Showing papers on "Quantum published in 1999"

Quantum Teleportation is a Universal Computational Primitive

Abstract: We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.

Quantum Games and Quantum Strategies

Abstract: We investigate the quantization of nonzero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.

Bosonization and Strongly Correlated Systems

Abstract: This volume provides a detailed account of bosonization. The first part of the book examines the technical aspects of bosonization including one-dimensional fermions, the Gaussian model, the structure of Hilbert space in conformal theories, Bose-Einstein condensation in two dimensions, non-Abelian bosonization, and the Ising and WZNW models. The second part presents applications of the bosonization technique to realistic models including the Tomonaga-Luttinger liquid, spin liquids in one dimension and the spin-1/2 Heisenberg chain with alternative exchange. The third part addresses the problems of quantum impurities. Chapters cover potential scattering, the X-ray edge problem, impurities in Tomonaga-Luttinger liquids and the multi-channel Kondo problem.

On the Holographic Renormalization Group

Abstract: We propose a direct correspondence between the classical evolution equations of 5-d supergravity and the renormalization group (RG) equations of the dual 4-d large $N$ gauge theory. Using standard Hamilton-Jacobi theory, we derive first order flow equations for the classical supergravity action $S$, that take the usual form of the Callan-Symanzik equations, including the corrections due to the conformal anomaly. This result gives direct support for the identification of $S$ with the quantum effective action of the gauge theory. In addition we find interesting new relations between the beta-functions and the counterterms that affect the 4-d cosmological and Newton constant.

Conductance viewed as transmission

Abstract: Early quantum theories of electrical conduction were semiclassical. Electrons were accelerated according to Bloch’s theorem; this was balanced by back scattering due to phonons and lattice defects. Cross sections for scattering, and band structures, were calculated quantum-mechanically, but the balancing process allowed only for occupation probabilities, not permitting a totally coherent process. Also, in most instances, scatterers at separate locations were presumed to act incoherently. Totally quantum-mechanical theories stem from the 1950s, and have diverse sources. Particularly intense concern with the need for more quantum mechanical approaches was manifested in Japan, and Kubo’s formulation became the most widely accepted version. Quantum theory, as described by the Schrodinger equation, is a theory of conservative systems, and does not allow for dissipation. The Schrodinger equation readily allows us to calculate polarizability for atoms, molecules, or other isolated systems that do not permit electrons to enter or leave. Kubo’s linear-response theory is essentially an extended theory of polarizability. Some supplementary handwaving is needed to calculate a dissipative effect such as conductance, for a sample with boundaries where electrons enter and leave (Anderson, 1997). After all, no theory that ignores the interfaces of a sample to the rest of its circuit can possibly calculate the resistance of such a sample of limited extent. Modern microelectronics has provided the techniques for fabricating very small samples. These permit us to study conductance in cases where the carriers have a totally quantum mechanically coherent history within the sample, making it essential to take the interfaces into account. Mesoscopic physics, concerned with samples that are intermediate in size between the atomic scale and the macroscopic one, can now demonstrate in manufactured structures much of the quantum mechanics we associate with atoms and molecules.

Theory of Quantum Error Correction for General Noise

Abstract: Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of errors'' e makes sense for any system in the presence of arbitrary environmental interactions. In fact, the notion is directly related to the lowest order in time with which uncorrectable errors are introduced, and this in turn is derived from a grading of the algebra generated by the interaction operators. As a result, e-error-correcting codes are effective at protecting quantum information without requiring the usual assumptions of independence and lack of correlation. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of certain operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes. An explicit example involving collective interactions is discussed.

Coherent Operation of a Tunable Quantum Phase Gate in Cavity QED

Abstract: We have realized a quantum phase gate operating on quantum bits carried by a single Rydberg atom and a zero- or one-photon field in a high- $Q$ cavity. The gate operation is based on the dephasing of the atom-field state produced by a full cycle of quantum Rabi oscillation. The dephasing angle, conditioned to the initial atom-field state, can be adjusted over a wide range by tuning the atom-cavity frequency difference. We demonstrate that the gate preserves qubit coherence and generates entanglement. This gate is an essential tool for the nondestructive measurement of single photons and for the manipulation of many-qubit entanglement in cavity QED.

A single-photon turnstile device

Abstract: Quantum-mechanical interference between indistinguishable quantum particles profoundly affects their arrival time and counting statistics. Photons from a thermal source tend to arrive together (bunching) and their counting distribution is broader than the classical Poisson limit1. Electrons from a thermal source, on the other hand, tend to arrive separately (anti-bunching) and their counting distribution is narrower than the classical Poisson limit2,3,4. Manipulation of quantum-statistical properties of photons with various non-classical sources is at the heart of quantum optics: features normally characteristic of fermions — such as anti-bunching, sub-poissonian and squeezing (sub-shot-noise) behaviours — have now been demonstrated5. A single-photon turnstile device was proposed6,7,8 to realize an effect similar to conductance quantization. Only one electron can occupy a single state owing to the Pauli exclusion principle and, for an electron waveguide that supports only one propagating transverse mode, this leads to the quantization of electrical conductance: the conductance of each propagating mode is then given by GQ = e2/h (where e is the charge of the electron and h is Planck's constant; ref. 9). Here we report experimental progress towards generation of a similar flow of single photons with a well regulated time interval.

Strong-coupling regime for quantum boxes in pillar microcavities: Theory

Abstract: A study of quantum box transitions coupled to three-dimensionally confined photonic modes in pillar microcavities is presented, focusing on the conditions for achieving a vacuum-field Rabi splitting. For a single InAs quantum box the oscillator strength is a factor of ten too small for being in strong coupling. A calculation of exciton states localized to monolayer fluctuations in quantum wells leads to much larger values of the oscillator strengths. Single localized excitons embedded in state-of-the-art micropillars can be in strong-coupling regime with a vacuum-field Rabi splitting.

Seeing a single photon without destroying it

Abstract: Light detection is usually a destructive process, in that detectors annihilate photons and convert them into electrical signals, making it impossible to see a single photon twice. But this limitation is not fundamental—quantum non-demolition strategies1,2,3 permit repeated measurements of physically observable quantities, yielding identical results. For example, quantum non-demolition measurements of light intensity have been demonstrated4,5,6,7,8,9,10,11,12,13,14, suggesting possibilities for detecting weak forces and gravitational waves3. But such experiments, based on nonlinear optics, are sensitive only to macroscopic photon fluxes. The non-destructive measurement of a single photon requires an extremely strong matter–radiation coupling; this can be realized in cavity quantum electrodynamics15, where the strength of the interaction between an atom and a photon can overwhelm all dissipative couplings to the environment. Here we report a cavity quantum electrodynamics experiment in which we detect a single photon non-destructively. We use atomic interferometry to measure the phase shift in an atomic wavefunction, caused by a cycle of photon absorption and emission. Our method amounts to a restricted quantum non-demolition measurement which can be applied only to states containing one or zero photons. It may lead to quantum logic gates16 based on cavity quantum electrodynamics, and multi-atom entanglement17.

Exponential separation of quantum and classical communication complexity

Abstract: Communication complexity has become a central completity model. In that model, we count the amount of communication bits needed between two parties in order to solve certain computational problems. We show that for certain communication complezity problems quantum communication protocols are exponentially faster than classical ores. More explicitly, we give an example for a communication complexity relation (0~ promise problem) P such that: 1) The quantum communication complexity of P is O(log m). 2) The classical probabilistic communication complexity of P is Q(m’l’/ logm). (where m is the length of the inputs). This gives an ezponential gap between quantum communication complexity and classical probabilistic communication complexity. Only a quadratic gap was previously known. Our problem P is of geometrical nature, and is a finite precision variation of the following problem: Player I gets as input a unit vector z E R” and two orthogonal subspaces MO, MI c R”. Player II gets as input an orthogonal matrixT : R” + R”. Their goal is to answer 0 if T(x) E MO and 1 if T(x) E M,, (and any an~luer in any other case). We give an almost tight analysis for the quantum communication complexity and for the classical-probabilistic communication complexity of this problem.

Quantum gravity as a dissipative deterministic system

Abstract: It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to describe the solutions statistically. Our theory removes some of the mysteries of the holographic principle; apparently non-local features are to be expected when the quantum degrees of freedom of the world are projected onto a lower-dimensional black hole horizon. Various examples and models illustrate the points we wish to make, notably a model showing that massless, non interacting neutrinos are deterministic.

Quantum Gravity as a Dissipative Deterministic System

Abstract: It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to describe the solutions statistically. Our theory removes some of the mysteries of the holographic principle; apparently non-local features are to be expected when the quantum degrees of freedom of the world are projected onto a lower-dimensional black hole horizon. Various examples and models illustrate the points we wish to make, notably a model showing that massless, non interacting neutrinos are deterministic.

Scheme to probe the decoherence of a macroscopic object

Abstract: We propose a quantum optical version of Schr\"odinger's famous gedanken experiment in which the state of a microscopic system (a cavity field) becomes entangled with and disentangled from the state of a massive object (a movable mirror). Despite the fact that a mixture of Schr\"odinger cat states is produced during the evolution (due to the fact that the macroscopic mirror starts off in a thermal state), this setup allows us to systematically probe the rules by which a superposition of spatially separated states of a macroscopic object decoheres. The parameter regime required to test environment-induced decoherence models is found to be close to those currently realizable, while that required to detect gravitationally induced collapse is well beyond current technology.

Quantum State Diffusion

Abstract: 1. Introduction 2. Brownian motion and Ito calculus 3. Open quantum systems 4. Quantum state diffusion 5. Localisation 6. Numerical methods and examples 7. Quantum foundations 8. Primary state diffusion 9. Classical dynamics of quantum localisation 10. Semiclassical theory and linear dynamics.

Fractional Quantum Mechanics and Levy Path Integrals

Abstract: The fractional quantum and statistical mechanics have been developed via new path integrals approach.

Gravity-wave interferometers as quantum-gravity detectors

Abstract: Nearly all theoretical approaches to the unification of quantum mechanics and gravity predict 1, 2, 3, 4 that, at very short distance scales, the classical picture of space-time breaks down, with space-time becoming somewhat ‘fuzzy’ (or ‘foamy’). The properties of this fuzziness and the length scale that characterizes itsonset are potentially a means for determining which (if any) of the existing models of quantum gravity is correct. But it is generally believed 5 that these quantum space-time effects are too small to be probed by technologies currently available. Here Iargue that modern gravity-wave interferometers are sensitive enough to test certain space-time fuzziness models, because quantum space-time effects should provide an additional source of noise in the interferometers that can be tightly constrained experimentally. The noise levels recently achieved in one interferometer 6 are sufficient to rule out values of the length scale that characterizes one of the space-time fuzziness models down to the Planck length (∼10 −35 m) and beyond, while the sensitivity required to test another model should be achievable with interferometers now under construction.

Methods for Reliable Teleportation

Abstract: Recent experimental results and proposals towards implementation of quantum teleportation are discussed. It is proved that reliable (theoretically, 100% probability of success) teleportation cannot be achieved using the methods applied in recent experiments, i.e., without quantum systems interacting with one another. Teleportation proposals involving atoms and electromagnetic cavities are reviewed and the most feasible methods are described. In particular, the language of nonlocal measurements has been applied; this language has also been used for presenting a method for teleportation of quantum states of systems with continuous variables.

Concatenating decoherence-free subspaces with quantum error correcting codes

Abstract: An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFS’s are the class of quantum error correcting codes (QECC’s) with fixed, unitary recovery operators and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against collective decoherence perturbed by independent decoherence. The code yields an error threshold which depends only on the perturbing independent decoherence rate. [S0031-9007(99)09301-1]

Separability and Distillability of Multiparticle Quantum Systems

Abstract: We present a family of 3-qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to $N$-particle states.

Terminology, relative photonic efficiencies and quantum yields in heterogeneous photocatalysis. Part I: Suggested protocol

Abstract: The term photocatalysis is one amongst several in a quagmire of labels used to describe a photon-driven catalytic process; a simple description of photocatalysis is proposed herein. Other labels such as quantum yield and/or quantum efficiency used in solid/liquid and solid/gas heterogeneous photocatalytic systems to express process efficiencies have come to refer (incorrectly) to the ratio of the rate of a given event to the rate of incident photons impinging on the reactor walls and typically for broadband radiation. There is no accord on the expression for process efficiency. At times quantum yield is defined; often, it is ill-defined and more frequently how it was assessed is not described. This has led to much confusion in the literature, not only because of its different meaning from homogeneous photochemistry, but also because the description of photon efficiency precludes comparison of results from different laboratories owing to variations in light sources, reactor geometries, and overall experimental conditions. The previously reported quantum yields are in fact apparent quantum yields, i.e. lower limits of the true quantum yields. We address this issue and argue that any reference to quantum yields or quantum efficiencies in a heterogeneous medium is inadvisable until the number of photons absorbed by the light harvester (the photocatalyst) is known. A practical and simple alternative is proposed for general use and in particular for processes employing complex reactor geometries: the concept of relative photonic efficiency (jr) is useful to compare process efficiencies using a given photocatalyst material and a given standard test molecule. A quantum yield can subsequently be calculated since F 1⁄4 jr Fphenol, where Fphenol denotes the quantum yield for the photocatalyzed oxidative transformation of phenol used as the standard secondary actinometer and Degussa P-25 TiO2 as the standard photocatalyst. For heterogeneous suspensions (only), an additional method to determine quantum yields F is also proposed.

Quantum Dynamics and Vibrational Relaxation

Abstract: The accurate numerical calculation of general quantum time correlation functions for many-body systems is not possible at present We discuss several schemes for obtaining approximate quantum time correlation functions using as input only the corresponding classical results, and assess the merits of each scheme by considering three exactly solvable model problems We then turn to the problem of the vibrational energy relaxation of a high-frequency oscillator in a liquid, where the relaxation rate constant can be related to a certain quantum force−force time correlation function Focusing specifically on the case of liquid oxygen, we calculate the classical force−force time correlation function using a molecular dynamics simulation and then determine various approximations to the relaxation rate constant by applying the schemes considered earlier The Egelstaff scheme is found to lead to reasonable agreement with experiment

Ab initio pseudopotential method for the calculation of conductance in quantum wires

Abstract: We develop a method to incorporate the Kleinman-Bylander--type ab initio pseudopotential in the calculation of conductance in quantum wires using the Landauer formalism. This method is computationally efficient and mathematically stable; it does not involve singularity in inverting the transfer matrix. We also describe the ab initio nonlocal pseudopotential method to calculate the complex band structure that is required in the wave-function matching between the resistive material and the realistic metal probe. We present, as an example, the calculated conductance of the $(10,10)$ carbon nanotube with a pentagon-heptagon-pair defect in the low-temperature limit.

Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation

Abstract: We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approximation of the quantum differential scattering cross section.

Quantum groupoids

Abstract: We introduce a general notion of quantum universal enveloping algebroids (QUE algebroids), or quantum groupoids, as a unification of quantum groups and star-products Some basic properties are studied including the twist construction and the classical limits In particular, we show that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit Conversely, we formulate a conjecture on the existence of a quantization for any Lie bialgebroid, and prove this conjecture for the special case of regular triangular Lie bialgebroids As an application of this theory, we study the dynamical quantum groupoid ${\cal D}\otimes_{\hbar} U_{\hbar}(\frakg)$, which gives an interpretation of the quantum dynamical Yang-Baxter equation in terms of Hopf algebroids

Quantum Noise and Correlations in Resonantly Enhanced Wave Mixing Based on Atomic Coherence

Abstract: We investigate the quantum properties of fields generated by resonantly enhanced wave mixing based on atomic coherence in Raman systems. We show that such a process can be used for generation of pairs of Stokes and anti-Stokes fields with nearly perfect quantum correlations, yielding almost complete (i.e. 100%) squeezing without the use of a cavity. We discuss the extension of the wave mixing interactions into the domain of a few interacting light quanta.

Nonrelativistic quantum Hamiltonian for Lorentz violation

Abstract: A method is presented for deriving the nonrelativistic quantum Hamiltonian of a free massive fermion from the relativistic Lagrangian of the Lorentz-violating standard-model extension. It permits the extraction of terms at arbitrary order in a Foldy–Wouthuysen expansion in inverse powers of the mass. The quantum particle Hamiltonian is obtained and its nonrelativistic limit is given explicitly to third order.