# Showing papers in "Physical Review A in 2002"

••

TL;DR: A measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system is presented and it is shown that it does not increase under local manipulations of the system.

Abstract: We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

3,287 citations

••

Abstract: A theoretical quantum key distribution scheme using Einstein-Podolsky-Rosen (EPR) pairs is presented. This scheme is efficient in that it uses all EPR pairs in distributing the key except those chosen for checking eavesdroppers. The high capacity is achieved because each EPR pair carries 2 bits of key code.

1,278 citations

••

Abstract: What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

1,218 citations

••

Abstract: We have extended the tunneling ionization model of Ammosov-Delone-Krainov (ADK) for atoms to diatomic molecules by considering the symmetry property and the asymptotic behavior of the molecular electronic wave function. The structure parameters of several molecules needed for calculating the ionization rates using this molecular ADK model have been obtained. The theory is applied to calculate the ratios of ionization signals for diatomic molecules with their companion atoms that have nearly identical binding energies. The origin of ionization suppression for some molecules has been identified. The predicted ratios for pairs with suppression $({\mathrm{D}}_{2}:\mathrm{Ar},$ ${\mathrm{O}}_{2}:\mathrm{Xe})$ and pairs without suppression $({\mathrm{N}}_{2}:\mathrm{Ar},$ CO:Kr) are in good agreement with the measurements. However, the theory predicts suppression for ${\mathrm{F}}_{2}:\mathrm{Ar},$ which is in disagreement with the experiment. The ionization signals of NO, ${\mathrm{S}}_{2},$ and of SO have also been derived from the experimental data, and the results are also shown to be in agreement with the prediction of the present molecular ADK theory.

576 citations

••

Abstract: An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven three-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in electromagnetically induced transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.

573 citations

••

Abstract: We consider a single copy of a pure four-partite state of qubits and investigate its behavior under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to Greenberger-Horne-Zeilinger-like entanglement. The other ones contain essentially two-or three-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of four qubits, giving rise to a seven-parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single-copy distillation protocol.

551 citations

••

Abstract: Starting from the three-dimensional (3D) Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent nonpolynomial nonlinear Schr\"odinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D nonpolynomial Schr\"odinger equation (2D NPSE) that models disk-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schr\"odinger-like equations with different polynomial nonlinearities.

515 citations

••

Abstract: Empirical relations are established between the cohesive energy, surface tension, and melting temperature of different bulk solids. An expression for the size-dependent melting for low-dimensional systems is derived on the basis of an analogy with the liquid-drop model and these empirical relations, and compared with other theoretical models as well as the available experimental data in the literature. The model is then extended to understand (i) the effect of substrate temperature on the size of the deposited cluster and (ii) the superheating of nanoparticles embedded in a matrix. It is argued that the exponential increase in particle size with the increase in deposition temperature can be understood by using the expression for the size-dependent melting of nanoparticles. Superheating is possible when nanoparticles with a lower surface energy are embedded in a matrix with a material of higher surface energy in which case the melting temperature depends on the amount of epitaxy between the nanoparticles and the embedding matrix. The predictions of the model show good agreement with the experimental results. A scaling for the size-dependent melting point suppression is also proposed.

498 citations

••

Abstract: The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which tends to the solution. We apply this time-dependent Hamiltonian approach to Grover's problem, i.e., searching a marked item in an unstructured database. We find that by adjusting the evolution rate of the Hamiltonian so as to keep the evolution adiabatic on each infinitesimal time interval, the total running time is of order $\sqrt{N},$ where N is the number of items in the database. We thus recover the advantage of Grover's standard algorithm as compared to a classical search, scaling as N. This is in contrast with the constant-rate adiabatic approach of Farhi et al. (e-print quant-ph/0001106), where the requirement of adiabaticity is expressed only globally, resulting in a time of order N.

475 citations

••

Yale University

^{1}Abstract: We report the demonstration of a sensitive absolute-gravity gradiometer based on light-pulse atom-interference techniques. The gradiometer consists of two absolute accelerometers operated in a differential mode. We report a differential acceleration sensitivity of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}g/{\mathrm{Hz}}^{1/2}$ and an inferred differential acceleration accuracy of less than ${10}^{\ensuremath{-}9}g.$ This corresponds to a gravity-gradient sensitivity of $4E/{\mathrm{Hz}}^{1/2}$ ${(1E=10}^{\ensuremath{-}9}{\mathrm{s}}^{\mathrm{\ensuremath{-}}2})$ and an accuracy of better than $1E$ for a 10-m separation between accelerometers. We demonstrate that the instrument can be used to detect nearby masses in a vibrationally noisy environment and characterize instrument sensitivity to spurious acceleration and rotation noise.

455 citations

••

Abstract: A beam splitter is a simple, readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. We conjecture that this is a general property of beam splitters: Nonclassicality of the inputs is a necessary condition for entangling fields in a beam splitter.

••

TL;DR: It is shown that Gaussian states cannot be distilled by local Gaussian operations and classical communication, and positive (but not completely positive) Gaussian maps are defined.

Abstract: We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations that can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes that can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.

••

Abstract: In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the classical world, maximal information about a physical system is complete in the sense of providing definite answers for all possible questions that can be asked of the system. In the quantum world, maximal information is not complete and cannot be completed. Using this distinction, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule, that maximal information about a quantum system leads to a unique quantum-state assignment, and that quantum theory provides a stronger connection between probability and measured frequency than can be justified classically. Finally, we give a Bayesian formulation of quantum-state tomography.

••

TL;DR: Dense coding or superdense coding in the case of high-dimension quantum states between two parties and multiparties is studied in this paper.

Abstract: Dense coding or superdense coding in the case of high-dimension quantum states between two parties and multiparties is studied in this paper. We construct explicitly the measurement basis and the forms of the single-body unitary operations corresponding to the basis chosen, and the rules for selecting the one-body unitary operations in a multiparty case.

••

Abstract: The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of a composite, i.e., many modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion---central in quantum information---by studying some, e.g., Hubbard, lattice fermionic models relevant to condensed matter physics.

••

TL;DR: The general principle for a quantum-signature scheme is proposed and investigated and can guarantee the unconditional security of the algorithm, mostly due to the correlation of the GHZ triplet states and the use of quantum one-time pads.

Abstract: The general principle for a quantum-signature scheme is proposed and investigated based on ideas from classical signature schemes and quantum cryptography. The suggested algorithm is implemented by a symmetrical quantum key cryptosystem and Greenberger-Horne-Zeilinger (GHZ) triplet states and relies on the availability of an arbitrator. We can guarantee the unconditional security of the algorithm, mostly due to the correlation of the GHZ triplet states and the use of quantum one-time pads.

••

Abstract: We study the entanglement properties of a closed chain of harmonic oscillators that are coupled via a translationally invariant Hamiltonian, where the coupling acts only on the position operators We consider the ground state and thermal states of this system, which are Gaussian states The entanglement properties of these states can be completely characterized analytically when one uses the logarithmic negativity as a measure of entanglement

••

Abstract: A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.

••

Abstract: We study universal quantum computation using optical coherent states. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.

••

Abstract: Given a spatially dependent mass distribution, we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wave functions are written down explicitly. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger equations with constant mass using point canonical transformation. The Oscillator, Coulomb, and Morse class of potentials are considered.

••

Abstract: We describe the operation and tolerances of a nondeterministic, coincidence basis, quantum controlled-NOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration. Its success probability is 1/9.

••

Abstract: We propose an alternative concept for a scalable spin quantum computer that combines aspects of other proposals with the advantageous features of endohedral fullerenes. The key advantages are that electron spins instead of nuclear spins are used and that the manipulation of fullerene molecules is fairly easy. Qubits are set and read out via pulsed electron-spin resonance. Addressing is provided by local magnetic fields or field gradients $(A$ gate). The qubit-qubit interaction is mediated by magnetic dipolar coupling and can be controlled via the direction of the magnetic field with respect to the distance vector of the qubits $(J$ gate). Molecular as well as solid-state architectures are discussed.

••

Abstract: As typically implemented, single-photon sources cannot be made to produce single photons with high probability, while simultaneously suppressing the probability of yielding two or more photons. Because of this, single-photon sources cannot really produce single photons on demand. We describe a multiplexed system that allows the probabilities of producing one and more photons to be adjusted independently, enabling a much better approximation of a source of single photons on demand.

••

Rice University

^{1}Abstract: Accurate values of the electron-impact ionization cross sections for the rare gases are needed in a variety of contexts. However, despite numerous investigations over many decades, uncertainty as to the correct values has persisted. The pioneering total-cross-section measurements of Rapp and Englander-Golden are generally regarded as the most reliable but no comprehensive study has independently verified their correctness. In this paper, measurements of electron-impact ionization cross sections of helium, neon, argon, krypton, and xenon are reported for energies ranging from the first ionization threshold to 1000 eV. These data confirm the essential correctness of Rapp and Englander-Golden's total measurements and at the same time provide a complete set of consistent absolute partial cross sections.

••

Abstract: We report a quantum eraser experiment which actually uses a Young double slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert, and Walther [Nature (London) 351, 111 (1991)]. One photon of an entangled pair is incident on a Young double slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the interference pattern. To recover interference, we measure the polarization of the other entangled photon. In addition, we perform the experiment under ``delayed erasure'' circumstances.

••

Abstract: We study high-order harmonic generation for ${\mathrm{H}}_{2}^{+}$ and ${\mathrm{H}}_{2}$ model molecules in linearly polarized laser pulses by numerical solution of the Schr\"odinger equation. Maxima and minima due to intramolecular interference are found in the dependence of the harmonic intensities on the internuclear distance and on the orientation of the molecules. These extrema can be approximately predicted by regarding them as the result of interference between two radiating point sources located at the positions of the nuclei.

••

Abstract: Physical systems, characterized by an ensemble of interacting constituents, can be represented and studied by different algebras of operators (observables). For example, a fully polarized electronic system can be studied by means of the algebra generated by the usual fermionic creation and annihilation operators or by the algebra of Pauli (spin-1/2) operators. The Jordan-Wigner isomorphism gives the correspondence between the two algebras. As we previously noted, similar isomorphisms enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental observation to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g., the spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian H.

••

Abstract: A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

••

IBM

^{1}TL;DR: It is shown that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension.

Abstract: We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [in Proceedings of the 33rd ACM Symposium on the Theory of Computing (2001), p. 114] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [E. Knill, R. Laflamme, and G. Milburn, Nature (London) 409, 46 (2001)].

••

Abstract: We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The origin of the peculiar surface-mode excitations is identified to be phase fluctuations at the low-density surface regime. The obtained dependence of a distortion parameter on time and that on the driving frequency agree with the recent experiments by Madison et al. [Phys. Rev. Lett. 86, 4443 (2001)].