Much of quantum mechanics may be derived if one adopts a very strong form of Mach's Principle, requiring that in the absence of mass, space-time becomes not flat but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can derive the uncertainty principle. In addition, the superposition of stochastic metrics and the identification of the space-time volume element (the square root of minus the determinant of the metric tensor) as the indicator of relative probability yields the phenomenon of interference. When space-time granularity is added to the theory and the stochasticity is modeled as a (modified) Wiener process, additional results are obtained, including a derivation of the Schwarzschild metric (without employing the general relativity field equations), the major role of the Planck mass in quantum mechanics, the explanation of why the Schwarzschild radius of the Planck mass is the Planck length, and finally, a model for the nature of time.

A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is given, and proposed as a multipartite Schmidt decomposition. Finally, we develop an ent vector and ent array to handle more general definitions of multipartite entanglement, and the ent is extended to general mixed states, providing a general multipartite entanglement measure.

Causal discovery algorithms allow for the inference of causal structures from probabilistic relations of random variables. A natural field for the application of this tool is quantum mechanics, where a long-standing debate about the role of causality in the theory has flourished since its early days. In this paper, a causal discovery algorithm is applied in the search for causal models to describe a quantum version of Wheeler's delayed-choice experiment. The outputs explicitly show the restrictions for the introduction of classical concepts in this system. The exclusion of models with two hidden variables is one of them. A consequence of such a constraint is the impossibility to construct a causal model that avoids superluminal causation and assumes an objective view of the wave and particle properties simultaneously.

An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden associated with online calculation of the quantum filter. By using a differential geometric approach, the quantum trajectory is constrained in a finite-dimensional differentiable manifold consisting of an unnormalized exponential family of quantum density operators, and an exponential quantum projection filter is then formulated as a number of stochastic differential equations satisfied by the finite-dimensional coordinate system of this manifold. A convenient design of the differentiable manifold is also presented through reduction of the local approximation errors, which yields a simplification of the quantum projection filter equations. It is shown that the computational cost can be significantly reduced by using the quantum projection filter instead of the quantum filter. It is also shown that when the quantum projection filtering approach is applied to a class of open quantum systems that asymptotically converge to a pure state, the input-to-state stability of the corresponding exponential quantum projection filter can be established. Simulation results from an atomic ensemble system example are provided to illustrate the performance of the projection filtering scheme. It is expected that the proposed approach can be used in developing more efficient quantum control methods.

We propose a strategy for engineering multi-qubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific XX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a 2-body driving term leads to the iSWAP$_N$ gate, which we numerically test for N = 4 and 6.

One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.

We study a driven harmonic oscillator operating an Otto cycle between two thermal baths of finite size. By making extensive use of the tools of Gaussian quantum mechanics, we directly simulate the dynamics of the engine as a whole, without the need to make any approximations. This allows us to understand the non-equilibrium thermodynamics of the engine not only from the perspective of the working medium, but also as it is seen from the thermal baths' standpoint. For sufficiently large baths, our engine is capable of running a number of ideal cycles, delivering finite power while operating very close to maximal efficiency. Thereafter, having traversed the baths, the perturbations created by the interaction abruptly deteriorate the engine's performance. We additionally study the correlations generated in the system, and relate the buildup of working medium-baths and bath-bath correlations to the degradation of the engine's performance over the course of many cycles.

We prove number of quantitative stability bounds for the cases of equality in Petz's monotonicity theorem for quasi-relative entropies defined in terms of an operator monotone decreasing functions. Included in our results is a bound in terms of the Petz recovery map, but we obtain more general results. The present treatment is entirely elementary and developed in the context of finite dimensional von Neumann algebras where the results are already non-trivial and of interest in quantum information theory.

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information processing and for exploring the intriguing physics behind this power.

We investigate the performance of a Kennedy receiver, which is known as a beneficial tool in optical coherent communications, to the quantum state discrimination of the two superpositions of vacuum and single photon states corresponding to the $\hat\sigma_x$ eigenstates in the single-rail encoding of photonic qubits. We experimentally characterize the Kennedy receiver in vacuum-single photon two-dimensional space using quantum detector tomography and evaluate the achievable discrimination error probability from the reconstructed measurement operators. We furthermore derive the minimum error rate obtainable with Gaussian transformations and homodyne detection. Our proof of principle experiment shows that the Kennedy receiver can achieve a discrimination error surpassing homodyne detection.

We model the broadband enhancement of single-photon emission from color centres in silicon carbide (SiC) nanocrystals coupled to a planar hyperbolic metamaterial (HMM) resonator. The design is based on positioning the single photon emitters within the HMM resonator, made of a dielectric index-matched with SiC material, and using a gold (Au) cylindrical antenna for improved collection efficiency. We show that employing this HMM resonator can result in a significant enhancement of the spontaneous emission of a single photon source and its collection efficiency, compared to previous designs.

In this work, our statements are based on the progress of current research on superatomic clusters. Combining the new trend of materials and device manufacture at the atomic level, we analyzed the opportunities for the development based on the use of superatomic clusters as units of functional materials, and presented a foresight of this new branch of science with relevant studies on superatoms.

In this work we consider the Kitaev Toric Code with specific open boundary conditions. Such a physical system has a highly degenerate ground state determined by the degrees of freedom localised at the boundaries. We can write down an explicit expression for the ground state of this model. Based on this, the entanglement properties of the model are studied for two types of bipartition: one, where the subsystem A is completely contained in B; and the second, where the boundary of the system is shared between A and B. In the former configuration, the entanglement entropy is the same as for the periodic boundary condition case, which means that the bulk is completely decoupled from the boundary on distances larger than the correlation length. In the latter, deviations from the torus configuration appear due to the edge states and lead to an increase of the entropy. We then determine an effective theory for the boundary of the system. In the case where we apply a small magnetic field as a perturbation the degrees of freedom on the boundary acquire a dispersion relation. The system can there be described by a Hamiltonian of the Ising type with a generic spin-exchange term.

We investigate the quantum phase transitions of the transverse-field quantum Ising model on the triangular lattice and Sierpi\'nski fractal lattices by employing multipartite entanglement and quantum coherence along with the quantum renormalization group method. It is shown that the quantum criticalities of these high-dimensional models closely relate to the behaviors of the multipartite entanglement and quantum coherence. As the thermodynamic limit is approached, the first derivatives of multipartite entanglement and quantum coherence exhibit singular behaviors and the consistent finite-size scaling behaviors for each lattice are also obtained from the first derivatives. The multipartite entanglement and quantum coherence are demonstrated to be good indicators for detecting the quantum phase transitions in the triangular lattice and Sierpi\'nski fractal lattices. Furthermore, the factors that determine the relations between the critical exponents and the correlation length exponents for these models are diverse. For the triangular lattice, the decisive factor is the spatial dimension, while for the Sierpi\'nski fractal lattices, it is the Hausdorff dimension.

We solve the non-stationary Schrodinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrodinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnikov-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

We propose a method to prepare states of given quantized circulation in annular Bose-Einstein condensates (BEC) confined in a ring trap using the method of phase imprinting without relying on a two-photon angular momentum transfer. The desired phase profile is imprinted on the atomic wave function using a short light pulse with a tailored intensity pattern generated with a Spatial Light Modulator. We demonstrate the realization of 'helicoidal' intensity profiles suitable for this purpose. Due to the diffraction limit, the theoretical steplike intensity profile is not achievable in practice. We investigate the effect of imprinting an intensity profile smoothed by a finite optical resolution onto the annular BEC with a numerical simulation of the time-dependent Gross-Pitaevskii equation. This allows us to optimize the intensity pattern for a given target circulation to compensate for the limited resolution.

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

Considering a spin-1/2 chain, we {suppose} that the entanglement passes from a given pair of particles to another one, thus establishing the relay transfer of entanglement along the chain. Therefore, we introduce the relay entanglement as a sum of all pairwise entanglements in a spin chain. For more detailed studying the effects of {remote} pairwise entanglements, we use the partial sums collecting entanglements between the spins separated by up to a certain number of nodes. The problem of entangled cluster formation is considered, and the geometric mean entanglement is introduced as a {characteristics} of quantum correlations in a cluster. Generally, the life-time of a cluster decreases with an increase in its size.

Author(s): Raúl A. Briceño, Jozef J. Dudek, and Ross D. Young

Hadrons and their interactions arise via the coupling between quarks and gluons, as dictated by quantum chromodynamics (QCD), the theory of strong interactions. Unlike protons and neutrons, very few hadrons observed in nature are stable under the strong interaction: the majority of them appear as resonances in scattering experiments. This work reviews progress and prospects in the studies of few-hadron reactions and resonance properties using lattice QCD techniques.

[Rev. Mod. Phys. 90, 025001] Published Wed Apr 18, 2018

Author(s): Igor Ferrier-Barbut, Matthias Wenzel, Fabian Böttcher, Tim Langen, Mathieu Isoard, Sandro Stringari, and Tilman Pfau

We report on the observation of the scissors mode of a single dipolar quantum droplet. The existence of this mode is due to the breaking of the rotational symmetry by the dipole-dipole interaction, which is fixed along an external homogeneous magnetic field. By modulating the orientation of this mag...

[Phys. Rev. Lett. 120, 160402] Published Wed Apr 18, 2018