We provide $poly\log$ sparse quantum codes for correcting the erasure channel arbitrarily close to the capacity. Specifically, we provide $[[n, k, d]]$ quantum stabilizer codes that correct for the erasure channel arbitrarily close to the capacity if the erasure probability is at least $0.33$, and with a generating set $\langle S_1, S_2, ... S_{n-k} \rangle$ such that $|S_i|\leq \log^{2+\zeta}(n)$ for all $i$ and for any $\zeta > 0$ with high probability. In this work we show that the result of Delfosse et al. is tight: one can construct capacity approaching codes with weight almost $O(1)$.

We have subjected the planar pendulum eigenproblem to a symmetry analysis with the goal of explaining the relationship between its conditional quasi-exact solvability (C-QES) and the topology of its eigenenergy surfaces, established in our earlier work [Frontiers in Physical Chemistry and Chemical Physics 2, 1-16, (2014)]. The present analysis revealed that this relationship can be traced to the structure of the tridiagonal matrices representing the symmetry-adapted pendular Hamiltonian, as well as enabled us to identify many more -- forty in total to be exact -- analytic solutions. Furthermore, an analogous analysis of the hyperbolic counterpart of the planar pendulum, the Razavy problem, which was shown to be also C-QES [American Journal of Physics 48, 285 (1980)], confirmed that it is anti-isospectral with the pendular eigenproblem. Of key importance for both eigenproblems proved to be the topological index $\kappa$, as it determines the loci of the intersections (genuine and avoided) of the eigenenergy surfaces spanned by the dimensionless interaction parameters $\eta$ and $\zeta$. It also encapsulates the conditions under which analytic solutions to the two eigenproblems obtain and provides the number of analytic solutions. At a given $\kappa$, the anti-isospectrality occurs for single states only (i.e., not for doublets), like C-QES holds solely for integer values of $\kappa$, and only occurs for the lowest eigenvalues of the pendular and Razavy Hamiltonians, with the order of the eigenvalues reversed for the latter. For all other states, the pendular and Razavy spectra become in fact qualitatively different, as higher pendular states appear as doublets whereas all higher Razavy states are singlets.

The concept of correlation is central to all approaches that attempt the description of many-body effects in electronic systems. Multipartite correlation is a quantum information theoretical property that is attributed to quantum states independent of the underlying physics. In quantum chemistry, however, the correlation energy (the energy not seized by the Hartree-Fock ansatz) plays a more prominent role. We show that these two different viewpoints on electron correlation are closely related. The key ingredient turns out to be the energy gap within the symmetry-adapted subspace. We then use a few-site Hubbard model and the stretched H$_2$ to illustrate this connection and to show how the corresponding measures of correlation compare.

I propose classical and quantum limits to the statistical resolution of two incoherent optical point sources from the perspective of minimax parameter estimation. Unlike earlier results based on the Cram\'er-Rao bound, the limits proposed here, based on the worst-case error criterion and a Bayesian version of the Cram\'er-Rao bound, are valid for any biased or unbiased estimator and obey photon-number scalings that are consistent with the behaviors of actual estimators. These results prove that, from the minimax perspective, the spatial-mode demultiplexing (SPADE) measurement scheme recently proposed by Tsang, Nair, and Lu [Phys. Rev. X 6, 031033 (2016)] remains superior to direct imaging for sufficiently high photon numbers.

Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and technology. In this paper, we generalize hypergraph states to qudit hypergraph states, i.e., each vertex in the generalized hypergraph (multi-hypergraph) represents a $d$-level quantum system instead of a qubit. It is shown that multi-hypergraphs (each vertex represents a $d$-level quantum system) and $d$-level hypergraph states have a one-to-one correspondence. We prove that if one part of a multi-hypergraph is connected with the other part, the corresponding subsystems are entangled. More generally, the structure of a multi-hypergraph reveals the entanglement property of the corresponding quantum state. These states' responses to the generalized $Z$ ($X$) operations and $Z$ ($X$) measurements are studied. Bell non-locality, an important resource in fulfilling quantum information tasks, is also investigated.

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable source for the coherent matter waves in these devices are Bose-Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross-Pitaevskii equation, requires suitable analytical and numerical methods which take into account the center-of-mass motion of the condensate, its rotation and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both, an approximate analytical solution for condensates in the Thomas-Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research.

It is demonstrated that the set of 40 states of a spin-3/2 particle used by Zimba and Penrose to give proofs of the Kochen-Specker and Bell theorems is identical (i.e., unitarily equivalent) in CP(3) to the set of 40 rays derived from the vertices of the Witting polytope, which is a regular complex polytope in C(4). The Witting polytope actually has two different apparitions in projective spaces of different dimensions: it appears in CP(3) as the Penrose dodecahedron and in RP(7) (after an initial inflation into R(8)) as a set of rays associated with the root vectors of the Lie algebra E8. The interest of these apparitions is that they provide proofs of the Kochen-Specker theorem, but of very different types: while the proofs provided by the Penrose dodecahedron are complex (in both senses of the word), those provided by the E8 system are real and easy to grasp (being parity proofs that take no more than simple counting to verify). The different proofs it provides in different settings would seem to justify calling the Witting polytope a "quantum chameleon", and we raise (but leave unanswered) the question of whether it is the only object of this type.

We investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of non-uniformly distributed lattice sites only. By adding or removing links between lattice sites, we change the spectral dimension of a lattice but keep the fractional Hausdorff dimension fixed. From the analysis of energy level statistics obtained via direct diagonalization of finite systems, we observe that eigenfunction localization strongly depends on the spectral dimension. Conversely, we show that localization properties of the system do not change significantly while we alter the Hausdorff dimension. In addition, for low spectral dimensions, we observe superlocalization resonances and a formation of an energy gap around the center of the spectrum.

Achieving the Heisenberg limit (HL) in an experiment with very large number of atoms N is a challenging task. One mechanism for doing so is to make use of the experimentally achievable one axis twist spin squeezing in combination with unsqueezing which results in the generation of a Schr\"odinger cat state corresponding to an equal superposition of the extremal Dicke collective states. However, the protocol for achieving this result critically requires the knowledge of whether the total number of atoms is even or odd. Here, we describe a protocol which employs null detection of one of the collective states that circumvents this problem. Specifically, we show that this detection process produces fringes that are narrowed by a factor of N with unit visibility when N is even, and yields zero signal when N is odd. Thus, over repeated measurements under which the probability of N being even or odd is equal, the signal from the odd cases get filtered out, and HL sensitivity is achieved for the $\sim N/2$ atoms corresponding to the even cases. For all N atoms, the sensitivity is below the HL by a factor of $\sqrt{2}$. We also show that a degree of sensitivity enhancement very close to this value can also be achieved for a much lower degree of squeezing than what is required for reaching the cat states. We show that the Schr\"odinger cat case corresponds to interference between collective states with Compton frequencies $\sim 10^{31}$ Hz for $^{87}$Rb atoms with $N = 10^6$. Aside from conventional application to precision metrology, such a Schr\"odinger cat atom interferometer may serve as a test-bed for various aspects of fundamental physics, such as the effect of gravitational interaction on macroscopic decoherence. Finally, we note that the proposed scheme can also be used to realize an HL Schr\"odinger cat atomic clock, for which the base frequency is effectively enhanced by a factor of N.

The laws of quantum mechanics allow for the distribution of a secret random key between two parties. Here we analyse the security of a protocol for establishing a common secret key between N parties (i.e. a conference key), using resource states with genuine N-partite entanglement. We compare this protocol to conference key distribution via bipartite entanglement, regarding the required resources, achievable secret key rates and threshold qubit error rates. Furthermore we discuss quantum networks with bottlenecks for which our multipartite entanglement-based protocol can benefit from network coding, while the bipartite protocol cannot. It is shown how this advantage leads to a higher secret key rate.

The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables to study finite time cycles limiting time on the adiabtic and the thermalization times. Explicit finite time solutions are found which are frictionless, meaning that no coherence is generated also known as shortcuts to adiabaticity. The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators.

We consider an exactly solvable inhomogeneous Dicke model which describes an interaction between a disordered ensemble of two-level systems with single mode boson field. The existing method for evaluation of Richardson-Gaudin equations in the thermodynamical limit is extended to the case of Bethe equations in Dicke model. Using this extension, we present expressions both for the ground state and lowest excited states energies as well as leading-order finite-size corrections to these quantities for an arbitrary distribution of individual spin energies. We then evaluate these quantities for an equally-spaced distribution (constant density of states). In particular, we study evolution of the spectral gap and other related quantities. We also reveal regions on the phase diagram, where finite-size corrections are of particular importance.

We discuss the equivalent form of Levy-Leblond equation [1, 2] such that the nilpotent matrices are two dimensional. We show that this equation can be obtained in the non-relativistic limit of the (2+1) dimensional Dirac equation. Furthermore, we analyze the case with four dimensional matrices and propose a Hamiltonian for the equation in (3+1) dimensions and solve it for a Coulomb potential. We show that the quantized energy levels for the hydrogen atom are obtained and the result is consistent with non-relativistic quantum mechanics.

Author(s): Farrokh Sarreshtedari and Mehdi Hosseini

The laser coupled Landau-Zener avoided crossing has been investigated with an aim towards obtaining the laser source parameters for precise controlling of the state dynamics in a two-level quantum system. The conventional Landau-Zener equation is modified for including the interaction of the system …

[Phys. Rev. A 95, 033834] Published Mon Mar 27, 2017

Author(s): Jonathan M. Silver, Changlei Guo, Leonardo Del Bino, and Pascal Del’Haye

Microresonator-based optical frequency combs (“microcombs”) have attracted lots of attention in the past few years thanks to their promising applications in telecommunications, spectroscopy, and optical clocks. The process of comb generation in microresonators can be modeled in the frequency domain …

[Phys. Rev. A 95, 033835] Published Mon Mar 27, 2017

Author(s): V. V. Ramasesh, E. Flurin, M. Rudner, I. Siddiqi, and N. Y. Yao

The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables th…

[Phys. Rev. Lett. 118, 130501] Published Mon Mar 27, 2017

Author(s): Luca Mancino, Marco Sbroscia, Ilaria Gianani, Emanuele Roccia, and Marco Barbieri

Standard thermometry employs the thermalization of a probe with the system of interest. This approach can be extended by incorporating the possibility of using the nonequilibrium states of the probe and the presence of coherence. Here, we illustrate how these concepts apply to the single-qubit therm…

[Phys. Rev. Lett. 118, 130502] Published Mon Mar 27, 2017

Author(s): József Fortágh and Andreas Günther

A refined version of a Bose-Einstein-condensate microscope detects static magnetic fields near the surface of a chip with unprecedented sensitivity and over a wide temperature range.

[Physics 10, 30] Published Mon Mar 27, 2017

Categories: Physics

Author(s): Johannes Fink

A new quantum communication protocol is robust in the presence of thermal noise, paving the way for all-microwave quantum networks.

[Physics 10, 32] Published Mon Mar 27, 2017

Categories: Physics

Author(s): Eyuri Wakakuwa

We introduce and analyze a task that we call *symmetrization*, in which a state of a quantum system, associated with a symmetry group, is transformed by a random unitary operation to a symmetric state. Each element of the unitary ensemble is required to be symmetry preserving, in the sense that it kee…

[Phys. Rev. A 95, 032328] Published Mon Mar 27, 2017