We propose a realistic system with separated optical and mechanical degrees of freedom, in which a high-mechanical-quality silicon nitride membrane is placed upon a high-optical-quality whispering gallery microcavity. The strongly enhanced linear optomechanical coupling, together with simultaneously low optical and mechanical losses in the present system, results in a remarkable single-photon cooperativity exceeding 300. This unprecedented cooperativity in the optomechanical system enables optical nonlinearity at low light intensities and holds great potential in generating, storing, and implementing quantum states. Moreover, the device gives rise to significantly stronger quadratic optomechanical coupling than achieved to date, which is desirable for measuring phonon shot noise with a high signal-to-noise ratio.

When a chain of $N$ superconducting qubits couples to a coplanar resonator, each of the qubits experiences a different dipole-field coupling strength due to the wave form of the cavity field. We find that this inhomogeneous coupling leads to a dependence of the collective ladder operators of the qubit chain on the qubit-interspacing $l$. Varying the spacing $l$ changes the transition amplitudes between the angular momentum levels. We derive an exact diagonalization of the general $N$-qubit Hamiltonian and, through the $N=4$ case, demonstrate how the $l$-dependent operators lead to a denser one-excitation spectrum and a probability redistribution of the eigenstates. Moreover, we show that the variation of $l$ between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting qubit chain.

We show that propagating optical fields bearing an axial symmetry are not truly hollow in spite of a null electric field on axis. The result, obtained by general arguments based upon the vectorial nature of electromagnetic fields, is of particular significance in the situation of an extreme focusing, when the paraxial approximation no longer holds. The rapid spatial variations of fields with a “complicated” spatial structure are extensively analyzed in the general case and for a Laguerre-Gauss beam as well, notably for beams bearing a $\left|l\right|=2$ orbital angular momentum for which a magnetic field and a gradient of the electric field are present on axis. We thus analyze the behavior of an atomic size light detector, sensitive as well to quadrupole electric transitions and to magnetic dipole transitions, and apply it to the case of a Laguerre-Gauss beam. We detail how the mapping of such a beam depends on the nature and on the specific orientation of the detector. We show also that the interplay of mixing of polarization and topological charge, respectively associated to spin and orbital momentum when the paraxial approximation holds, modifies the apparent size of the beam in the focal plane. This even leads to a breaking of the cylindrical symmetry in the case of a linearly polarized transverse electric field.

Recently, Zou, and Qiu [Phys. Rev. A 82, 042325 (2010)] demonstrated that two arbitrated quantum signature (AQS) schemes are not secure because an arbitrator cannot arbitrate the dispute between two users when a receiver repudiates the integrity of a signature. By using a public board, Zou and Qiu's proposed two AQS schemes to solve the problem. This work shows that the same security problem may exist in Zou and Qiu's schemes. Moreover, a malicious verifier, Bob, can actively negate a signed order if he wants to. This attack, a special case of the denial-of-service (DoS) attack mentioned by Cai [Phys. Rev. Lett. 91, 109801 (2003)], is important in quantum cryptography. Bob may get some benefits from this DoS attack since he can actively deny Alice's signed order without being detected. This work also shows that a malicious signer can reveal the verifier's secret key without being detected by using Trojan-horse attacks.

Motivated by thermodynamic considerations, we analyze the variation of the quantum mutual information on a unitary orbit of a bipartite system's state with and without global constraints such as energy conservation. We solve the full optimization problem for the smallest system of two qubits and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward for equal-sized subsystems, however their minimization displays nontrivial structures. We characterize a set of separable states in which the minimally correlated state resides: a collection of classically correlated states admitting a particular “Young tableau” form. Furthermore, a partial order exists on this set with respect to individual marginal entropies, and the presence of a “see-saw effect” for these entropies forces a finer analysis to determine the optimal tableau.

Quantum discord is usually referred to as a measure for quantum correlations. In the search of the fundamental resource to gain a quantum advantage in quantum information applications, quantum discord is considered a promising candidate. In this paper we present an alternative view on quantum correlations in terms of the rank of the correlation matrix as introduced by Dakić, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)]. According to our analysis, information about the quantum discord does not necessarily determine the amount of quantum correlations but rather the quantumness of the state. Nonzero quantum discord is only a necessary but not a sufficient condition for correlations above the classically achievable limit. This becomes clear when we consider states of nonzero discord, which can be created from zero discord states only by a single local operation. We further show that the set of these states has measure zero.

In a recent paper, Bender and Klevansky [Phys. Rev. A 84, 024102 (2011)] considered $\mathcal{PT}$-symmetric matrix representations for fermionic operator algebras of the form ${\xi }^2={\overline{\xi }}^2=0$, $\xi \overline{\xi }+\overline{\xi }\xi =\varepsilon 1$, where $\overline{\xi }$ is the $\mathcal{PT}$ transform of $\xi$. They constructed such algebras for $\varepsilon =-1$ and established that it is not possible to construct a matrix representation for the standard fermionic algebra ($\varepsilon =1$). Bender and Klevansky used the formalism developed by Jones-Smith and Mathur [Phys. Rev. A 82, 042101 (2010)] which extends $\mathcal{PT}$-symmetric quantum mechanics to the case of odd time-reversal symmetry (fermionic case). By using the same formalism, we show that $\mathcal{PT}$-symmetric matrix representations exist for both standard ($\varepsilon =1)$ and abnormal ($\varepsilon =-1)$ fermionic algebras if one takes $\overline{\xi }$ as adjoint $\xi$ with respect to the $\mathcal{CPT}$ and $\mathcal{PT}$ inner products, respectively. This general result is illustrated for the example of a typical quaternionic four-level model by an explicit construction of the fermionic creation and annihilation operators which satisfy all the criteria of $\mathcal{PT}$ quantum mechanics for the odd time-reversal symmetry.

We report results from a joint experimental and theoretical study of the angular momentum transfer in electron-impact excitation of the $\left(2p^6\right){}^1{S}_0\to \left(2p{}^{5}3s\right){}^1{P}_1$ resonance transition in Ne. Both the measured and calculated data show the circular light polarization $P_3$ to be positive for an incident energy of 25 eV at scattering angles below 40${}^{\circ }$. This observation implies a negative angular momentum transfer $L_{\perp }$, which is the opposite sign of orientation expected from a well-known propensity rule for $S\to P$ excitation at small scattering angles.

Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark-soliton excitations that show periodic density dynamics in real space. In addition to the density feature, the solitons also carry a localized pseudospin magnetization that exhibits a rich and tunable dynamics. Analytical results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.

We demonstrate quantum-noise-limited frequency-comb cavity-enhanced absorption spectroscopy with spectrally multiplexed detection for acquisition times ranging from 10 ms up to 10 min, where a record absorption sensitivity of $7\times {10}^{-13}$ ${\mathrm{cm}}^{-1}$ per spectral element is attained with nW power levels. For this, a widely tuneable frequency-doubled free-running fs Ti:sapphire laser oscillator is coupled to a cavity of extreme finesse (32 000) whose length is modulated and whose output is spectrally dispersed over a linear charge coupled device array. This scheme is robust, as it does not require tight frequency locking or controlling the comb frequency offset, and works with spectrally broad combs, as it is not limited by cavity dispersion.

In a previous paper it was shown that a one-turning-point Wentzel-Kramers-Brillouin (WKB) approximation gives an accurate picture of the spectrum of certain non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians on a finite interval with Dirichlet boundary conditions. Potentials to which this analysis applies include the linear potential $V=igx$ and the sinusoidal potential $V=ig\sin \left(\alpha x\right)$. However, the one-turning-point analysis fails to give the full structure of the spectrum for the cubic potential $V=ig{x}^3$, and in particular, it fails to reproduce the critical points at which two real eigenvalues merge and become a complex-conjugate pair. The present paper extends the method to cases where the WKB path goes through a pair of turning points. The extended method gives an extremely accurate approximation to the spectrum of $V=ig{x}^3$, and more generally it works for potentials of the form $V=ig{x}^{2N+1}$. When applied to potentials with half-integral powers of $x$, the method again works well for one sign of the coupling, namely, that for which the turning points lie on the first sheet in the lower-half plane.

Explicit expressions for most interesting quantum observable operators in optical tomography representation are found. A general formalism of the symbols of the operators is presented in the optical tomography representation. The symbols of the operators in the form of singular and regular generalized functions are found, and suggestions for their use in experimental data processing in quantum tomography are given.

In this paper we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of the experiment, we allow for measurements to be adaptively and efficiently reoptimized depending on data collected so far. We develop an adaptive statistical framework based on Bayesian inference and Shannon's information, and demonstrate a significant reduction in the total number of measurements required as compared to nonadaptive methods, including mutually unbiased bases.

We present a scheme for universal quantum computation based on spinless interacting bosonic quantum walkers on a piecewise-constant graph, described by the two-dimensional Bose-Hubbard model. Arbitrary $X$ and $Z$ rotations are constructed, as well as an entangling two-qubit cphase gate and a swap gate. Quantum information is encoded in the positions of the walkers on the graph, as in previous quantum walk-based proposals for universal quantum computation, though in contrast to prior schemes this proposal requires a number of vertices only linear in the number of encoded qubits. It allows single-qubit measurements to be performed in a straightforward manner with localized operators and can make use of existing quantum error-correcting codes either directly within the universal gate set provided or by extending the lattice to a third dimension. We present an intuitive example of a logical encoding to implement the seven-qubit Steane code. Finally, an implementation in terms of ultracold atoms in optical lattices is suggested.

The quantum correlations between a qubit and its environment are described quantitatively in terms of interatomic distance. Specifically, considering a realistic system of two two-level atoms and taking into account the dipole-dipole interaction and collective damping, the quantum entanglement and quantum discord are investigated during the dissipative process as functions of the interatomic distance. For atoms that are initially maximally entangled, it turns out that there is a critical distance at which each atom is maximally quantum correlated with its environment. Counterintuitively, the approach of the two atoms can maximize the entanglement between each one and the environment and, even at the same distance, minimize the loss of entanglement between the pair.

We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find a first, but somewhat unsatisfactory, continuous set which does not relate to an underlying Heisenberg pair of complementary observables. Then, by a nonsingular mapping of the discrete angular momentum basis of the rotor onto the Fock basis for linear motion, we construct such a Heisenberg pair for the rotor and use it to obtain a second, fully satisfactory, set of mutually unbiased bases.

We consider a network whose nodes are electromagnetic cavities, each coupled to a single three-level atom. The nodes are connected by optical fibers. Each atom is addressed by a control laser, which along with the cavity field drives atomic transitions. The network can be in the form of chain or two- and three-dimensional arrays of $N$ cavities connected by $N_B$ fibers. Following the work on a two-cavity system by Pellizzari, we find that under certain conditions the system possesses two kinds of dark states. The first kind are $N$ states corresponding to atomic excitations at each node and these are our logical states for quantum processing. The second kind are $N_B$ degenerate dark states on pairs of sites connected by a fiber. By manipulating intensities and phases of control lasers on the cavities, one can pass adiabatically among these dark states due to their degeneracy. This network operates as an $N$-level quantum system in which one can generate computationally useful states by protocols of external controls. We obtain numerical results for small chains and lattices to demonstrate some quantum operations such as the transport of states across the array, generation of $W$ states, and Fourier-like states. We also discuss effects of dissipation and limitations of the model.

We show that the finite-basis optimized effective potential (OEP) equations exhibit previously unknown singular behavior. Imposing continuity, we derive new well-behaved finite-basis-set OEP equations that determine OEP for any orbital and any large enough potential basis sets and which adopt an analytic solution via matrix inversion.