplitudes, the nuclear spin can restore the single-frequency precession. These results are obtained by solving an effective master equation of the nuclear spins in a rotating frame from which both the steady-state solutions and the dynamics of the system are shown.

The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean-squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.

We proposed a spectroscopic method that extends Ramsey's atomic spectroscopy to detect the transition frequency of a qubit fabricated on a superconducting circuit. The method uses a multi-interval train of qubit biases to implement an alternate resonant and dispersive couplings to an incident probe field. The consequent absorption spectrum of the qubit has a narrower linewidth at its transition frequency than that obtained from constantly biasing the qubit to resonance while the middle dispersive evolution incurs only a negligible shift in detected frequency. Modeling on transmon qubits, we find that the linewidth reduction reaches 23% and Ramsey fringes are simultaneously suppressed at extreme duration ratio of dispersion over resonance for a double-resonance scheme. If the scheme is augmented by an extra resonance segment, a further 37% reduction can be achieved.

Strongly long-range interacting quantum systems—those with interactions decaying as a power law $1/r^{\alpha }$ in the distance $r$ on a $D$-dimensional lattice for $\alpha \le D$—have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\alpha \le D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all $\alpha <D$. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.

In this Rapid Communication, we propose a protocol to reverse a quantum many-body dynamic process. We name it “many-body echo” because the underlying physics is closely related to the spin echo effect in nuclear magnetic resonance systems. We consider a periodical modulation of the interaction strength in a weakly interacting Bose condensate, which resonantly excites quasiparticles from the condensate. A dramatic phenomenon is that, after pausing the interaction modulation for half a period and then continuing on with the same modulation, nearly all the excited quasiparticles in the resonance modes will be absorbed back into the condensate. During the intermediate half-period, the free evolution introduces a $\pi$ phase, which plays a role reminiscent of that played by the $\pi$ pulse in the spin echo. Comparing our protocol with another one implemented by the Chicago group in a recent experiment, we find that ours is more effective at reversing the many-body process. The difference between these two schemes manifests the physical effect of the micromotion in the Floquet theory.

We study the effect of feedback controls in quantum parameter estimation. In particular, we study the estimation of a magnetic field with a spin in the presence of the spontaneous emission where feedback control, triggered by the detection of the emitted photons, is employed to improve the precision limit. We also study the effect of additional Hamiltonian controls and show that they can provide further improvement on the precision limit.