We report an all-optical experiment to investigate the uncertainty relations based on linear entropy. First we prepare two kinds of biphoton states initially, i.e., Bell-like states and Werner states. Then we perform projective measurements on one subsystem over a complete or incomplete set of mutually unbiased bases; the corresponding measurement probabilities can be directly determined by the photon coincidence counting. Together with the initial state and the postmeasurement states of the system available by quantum state tomography, linear-entropy-based uncertainty relations can be fully verified. It is shown that the experimental results agree very well with the theoretical predictions. Also, it is revealed that entanglement of the initial biphoton states is anticorrelated with the total of uncertainties. Our experimental results could not only deepen the understanding of uncertainty relations, but also facilitate potential applications to quantum technologies.

We generalize the Majorana stellar representation of spin-$s$ pure states to mixed states, and in general to any Hermitian operator, defining a bijective correspondence between three spaces: the spin-density matrices, a projective space of homogeneous polynomials of four variables, and a set of equivalence classes of points (constellations) on spheres of different radii. The representation behaves well under rotations by construction, and also under partial traces where the reduced density matrices inherit their constellation classes from the original state $\rho$. We express several concepts and operations related to density matrices in terms of the corresponding polynomials, such as the anticoherence criterion and the tensor representation of spin-$s$ states described in Giraud et al. [Phys. Rev. Lett. 114, 080401 (2015)].

In this paper, we prove a family of Lieb-Robinson bounds for discrete spin systems with long-range interactions. Our results apply for arbitrary $k$-body interactions, so long as they decay with a power law greater than $kd$, where $d$ is the dimension of the system. More precisely, we require that the sum of the norm of terms with diameter greater than or equal to $R$, acting on any one site, decays as a power law $1/R^{\alpha }$, with $\alpha >d$. These bounds allow us to prove that, at any fixed time, the spatial decay of a time evolved operator follows arbitrarily closely to $1/r^{\alpha }$. Moreover, we introduce an alternative light cone definition for power-law interacting quantum systems which captures the region of the system where changing the Hamiltonian can affect the evolution of a local operator. In short-range interacting systems, this light cone agrees with the conventional definition. However, in long-range interacting systems, our definition yields a stricter light cone, which is more relevant in most physical contexts.

We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely positive process with no spurious a priori information. It uses randomly chosen input states and adaptive output von Neumann measurements. Both entangled and tensor-product configurations are flexibly employable in our scheme, the latter of which are especially compatible with many-body quantum computing. Two main features of this scheme are the certification protocol that verifies whether the accumulated data uniquely characterize the quantum process and a compressive reconstruction method for the output states. We emulate multipartite scenarios with high-order transverse modes and optical fibers to demonstrate that, in terms of measurement resources, our assumption-free compressive strategy can reconstruct quantum processes almost equally efficiently using all types of input states and basis measurements.

We propose a general method to operationally quantify the “resourcefulness” of quantum channels via channel discrimination, an important information processing task. A main result is that the maximum success probability of distinguishing a given channel from the set of free channels by free probe states is exactly characterized by the resource generating power, i.e., the maximum amount of resource produced by the action of the channel, given by the trace distance to the set of free states. We apply this framework to the resource theory of quantum coherence, as an informative example. The general results can also be easily applied to other resource theories such as entanglement, magic states, and asymmetry.

For an atomic state with two electrons missing from different core orbitals one may assume that the deeper hole decays first. However, it is quite probable that the double core-hole state will decay by emission of a slow Auger electron where the deeper core hole remains a spectator, especially if the outer core hole can be filled by Coster-Kronig transition, while the deeper cannot. We study here the competition of both Auger decay channels in a model system, the $1s2s2p^6\left(3s/3p\right)$ states of $\mathrm{N}{\mathrm{e}}^{+}$ ions. As the phenomenon can take place in any decay chain involving multiple core-excited states it can be critical to understand the ion yields, the electron and x-ray emission spectra, and the molecular fragmentation.

We find the geometric phase of a two-level system undergoing pure dephasing via interaction with an arbitrary environment, taking into account the effect of the initial system-environment correlations. We use our formalism to calculate the geometric phase for the two-level system in the presence of both harmonic-oscillator and spin environments, and we consider the initial state of the two-level system to be prepared by a projective measurement or a unitary operation. The geometric phase is evaluated for a variety of parameters such as the system-environment coupling strength to show that the initial correlations can affect the geometric phase very significantly even for weak and moderate system-environment coupling strengths. Moreover, the correction to the geometric phase due to the system-environment coupling generally becomes smaller (and can even be zero) if initial system-environment correlations are taken into account, thus implying that the system-environment correlations can increase the robustness of the geometric phase.

In reverse quantum annealing, the initial state is an eigenstate of the final problem Hamiltonian and the transverse field is cycled rather than strictly decreased as in standard (forward) quantum annealing. We present a numerical study of the reverse quantum annealing protocol applied to the $p$-spin model ($p=3$), including pausing, in an open-system setting accounting for dephasing in the energy eigenbasis, which results in thermal relaxation. We consider both independent and collective dephasing and demonstrate that in both cases the open-system dynamics substantially enhances the performance of reverse annealing. Namely, including dephasing overcomes the failure of purely closed-system reverse annealing to converge to the ground state of the $p$-spin model. We demonstrate that pausing further improves the success probability. The collective dephasing model leads to somewhat better performance than independent dephasing. The protocol we consider corresponds closely to the one implemented in the current generation of commercial quantum annealers, and our results help to explain why recent experiments demonstrated enhanced success probabilities under reverse annealing and pausing.

We present a time-resolved study of disintegration within atomic clusters ionized by a hard-x-ray pulse of moderate fluence. It was performed with electron and ion spectroscopy, and complemented by theoretical simulations. The expanding clusters were probed with a near-infrared (NIR) laser pulse over a range of pump-probe delays from −4 to 10 ps. In addition to an increasing number of singly charged atomic ions, originating from the ionization of Rydberg atoms formed through electron-ion recombination, we observe a decrease of oligomer yields. The latter is due to the interaction of oligomers with the NIR probe pulse, leading to their dissociation. At time delays between −1 and 2 ps, efficient absorption of the NIR laser energy occurs, even though the NIR intensity is too low to trigger tuneling ionization of Ar atoms. Our observations are similar to earlier observations of the fragmentation behavior of clusters excited by soft-x-ray pulses. This indicates that the relaxation dynamics of x-ray-excited nano-objects are universal over a wide range of excitation photon energies.

We study an interaction-induced dimensional crossover from two to three dimensions in a weakly interacting ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate (BEC). A highly oblate harmonic optical dipole trap was used where we independently controlled the chemical potential and the temperature of the gas. The dimensional crossover was studied from the thermal state occupancy of atoms. In particular, the growth rate of the thermal component was measured, which contradicted the expected behavior in a fixed dimension. Crossover chemical potential and temperature were obtained at the crossover point. We further validate our observation by numerical calculations based on mean-field Hartree-Fock theory and local density approximation, which not only provided a qualitative picture of the underlying mechanism for the dimensional crossover, but also matched well with the experimentally measured crossover parameter.

A metal-clad waveguide backed by a coherent atomic medium is proposed to achieve tunable giant spatial and angular Goos-Hänchen (GH) shifts. With a metal layer of appropriate thickness, a large GH shift can occur simultaneously for transverse-magnetic- and transverse-electric-polarized light beams when the waveguide modes are resonantly excited. The phase change and dip slope of the reflection coefficient around the resonance angle are closely related to the system's internal damping, which depends on the absorption of the medium. Then based on the quantum coherence effect, the spatial and angular shifts can be greatly enhanced by adjusting the parameters of the atomic system. The lateral displacement can also be switched from positive to negative or vice versa via coherent control of the absorption by the medium. Moreover, the dependence of the resonance angle of the guided mode on the refractive index makes the peak position of GH shifts tunable. The proposed scheme provides more flexibility for manipulating the spatial and the angular GH shifts, and it has potential applications in optical switches, beam steering, etc.

Optomechanical systems, due to its inherent nonlinear optomechanical coupling, owns rich nonlinear dynamics of different types of motion. The interesting question is that whether there exist some common quantum features to infer the nonlinear dynamical transitions from one type to another. In this paper, we study the quantum signatures of transitions from stable fixed points to limit cycles in an optomechanical phonon laser system. Our calculations show that the entanglement of stable fixed points in the long run does not change with time; however, it oscillates periodically with time at the mechanical vibration frequency for the limit cycles. Most strikingly, the entanglement quite close to the boundary line remains constant, and it is very robust against thermal phonon noise, as strong indications of this particular classical transitions.

Molecular chirality is an omnipresent phenomenon of fundamental significance in physics, chemistry, and biology. For this reason, the search for various techniques for enantioselective control, detection, and separation of chiral molecules is of particular importance. It has been recently predicted that laser fields with twisted polarization may induce a persistent enantioselective field-free orientation of chiral molecules. Here, we report an experimental observation of this phenomenon using propylene oxide molecules (${\mathrm{CH}}_3{\mathrm{CHCH}}_2\mathrm{O}$, or PPO) spun by an optical centrifuge—a laser pulse—whose linear polarization undergoes an accelerated rotation around its propagation direction. We show that PPO molecules remain oriented on a timescale exceeding the duration of the centrifuge pulse by several orders of magnitude. The demonstrated long-time field-free enantioselective orientation may open new avenues for optical manipulation, discrimination, and, potentially, the separation of molecular enantiomers.

A scheme for characterizing entanglement using the statistical measure of correlation given by the Pearson correlation coefficient (PCC) was recently suggested that has remained unexplored beyond the qubit case. Towards the application of this scheme for the high-dimensional states, a key step has been taken in a very recent work by experimentally determining PCC and analytically relating it to Negativity for quantifying entanglement of the empirically produced bipartite pure state of spatially correlated photonic qutrits. Motivated by this work, we present here a comprehensive study of the efficacy of such an entanglement characterizing scheme for a range of bipartite qutrit states by considering suitable combinations of PCCs based on a limited number of measurements. For this purpose, we investigate the issue of necessary and sufficient certification together with quantification of entanglement for the two-qutrit states comprising maximally entangled state mixed with white noise and colored noise in two different forms, respectively. Further, by considering these classes of states for $d=4$ and 5, extension of this PCC-based approach for higher dimensions ($d$) is discussed.

An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for the initial state with quantum coherence. In this paper, work statistics is considered from the perspective of “wave-particle” duality. Based on the generalized quantum work measurement, predictability of energy levels ${\mathcal{D}}_W$ and effectiveness of coherence ${\mathcal{V}}_W$ are defined, and they obey inequality ${\mathcal{D}}_W^2+{\mathcal{V}}_W^2\le 1$, which is the fundamental tradeoff relations between the contributions of population and coherence to quantum work distribution. As an application, we consider a driven two-level system and discuss the condition of the bound of above tradeoff relation. These results shed light on the effects of quantum coherence in quantum thermodynamics.

The evaluation of expectation values $\text{Tr}\left[\rho \mathcal{O}\right]$ for some pure state $\rho$ and Hermitian operator $\mathcal{O}$ is of central importance in a variety of quantum algorithms. Near-optimal techniques have been developed in the past and require a number of measurements $N$ approaching the Heisenberg limit $N=O\left(1/\epsilon \right)$ as a function of target accuracy $\epsilon$. The use of quantum phase estimation (QPE) requires, however, long circuit depths $C=O\left(1/\epsilon \right)$ making its implementation difficult on near-term noisy devices. The more direct strategy of operator averaging is usually preferred as it can be performed using $N=O\left(1/{\epsilon }^2\right)$ measurements and no additional gates aside from those needed for the state preparation. In this work we use a simple but realistic model to describe the bound state of a neutron and a proton (the deuteron) to show that the latter strategy can require an overly large number of measurements in order to achieve a prefixed relative target accuracy ${\epsilon }_r$. We propose to overcome this problem using a single step of QPE and classical postprocessing. This approach leads to a circuit depth $C=O\left({\epsilon }^{\mu }\right)$ (with $\mu \ge 0$) and to a number of measurements $N=O\left(1/{\epsilon }^{2+\nu }\right)$ for $0<\nu \le 1$ and a much smaller prefactor. We provide detailed descriptions of two implementations of our strategy for $\nu =1$ and $\nu \approx 0.5$ and derive appropriate conditions that a particular problem instance has to satisfy in order for our method to provide an advantage.

Surface acoustic waves (SAWs) can create moving quantum dots in piezoelectric materials. Here we show how electron-spin qubits located on dynamic quantum dots can be entangled. Previous theoretical and numerical models of quantum-dot entanglement generation have been insufficient to study quantum dynamics in realistic experimental devices. We utilize state-of-the-art graphics processing units to simulate the wave-function dynamics of two electrons carried by a SAW through a two-dimensional semiconductor heterostructure. We build a methodology to implement a power-of-swap gate via the Coulomb interaction. A benefit of the SAW architecture is that it provides a coherent way of transporting the qubits through an electrostatic potential. This architecture allows us to avoid problems associated with fast control pulses and guarantees operation consistency, providing an advantage over static qubits. For interdot barrier heights where the double occupation energy is sufficiently greater than the double-dot hopping energy, we find that parameters based on experiments in GaAs/AlGaAs heterostructures can produce a high-fidelity root-of-swap operation. Our results provide a methodology for a crucial component of dynamic-qubit quantum computing.

Fast and robust quantum gates are the cornerstones of fault-tolerance quantum computation. In this paper, as opposed to the previous proposals which use cyclic geometric phases, we propose to realize quantum computation based on noncyclic geometric evolution. The superiority of the noncyclic scheme is that the operation time is proportional to the rotation angle of the quantum state. Therefore, the noncyclic scheme becomes fairly fast in the case of quantum gates with small rotation angle, which will be more insensitive to the decoherence and the leakage to the states outside the computational basis. Similar to the cyclic version of geometric quantum computation, dynamical phases here during the evolution are canceled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabaticity. The proposed scheme is robust against random noise due to the geometric characteristic of projective Hilbert space. Since the proposed scheme is fast and robust, it is a particularly suitable way to manipulate the physical systems with weak nonlinearity, such as superconducting systems.

Quantum reflection of thermal He atoms from various surfaces (glass slide, GaAs wafer, flat, and structured Cr) at grazing conditions is studied within the elastic close-coupling formalism. Comparison with the experimental results of Zhao et al. [Phys. Rev. Lett. 105, 133203 (2010)] is quite reasonable but the conclusions of the present theoretical analysis are different from those discussed in the experimental work. The universal linear behavior observed in the dependence of the reflection probability on the incident wave-vector component perpendicular to the surface is only valid at small values of the component whereas, at larger values, deviation from the linearity is evident, approaching a quadratic dependence at higher values. The surface roughness seems to play no important role in this scattering. Moreover, the claim that one observes a transition from quantum to classical reflection seems to be imprecise.