Showing papers on "Open quantum system published in 2007"

Quantum computation and quantum information

Abstract: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal with entanglement. The paper by R. Mosseri and P. Ribeiro presents a detailed description of the two-and three-qubit geometry in Hilbert space, dealing with the geometry of fibrations and discrete geometry. The paper by J.-G.Luque et al. is more algebraic and considers invariants of pure k-qubit states and their application to entanglement measurement.

Spins in few-electron quantum dots

Abstract: The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

Quantum nature of a strongly coupled single quantum dot–cavity system

Abstract: Cavity quantum electrodynamics (QED) studies the interaction between a quantum emitter and a single radiation-field mode. When an atom is strongly coupled to a cavity mode, it is possible to realize important quantum information processing tasks, such as controlled coherent coupling and entanglement of distinguishable quantum systems. Realizing these tasks in the solid state is clearly desirable, and coupling semiconductor self-assembled quantum dots to monolithic optical cavities is a promising route to this end. However, validating the efficacy of quantum dots in quantum information applications requires confirmation of the quantum nature of the quantum-dot-cavity system in the strong-coupling regime. Here we find such confirmation by observing quantum correlations in photoluminescence from a photonic crystal nanocavity interacting with one, and only one, quantum dot located precisely at the cavity electric field maximum. When off-resonance, photon emission from the cavity mode and quantum-dot excitons is anticorrelated at the level of single quanta, proving that the mode is driven solely by the quantum dot despite an energy mismatch between cavity and excitons. When tuned to resonance, the exciton and cavity enter the strong-coupling regime of cavity QED and the quantum-dot exciton lifetime reduces by a factor of 145. The generated photon stream becomes antibunched, proving that the strongly coupled exciton/photon system is in the quantum regime. Our observations unequivocally show that quantum information tasks are achievable in solid-state cavity QED.

Entanglement-based quantum communication over 144km

Abstract: Quantum entanglement is the main resource to endow the field of quantum information processing with powers that exceed those of classical communication and computation. In view of applications such as quantum cryptography or quantum teleportation, extension of quantum-entanglement-based protocols to global distances is of considerable practical interest. Here we experimentally demonstrate entanglement-based quantum key distribution over 144 km. One photon is measured locally at the Canary Island of La Palma, whereas the other is sent over an optical free-space link to Tenerife, where the Optical Ground Station of the European Space Agency acts as the receiver. This exceeds previous free-space experiments by more than an order of magnitude in distance, and is an essential step towards future satellite-based quantum communication and experimental tests on quantum physics in space.

Matrix product state representations

Abstract: This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.

An introduction to quantum computing

Abstract: Preface 1. Introduction and background 2. Linear algebra and the Dirac notation 3. Qubits and the framework of quantum mechanics 4. A quantum model of computation 5. Superdense coding and quantum teleportation 6. Introductory quantum algorithms 7. Algorithms with super-polynomial speed-up 8. Algorithms based on amplitude amplification 9. Quantum computational complexity theory and lower bounds 10. Quantum error correction Appendices Bibliography Index

Quantum Information Theory and Quantum Statistics

Abstract: Prerequisites from Quantum Mechanics.- Information and its Measures.- Entanglement.- More About Information Quantities.- Quantum Compression.- Channels and Their Capacity.- Hypothesis Testing.- Coarse-grainings.- State Estimation.- Appendix: Auxiliary Linear and Convex Analysis.

Generation of optical `Schrödinger cats' from photon number states

Abstract: Schrodinger's cat is a Gedankenexperiment in quantum physics, in which an atomic decay triggers the death of the cat. Because quantum physics allow atoms to remain in superpositions of states, the classical cat would then be simultaneously dead and alive. By analogy, a 'cat' state of freely propagating light can be defined as a quantum superposition of well separated quasi-classical states-it is a classical light wave that simultaneously possesses two opposite phases. Such states play an important role in fundamental tests of quantum theory and in many quantum information processing tasks, including quantum computation, quantum teleportation and precision measurements. Recently, optical Schrodinger 'kittens' were prepared; however, they are too small for most of the aforementioned applications and increasing their size is experimentally challenging. Here we demonstrate, theoretically and experimentally, a protocol that allows the generation of arbitrarily large squeezed Schrodinger cat states, using homodyne detection and photon number states as resources. We implemented this protocol with light pulses containing two photons, producing a squeezed Schrodinger cat state with a negative Wigner function. This state clearly exhibits several quantum phase-space interference fringes between the 'dead' and 'alive' components, and is large enough to become useful for quantum information processing and experimental tests of quantum theory.

Experimental entanglement of six photons in graph states

Abstract: Graph states1,2,3—multipartite entangled states that can be represented by mathematical graphs—are important resources for quantum computation4, quantum error correction3, studies of multiparticle entanglement1 and fundamental tests of non-locality5,6,7 and decoherence8. Here, we demonstrate the experimental entanglement of six photons and engineering of multiqubit graph states9,10,11. We have created two important examples of graph states, a six-photon Greenberger–Horne–Zeilinger state5, the largest photonic Schrodinger cat so far, and a six-photon cluster state2, a state-of-the-art ‘one-way quantum computer’4. With small modifications, our method allows us, in principle, to create various further graph states, and therefore could open the way to experimental tests of, for example, quantum algorithms4,12 or loss- and fault-tolerant one-way quantum computation13,14.

Introduction to Quantum Effects in Gravity

Abstract: This book, first published in 2007, is an introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.

nextnano: General Purpose 3-D Simulations

Abstract: nextnano is a semiconductor nanodevice simulation tool that has been developed for predicting and understanding a wide range of electronic and optical properties of semiconductor nanostructures. The underlying idea is to provide a robust and generic framework for modeling device applications in the field of nanosized semiconductor heterostructures. The simulator deals with realistic geometries and almost any relevant combination of materials in one, two, and three spatial dimensions. It focuses on an accurate and reliable treatment of quantum mechanical effects and provides a self-consistent solution of the Schrodinger, Poisson, and current equations. Exchange-correlation effects are taken into account in terms of the local density scheme. The electronic structure is represented within the single-band or multiband kldrp envelope function approximation, including strain. The code is not intended to be a ldquoblack boxrdquo tool. It requires a good understanding of quantum mechanics. The input language provides a number of tools that simplify setting up device geometry or running repetitive tasks. In this paper, we present a brief overview of nextnano and present four examples that demonstrate the wide range of possible applications for this software in the fields of solid-state quantum computation, nanoelectronics, and optoelectronics, namely, 1) a realization of a qubit based on coupled quantum wires in a magnetic field, 2) and 3) carrier transport in two different nano-MOSFET devices, and 4) a quantum cascade laser.

Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences

Abstract: A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and backaction effects. It is based on an optimized $\ensuremath{\pi}$-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill cycle. The optimized sequence is very efficient, in particular, for strong couplings to the environment.

An Introduction to Quantum Filtering

Abstract: This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Ito calculus and its use in the modeling of physical systems. We use both reference probability and innovations methods to obtain quantum filtering equations for system-probe models from quantum optics.

Cavity QED with a Bose–Einstein condensate

Abstract: A central goal of physics is to understand the interaction between matter and light In cavity quantum electrodynamics, an optical resonator can be used to enhance this interaction for atoms Previous studies have demonstrated 'strong coupling', a regime in which the radiative properties of individual atoms are intimately linked to the state of the optical field Two groups have now demonstrated a conceptually new regime of cavity quantum electrodynamics The atoms are cooled until they form a Bose–Einstein condensate (occupying a single mode of a matter-wave field) and couple identically and strongly to the light field, sharing a single excitation This may open the way for applications in quantum communication and information processing There has been considerable recent experimental progress in cavity quantum electrodynamics, involving the quantum-mechanical coupling of cold atoms to a confined light field Here, the trapped atoms are in the form of a Bose—Einstein condensate, and so all couple identically to a single mode of the light field Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing1 By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in This has led to fundamental studies with both microwave2,3 and optical resonators4 To meet the challenges posed by quantum state engineering5 and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity6,7,8 However, the tremendous degree of control over atomic gases achieved with Bose–Einstein condensation9 has so far not been used for cavity QED Here we achieve the strong coupling of a Bose–Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation This opens possibilities ranging from quantum communication10,11,12 to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions13,14

Single-Atom Single-Photon Quantum Interface

Abstract: A major challenge for a scalable quantum computing architecture is the faithful transfer of information from one node to another. We report on the realization of an atom-photon quantum interface based on an optical cavity, using it to entangle a single atom with a single photon and then to map the quantum state of the atom onto a second single photon. The latter step disentangles the atom from the light and produces an entangled photon pair. Our scheme is intrinsically deterministic and establishes the basic element required to realize a distributed quantum network with individual atoms at rest as quantum memories and single flying photons as quantum messengers.

Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation

Abstract: Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which implies that the adiabatic computation model and the conventional quantum computation model are polynomially equivalent. Our result can be extended to the physically realistic setting of particles arranged on a two-dimensional grid with nearest neighbor interactions. The equivalence between the models allows stating the main open problems in quantum computation using well-studied mathematical objects such as eigenvectors and spectral gaps of sparse matrices.

Information-theoretic differential geometry of quantum phase transitions.

Abstract: The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential geometric and information theoretic at the same time.

Probing Quantum Commutation Rules by Addition and Subtraction of Single Photons to/from a Light Field

Abstract: The possibility of arbitrarily "adding" and "subtracting" single photons to and from a light field may give access to a complete engineering of quantum states and to fundamental quantum phenomena. We experimentally implemented simple alternated sequences of photon creation and annihilation on a thermal field and used quantum tomography to verify the peculiar character of the resulting light states. In particular, as the final states depend on the order in which the two actions are performed, we directly observed the noncommutativity of the creation and annihilation operators, one of the cardinal concepts of quantum mechanics, at the basis of the quantum behavior of light. These results represent a step toward the full quantum control of a field and may provide new resources for quantum information protocols.

Quantum critical scaling of the geometric tensors.

Abstract: Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this Letter we unify these two approaches showing that the underlying mechanism is the critical singular behavior of a complex tensor over the Hamiltonian parameter space. This is achieved by performing a scaling analysis of this quantum geometric tensor in the vicinity of the critical points. In this way most of the previous results are understood on general grounds and new ones are found. We show that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible. The validity of this analysis is further checked by exact diagonalization of the spin-1/2 XXZ Heisenberg chain.

Effective Hamiltonian theory and its applications in quantum information

Abstract: This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged d...

Decoherence in quantum walks – a review

Abstract: The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, has led rapidly to several new quantum algorithms. These all follow a unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.

Control of Linear Quantum Stochastic Systems

Abstract: The purpose of this paper is to formulate and solve a H?controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H?control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements.

Generalized limits for single-parameter quantum estimation.

Abstract: We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with k-system parameter-sensitive terms, the quantum limit scales as 1/Nk, where N is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.

Relaxation, dephasing, and quantum control of electron spins in double quantum dots

Abstract: Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions Here we present a detailed theory for electron-spin dynamics in two-electron double-dot systems that was used to guide those experiments and analyze the results Specifically, we analyze both spin- and charge-relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron systems We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits

High-speed linear optics quantum computing using active feed-forward

Abstract: As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results This technique is crucial for achieving deterministic quantum computation once a cluster state (the highly entangled multiparticle state on which one-way quantum computation is based) is prepared Here we realize a concatenated scheme of measurement and active feed-forward in a one-way quantum computing experiment We demonstrate that, for a perfect cluster state and no photon loss, our quantum computation scheme would operate with good fidelity and that our feed-forward components function with very high speed and low error for detected photons With present technology, the individual computational step (in our case the individual feed-forward cycle) can be operated in less than 150 ns using electro-optical modulators This is an important result for the future development of one-way quantum computers, whose large-scale implementation will depend on advances in the production and detection of the required highly entangled cluster states

Stabilizing Feedback Controls for Quantum Systems

Abstract: No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator

Toward a general theory of quantum games

Abstract: We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation of quantum strategies that generalizes the Choi-Jamiolkowski representation of quantum , with respect to which each strategy is described by a single operations. This new representation associates with each strategy a positive semidefinite operator acting only on the tensor product of its input and output spaces. Various facts about such representations are established, and two applications are discussed: the first is a new and conceptually simple proof of Kitaev's lower bound for strong coin-flipping, and the second is a proof of the exact characterization QRG = EXP of the class of problems having quantum refereed games.

Fundamental structure of loop quantum gravity

Abstract: In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help ...

A single-photon server with just one atom

Abstract: Neutral atoms are ideal objects for the deterministic processing of quantum information. Entanglement operations have been carried out by photon exchange1 or controlled collisions2, and atom–photon interfaces have been realized with single atoms in free space3,4 or strongly coupled to an optical cavity5,6. A long-standing challenge with neutral atoms, however, is to overcome the limited observation time. Without exception, quantum effects appeared only after ensemble averaging. Here, we report on a single-photon source with one, and only one, atom quasi-permanently coupled to a high-finesse cavity. ‘Quasi-permanent’ refers to our ability to keep the atom long enough to, first, quantify the photon-emission statistics and, second, guarantee the subsequent performance as a single-photon server delivering up to 300,000 photons for up to 30 s. This is achieved by a unique combination of single-photon generation and atom cooling7,8,9. Our scheme brings deterministic protocols of quantum information science with light and matter10,11,12,13,14,15,16 closer to realization.