Kauffman and Lomonaco explored the idea of understanding quantum entanglement (the non-local correlation of certain properties of particles) topologically by viewing unitary entangling operators as braiding operators. In the work of G. Alagic, M. Jarret, and S. Jordan it is shown that entanglement is a necessary condition for forming invariants of knots from braid closures via solutions to the Yang-Baxter Equation. We show that the arguments used by these authors generalize to essentially the same results for quantum invariant state summation models of knots. We also give a class of R-matrices that are entangling and are weak invariants of classical knots and links yet strong invariants of virtual knots and links. We also given an example of an SU(2) representation of the three-strand braid group that models the Jones polynomial for closures of three-strand braids. This invariant is a quantum model for the Jones polynomial restricted to three strand braids, and it does not involve quantum entanglement. These relationships between topological braiding and quantum entanglement can be used as a framework for future work in understanding the properties of entangling gates in topological quantum computing.

This paper provides a novel approach to solving the transmission of electrons through large graphene Nano-structures, which is shown to be accurate both at high and low speeds. The model for graphene being solved is the continuum model governed by an analogue to the Dirac equation. For finding a favorite solution, the Dirac equation is scalarised using the Foldy-Wouthuysen expansion approximation, to reduce the problem of calculating the electron wave propagation to a scalar differential equation. Also transformed wave functions provides the exact solution of the Dirac equation in homogeneous space for the calculation of the propagation of electron waves.By analytically calculating the boundary conditions of the transformed wave functions, we have been able to generate transfer matrices for the scalar propagation equations.Furthermore,we have implemented the scattering matrix method upon these transfer matrices. Implementing the scattering matrix method makes a numerical stable propagation of the waves through the graphene.Finally we test the convergence and accuracy of the new method compared to analytical solutions.Hence , we conclude that our achievement is a rich appendix detailing for the results of our research into relativistic Green's functions.

Author(s): Milan S. Petrović, Najdan B. Aleksić, Branislav N. Aleksić, Aleksandra I. Strinić, and Milivoj R. Belić

In a recent paper [Alberucci, Jisha, Smyth, and Assanto, Phys. Rev. A **91**, 013841 (2015)], Alberucci *et al.* have studied the propagation of bright spatial solitary waves in highly nonlocal media. We find that the main results in that and related papers concerning soliton shape and dynamics, based on …

[Phys. Rev. A 95, 057801] Published Thu May 25, 2017

Author(s): Alessandro Alberucci, Chandroth P. Jisha, Noel F. Smyth, and Gaetano Assanto

In their Comment, Petrović *et al.* claim that some of the results previously published by us on the use of the “accessible soliton” model of Snyder *et al.* are incorrect, and they claim that the correct results were published elsewhere. In order to give our perspective on the problem, we discuss and c…

[Phys. Rev. A 95, 057802] Published Thu May 25, 2017

Author(s): Mainak Sadhukhan and Alexandre Tkatchenko

It is an undisputed textbook fact that nonretarded van der Waals (vdW) interactions between isotropic dimers are attractive, regardless of the polarizability of the interacting systems or spatial dimensionality. The universality of vdW attraction is attributed to the dipolar coupling between fluctua…

[Phys. Rev. Lett. 118, 210402] Published Thu May 25, 2017

Author(s): Diego A. Alcala, Joseph A. Glick, and Lincoln D. Carr

Tunneling of a quasibound state is a nonsmooth process in the entangled many-body case. Using time-evolving block decimation, we show that repulsive (attractive) interactions speed up (slow down) tunneling. While the escape time scales exponentially with small interactions, the maximization time of …

[Phys. Rev. Lett. 118, 210403] Published Thu May 25, 2017

Observations of the orbits of two stars at the center of the Milky Way constrain gravitational models involving a hypothetical fifth force.

[Physics] Published Thu May 25, 2017

Categories: Physics

Author(s): Alley Hameedi, Debashis Saha, Piotr Mironowicz, Marcin Pawłowski, and Mohamed Bourennane

Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the enta…

[Phys. Rev. A 95, 052345] Published Thu May 25, 2017

An important class of contextuality arguments in quantum foundations are the All-versus-Nothing (AvN) proofs, generalising a construction originally due to Mermin. We present a general formulation of All-versus-Nothing arguments, and a complete characterisation of all such arguments which arise from stabiliser states. We show that every AvN argument for an n-qubit stabiliser state can be reduced to an AvN proof for a three-qubit state which is local Clifford-equivalent to the tripartite GHZ state. This is achieved through a combinatorial characterisation of AvN arguments, the AvN triple Theorem, whose proof makes use of the theory of graph states. This result enables the development of a computational method to generate all the AvN arguments in $\mathbb{Z}_2$ on n-qubit stabiliser states. We also present new insights into the stabiliser formalism and its connections with logic.

Dissipative entanglement generation protocols embrace environmental interactions in order to generate long-lived entangled states. In this letter, we report on anti-bunching in the second order correlation function for a pair of actively driven quantum emitters coupled to a shared dissipative plasmonic reservoir. We find that anti-bunching is a universal signature for entangled states generated by dissipative means and examine its use as an entanglement diagnostic. We discuss the experimental validation of anti-bunching on realistic timescales, determined by an effective two-qubit Rabi frequency, and analyze the robustness of entanglement generation with respect to perturbations in local detunings, couplings, and driving fields.

We have recently demonstrated the laser cooling of a single $^{40}$Ca$^+$ ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S$_{1/2} \leftrightarrow$ D$_{5/2}$. Here we report on the extension of this technique to small ion Coulomb crystals made of two or three $^{40}$Ca$^+$ ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two- and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling of $\bar n_\text{COM}=0.30(4)$ for the centre of mass mode and $\bar n_\text{B}=0.07(3)$ for the breathing mode of the two-ion string with corresponding heating rates of 11(2) s$^{-1}$ and 1(1) s$^{-1}$ at a trap frequency of 162 kHz. The ground state occupation of the axial modes is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5) s$^{-1}$ at a trap frequency of 355 kHz.

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group $\mathbb Z^3$, that in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of $\mathbb Z^3$ that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices.

In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensor-network states. The computational cost for carrying out this contraction is generally very high, which limits the largest bond dimension of tensor-network states that can be accurately studied to a relatively small value. We propose a dimension reduction scheme to solve this problem by mapping the double-layer tensor network onto an intersected single-layer tensor network. This reduces greatly the bond dimensions of local tensors to be contracted, and improves dramatically the efficiency and accuracy in the evaluation of expectation values of tensor-network states. It almost doubles the largest bond dimension of tensor-network states whose physical properties can be efficiently and reliably calculated, and extends significantly the application scope of tensor-network methods.

We present a general approach to speed up the adiabatic process without adding the traditional counterdiabatic driving (CD) Hamiltonian. The strategy is to design an easy-to-get intermediate Hamiltonian to connect the original Hamiltonian and final transitionless Hamiltonian. With final transitionless Hamiltonian, the same target can be achieved as in the adiabatic process governed by the original Hamiltonian, but in a shorter time. We apply the present approach to a three-level system, and the result shows that the final transitionless Hamiltonian usually has the same structure as the original Hamiltonian but with different time-dependent coefficients, allowing speedup to be achieved in a much easier way compared to previous methods.

In this paper, a scheme is put forward to design pulses which drive a three-level system based on the reverse engineering with Lewis-Riesenfeld invariant theory. The scheme can be applied to a three-level system even when the rotating-wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.

We investigate ground state properties of spin-1 bosonic system trapped in optical lattice with extended standard basis operator (SBO) method. For both ferromagnetic ($U_2<0$) and antiferromagnetic ($U_2>0$) systems, we analytically figure out the symmetry properties in Mott-insulator and superfluid phases, which would provide a deeper insight into the MI-SF phase transition process. Then by applying self-consistent approach to the method, we include the effect of quantum and thermal fluctuations and derive the MI-SF transition phase diagram, which is in quantitative agreement with recent Monte-Carlo simulation at zero temperature, and at finite temperature, we find the underestimation of finite-temperature-effect in the mean-field approximation method. If we further consider the spin excitations in the insulating states of spin-1 system in external field, distinct spin phases are expected. Therefore, in the Mott lobes with $n=1$ and $n=2$ atoms per site, we give analytical and numerical boundaries of the singlet, nematic, partially magnetic and ferromagnetic phases in the magnetic phase diagrams.

We study the unidirectional amplification of optical probe fields in a three-mode optomechanical system, where the mechanical resonator interacts with two linearly-coupled optical cavities and the cavities are driven by strong optical pump fields. An optical probe field is injected into one of the cavity modes, and at the same time, it is applied to the mechanical mode after being down-converted by the optical pump frequency. We show that the transmission of the probe field can be amplified in one direction and de-amplified in the opposite direction. This unidirectional amplification or de-amplification results from the constructive or destruction interference between different transmission paths in this three-mode optomechanical system.

We propose a bosonic Josephson junction (BJJ) in two nonlinear mechanical resonator coupled through two-phonon exchange interaction induced by quadratic optomechanical couplings. The nonlinear dynamic equations and effective Hamiltonian are derived to describe behaviors of the BJJ. We show that the BJJ can work in two different dynamical regimes: Josephson oscillation and macroscopic self-trapping. The system can transfer from one regime to the other one when the self-interaction and asymmetric parameters exceed their critical values. We predict that a transition from Josephson oscillation to macroscopic self-trapping can be induced by the phonon damping in the asymmetric BJJs. Our results opens up a way to demonstrate BJJ with two-phonon exchange interaction and can be applied to other systems, such as the optical and microwave systems.

We consider two chains, each made of $N$ independent oscillators, immersed in a common thermal bath and study the dynamics of their mutual quantum correlations in the thermodynamic, large-$N$ limit. We show that dissipation and noise due to the presence of the external environment are able to generate collective quantum correlations between the two chains at the mesoscopic level. The created collective quantum entanglement between the two many-body systems turns out to be rather robust, surviving for asymptotically long times even for non vanishing bath temperatures.

We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be directly obtained from the underlying dynamics. Examples are then provided to demonstrate the usefulness of the maximal quantum Fisher information matrix by deriving various tradeoff relations in multi-parameter quantum estimation and obtaining the bounds for the scalings of the precision limit.