Showing papers on "Quantum state published in 2009"

Quantum repeaters based on atomic ensembles and linear optics

Abstract: The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here we review the theoretical and experimental status quo of this very active field. We compare the potential of different approaches quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.

Observation of Rydberg blockade between two atoms

Abstract: When two single Rydberg atoms—those having electrons in highly excited states—interact, one can be used to control the quantum state of the other. Two independent experiments now demonstrate a ‘Rydberg blockade’, an effect that might make long-range quantum gates between neutral atoms possible. Blockade interactions whereby a single particle prevents the flow or excitation of other particles provide a mechanism for control of quantum states, including entanglement of two or more particles. Blockade has been observed for electrons1,2,3, photons4 and cold atoms5. Furthermore, dipolar interactions between highly excited atoms have been proposed as a mechanism for ‘Rydberg blockade’6,7, which might provide a novel approach to a number of quantum protocols8,9,10,11. Dipolar interactions between Rydberg atoms were observed several decades ago12 and have been studied recently in a many-body regime using cold atoms13,14,15,16,17,18. However, to harness Rydberg blockade for controlled quantum dynamics, it is necessary to achieve strong interactions between single pairs of atoms. Here, we demonstrate that a single Rydberg-excited rubidium atom blocks excitation of a second atom located more than 10 μm away. The observed probability of double excitation is less than 20%, consistent with a theoretical model of the Rydberg interaction augmented by Monte Carlo simulations that account for experimental imperfections.

Observation of collective excitation of two individual atoms in the Rydberg blockade regime

Abstract: When two single Rydberg atoms—those with electrons in highly excited states—interact, one can be used to control the quantum state of the other. Two independent experiments demonstrate such ‘Rydberg blockade’, an effect that might make long-range quantum gates between neutral atoms possible.

Quantum Optical Metrology -- The Lowdown on High-N00N States

Abstract: Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state -- the High-N00N state.

Mathematical Methods in Quantum Mechanics

Abstract: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators Part 1 of the book is a concise introduction to the spectral theory of unbounded operators Only those topics that will be needed for later applications are covered The spectral theorem is a central topic in this approach and is introduced at an early stage Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution Position, momentum, and angular momentum are discussed via algebraic methods Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required In particular, no functional analysis and no Lebesgue integration theory are assumed It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature This new edition has additions and improvements throughout the book to make the presentation more student friendly

Optimal quantum phase estimation.

Abstract: By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.

Nanomechanical measurements of a superconducting qubit

Abstract: The observation of the quantum states of motion of a macroscopic mechanical structure remains an open challenge in quantum-state preparation and measurement. One approach that has received extensive theoretical attention is the integration of superconducting qubits as control and detection elements in nanoelectromechanical systems (NEMS). Here we report measurements of a NEMS resonator coupled to a superconducting qubit, a Cooper-pair box. We demonstrate that the coupling results in a dispersive shift of the nanomechanical frequency that is the mechanical analogue of the 'single-atom index effect' experienced by electromagnetic resonators in cavity quantum electrodynamics. The large magnitude of the dispersive interaction allows us to perform NEMS-based spectroscopy of the superconducting qubit, and enables observation of Landau–Zener interference effects—a demonstration of nanomechanical read-out of quantum interference.

State-independent experimental test of quantum contextuality

Abstract: Quantum mechanics has had notable success in the almost 90 years since it was first introduced, and its predictions have been confirmed in numerous experiments. Nevertheless, many physicists not content with the axioms of the theory have been searching for an explanation of quantum physical predictions in terms of a classical theory. An intuitive feature of classical models is non-contextuality: the property that any measurement has a value independent of other compatible measurements being carried out at the same time. Theory suggests that non-contextuality is in conflict with quantum mechanics, and experiments undertaken with photons and neutrons seem to support this. However, these tests required the generation of special quantum states and left various loopholes open. Here, Kirchmair et al. perform an experiment with trapped ions that overcomes these problems and cannot be explained in non-contextual terms. Contextuality is therefore a property of nature that does not require the generation of special quantum states or quantum entanglement. The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. One feature of classical models that is thought to be in conflict with quantum mechanics is non-contextuality, with experiments undertaken with photons and neutrons seeming to support this. However, these tests required the generation of special quantum states and left various loopholes open. Here an experiment is performed with trapped ions that overcomes these problems and cannot be explained in non-contextual terms. The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate1,2. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles, and some types of hidden variable models3,4,5,6,7,8,9 have been experimentally ruled out. An intuitive feature of classical models is non-contextuality: the property that any measurement has a value independent of other compatible measurements being carried out at the same time. However, a theorem derived by Kochen, Specker and Bell10,11,12 shows that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen–Specker theorem could be experimentally tested at all13,14. First tests of quantum contextuality have been proposed only recently, and undertaken with photons15,16 and neutrons17,18. But these tests required the generation of special quantum states and left various loopholes open. Here we perform an experiment with trapped ions that demonstrates a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.

Contextual Approach to Quantum Formalism

Abstract: The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bells inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bells theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.

Tomography of quantum detectors

Abstract: In quantum mechanics, measurement has a fundamentally different role than in classical physics. Now a general method has been devised to characterize a quantum measurement device, completing the suite of so-called tomography techniques required to fully specify an experiment. Measurement connects the world of quantum phenomena to the world of classical events. It has both a passive role—in observing quantum systems—and an active one, in preparing quantum states and controlling them. In view of the central status of measurement in quantum mechanics, it is surprising that there is no general recipe for designing a detector that measures a given observable1. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (that is, tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography2,3,4. We identify the positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state5,6,7,8,9,10,11, process12,13,14,15,16,17 and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon-number-resolving detector capable of detecting up to eight photons18. This creates a new set of tools for accurately detecting and preparing non-classical light.

A coherent single-hole spin in a semiconductor.

Abstract: Semiconductors have uniquely attractive properties for electronics and photonics. However, it has been difficult to find a highly coherent quantum state in a semiconductor for applications in quantum sensing and quantum information processing. We report coherent population trapping, an optical quantum interference effect, on a single hole. The results demonstrate that a hole spin in a quantum dot is highly coherent.

An introduction to the tomographic picture of quantum mechanics

Abstract: Starting from the famous Pauli problem on the possibility of associating quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference between those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to non-negativity of probability density on phase space in the classical domain. The intersection of such sets is studied. The mathematical mechanism that allows us to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc is clarified and a connection with abstract Hilbert space properties is established. The superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equations like quantum evolution and energy spectra equations are given in an explicit form. A method to check experimentally the uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two-qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity

Abstract: Preparing and manipulating quantum states of mechanical resonators is a highly interdisciplinary undertaking that now receives enormous interest for its far-reaching potential in fundamental and applied science. Up to now, only nanoscale mechanical devices achieved operation close to the quantum regime. We report a new micro-optomechanical resonator that is laser cooled to a level of 30 thermal quanta. This is equivalent to the best nanomechanical devices, however, with a mass more than four orders of magnitude larger (43 ng versus 1 pg) and at more than two orders of magnitude higher environment temperature (5 K versus 30 mK). Despite the large laser-added cooling factor of 4,000 and the cryogenic environment, our cooling performance is not limited by residual absorption effects. These results pave the way for the preparation of 100-m scale objects in the quantum regime. Possible applications range from quantum-limited optomechanical sensing devices to macroscopic tests of quantum physics.

Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum.

Abstract: We analyze the influence of atmospheric turbulence on the propagation of an optical vortex beam having the form V(r,theta)=A(0)e(imtheta). The probability that a detected photon after propagating through the atmosphere has the same value of the orbital angular momentum as the launched photon is found to be given by s(0)=[1+(1.845D/r(0))(2)](-1/2), where D is the aperture diameter and r(0) is the Fried coherence diameter. These vortex beams behave very similarly to Laguerre-Gauss beams under the influence of atmospheric turbulence. These results have important implications for atmospheric laser communication systems that employ quantum encryption.

Resonantly driven coherent oscillations in a solid-state quantum emitter

Abstract: Two experiments observe the so-called Mollow triplet in the emission spectrum of a quantum dot—originating from resonantly driving a dot transition—and demonstrate the potential of these systems to act as single-photon sources, and as a readout modality for electron-spin states. Single-quantum emitters emit only one photon at a time1,2, but the properties of the photon depend on how the emitter is excited3. Incoherent excitation is simple and broadly used with solid-state emitters such as quantum dots, but does not allow direct manipulation of the quantum state. Coherent, resonant excitation on the other hand is used in pump–probe techniques to examine the quantum state of the emitter4, but does not permit collection of the single-photon emission. Coherent control with simultaneous generation of photons has been an elusive goal in solid-state approaches, where, because of strong laser scattering at the detection wavelength, measurement of resonant emission has been limited to cross-polarized detection5 or Stokes-shift techniques6,7. Here we demonstrate that a semiconductor quantum dot in a microcavity can be resonantly driven and its single-photon emission extracted background free. Under strong continuous-wave excitation, the dot undergoes several Rabi oscillations before emitting, which are visible as oscillations in the second-order correlation function. The quantum-dot states are therefore ‘dressed’, resulting in a Mollow-triplet emission spectrum. Such coherent control will be necessary for future high-efficiency sources of indistinguishable single photons3,8, which can be used for quantum key distribution9 or through post-selection10 to generate entangled photon pairs11,12.

Mesoscopic Rydberg gate based on electromagnetically induced transparency.

Abstract: We demonstrate theoretically a parallelized C-NOT gate which allows us to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering electromagnetically induced transparency. By this we can robustly implement a conditional transfer of all ensemble atoms between two logical states, depending on the state of the control atom. We outline a many-body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.

Quantum signatures of chaos in a kicked top

Abstract: Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrodinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum-classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos-the quantum kicked top- and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos.

Quantum gas of rovibronic ground-state molecules in an optical lattice

Abstract: Control over all internal and external degrees of freedom of molecules at the level of single quantum states will enable a series of fundamental studies in physics and chemistry. In particular, samples of ground-state molecules at ultralow temperatures and high number densities will allow novel quantum-gas studies and future applications in quantum information science. However, high phase-space densities for molecular samples are not readily attainable as efficient cooling techniques such as laser cooling are lacking. Here we produce an ultracold and dense sample of molecules in a single hyperfine level of the rovibronic ground state with each molecule individually trapped in the motional ground state of an optical lattice well. Starting from a zero-temperature atomic Mott-insulator state with optimized double-site occupancy, weakly-bound dimer molecules are efficiently associated on a Feshbach resonance and subsequently transferred to the rovibronic ground state by a stimulated four-photon process with >50 % efficiency. The molecules are trapped in the lattice and have a lifetime of 8 s. Our results present a crucial step towards Bose-Einstein condensation of ground-state molecules and, when suitably generalized to polar heteronuclear molecules, the realization of dipolar quantum-gas phases in optical lattices.

Sampling from the Thermal Quantum Gibbs State and Evaluating Partition Functions with a Quantum Computer

Abstract: We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound D(alpha) on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and alpha < or = 1/2 is proportional to the Helmholtz free energy density. We also derive an algorithm to evaluate the partition function of a quantum system in a time proportional to the system's thermalization time and inversely proportional to the targeted accuracy squared.

Relaxation of Antiferromagnetic Order in Spin-1/2 Chains Following a Quantum Quench

Abstract: We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending on the anisotropy parameter, oscillatory or nonoscillatory relaxation dynamics is observed. Furthermore, the corresponding relaxation time exhibits a minimum at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected.

A Review of Perfect State Transfer and its Application as a Constructive Tool

Abstract: We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.

Distinguishability of Quantum States Under Restricted Families of Measurements with an Application to Quantum Data Hiding

Abstract: We consider the problem of ambiguous discrimination of two quantum states when we are only allowed to perform a restricted set of measurements. Let the bias of a POVM be defined as the total variational distance between the outcome distributions for the two states to be distinguished. The performance of a set of measurements can then be defined as the ratio of the bias of this POVM and the largest bias achievable by any measurements. We first provide lower bounds on the performance of various POVMs acting on a single system such as the isotropic POVM, and spherical 2 and 4-designs, and show how these bounds can lead to certainty relations. Furthermore, we prove lower bounds for several interesting POVMs acting on multipartite systems, such as the set of local POVMS, POVMs which can be implemented using local operations and classical communication (LOCC), separable POVMs, and finally POVMs for which every bipartition results in a measurement having positive partial transpose (PPT). In particular, our results show that a scheme of Terhal et. al. for hiding data against local operations and classical communication [31] has the best possible dimensional dependence.

Coherent optical pulse sequencer for quantum applications

Abstract: The bandwidth and versatility of optical devices have revolutionized information technology systems and communication networks. Precise and arbitrary control of an optical field that preserves optical coherence is an important requisite for many proposed photonic technologies. For quantum information applications, a device that allows storage and on-demand retrieval of arbitrary quantum states of light would form an ideal quantum optical memory. Recently, significant progress has been made in implementing atomic quantum memories using electromagnetically induced transparency, photon echo spectroscopy, off-resonance Raman spectroscopy and other atom-light interaction processes. Single-photon and bright-optical-field storage with quantum states have both been successfully demonstrated. Here we present a coherent optical memory based on photon echoes induced through controlled reversible inhomogeneous broadening. Our scheme allows storage of multiple pulses of light within a chosen frequency bandwidth, and stored pulses can be recalled in arbitrary order with any chosen delay between each recalled pulse. Furthermore, pulses can be time-compressed, time-stretched or split into multiple smaller pulses and recalled in several pieces at chosen times. Although our experimental results are so far limited to classical light pulses, our technique should enable the construction of an optical random-access memory for time-bin quantum information, and have potential applications in quantum information processing.

Compendium of Quantum Physics

Abstract: Aharonov-Bohm Effect.- Aharonov-Casher Effect.- Algebraic Quantum Mechanics.- Angular Momentum.- Anyons.- Aspect Experiment.- Asymptotic Freedom.- Atomic Model.- Atomic Models, J.J. Thomson's "Plum Pudding" Model.- Atomic Models, Nagaoka's Saturnian Model.- Bell's Theorem.- Berry's Phase.- Black Body.- Black-Body Radiation.- Bohm Interpretation of Quantum Mechanics.- Bohmian Mechanics.- Bohm's Approach to the EPR Paradox.- Bohr's Atomic Model.- Bohr-Kramers-Slater Theory.- Born Rule and its Interpretation.- Bose-Einstein Condensation.- Bose-Einstein Statistics.- Bremsstrahlung.- Brownian Motion.- Bub-Clifton Theorem.- Casimir Effect.- Cathode Rays.- Causal Inference and EPR.- Clauser-Horne-Shimony-Holt (CHSH) - Theorem.- Cluster States.- Coherent States.- Color Charge Degree of Freedom in Particle Physics.- Complementarity Principle.- Complex-Conjugate Number.- Compton Experiment (or Compton Effect).- Consistent Histories.- Copenhagen Interpretation.- Correlations in Quantum Mechanics.- Correspondence Principle.- Counterfactuals in Quantum Mechanics.- Covariance.- CPT Theorem.- Creation and Annihilation Operators.- Creation and Detection of Entanglement.- Davisson-Germer Experiment.- De Broglie Wavelength (? = h/p).- Decay.- Decoherence.- Degeneracy.- Delayed-Choice Experiments.- Density Matrix.- Density Operator.- Diffeomorphism Invariance.- Dirac Equation.- Dirac Notation.- Double-Slit Experiment (or Two-Slit Experiment).- Effect.- Ehrenfest Theorems.- Eigenstates, Eigenvalues.- Einstein Locality.- Electron Interferometry.- Electrons.- Ensembles in Quantum Mechanics.- Entanglement.- Entanglement Purification and Distillation.- Entropy of Entanglement.- EPR-Problem (Einstein-Podolsky-Rosen Problem).- Errors and Paradoxes in Quantum Mechanics.- Exclusion Principle (or Pauli Exclusion Principle).- Experimental Observation of Decoherence.- Fermi-Dirac Statistics.- Feynman Diagrams.- Fine-Structure Constant.- Franck-Hertz Experiment.- Functional Integration Path Integrals.- Gauge Symmetry.- Generalizations of Quantum Statistics.- GHZ (Greenberger-Horne-Zeilinger) Theorem and GHZ States.- Gleason's Theorem.- Grover's Algorithm.- GRW Theory (Ghirardi, Rimini, Weber Model of Quantum Mechanics).- Hamiltonian Operator.- Hardy Paradox.- Heisenberg Microscope.- Heisenberg Picture.- Heisenberg Uncertainty Relation (Indeterminacy Relations).- Hermitian Operator.- Hidden Variables.- Hidden-Variables Models of Quantum Mechanics (Noncontextual and Contextual).- Hilbert Space.- Holism in Quantum Mechanics.- Identity of Quanta.- Identity Operator.- Ignorance Interpretation of Quantum Mechanics.- Indeterminacy Relations.- Indeterminism and Determinism in Quantum Mechanics.- Indistinguishability.- Interaction-Free Measurements (Elitzur-Vaidman, EV IFM).- Interpretations of Quantum Mechanics.- Invariance.- Ithaca Interpretation of Quantum Mechanics.- jj-Coupling.- Kaluza-Klein Theory.- Kochen-Specker Theorem.- Landes g-factor and g-formula.- Large-Angle Scattering.- Light Quantum.- Locality.- Loopholes in Experiments.- Luders Rule.- Mach-Zehnder Interferometer.- Magnetic Resonance.- Many Worlds Interpretation of Quantum Mechanics.- Matrix Mechanics.- Matter Waves.- Measurement Problem.- Measurement Theory.- Mesoscopic Quantum Phenomena.- Metaphysics of Quantum Mechanics.- Mixed State.- Mixing and Oscillations of Particles.- Modal Interpretations of Quantum Mechanics.- Neutron Interferometry.- No-Cloning Theorem.- Nonlocality.- Nuclear Fission.- Nuclear Models.- Objectification.- Objective Quantum Probabilities.- Observable.- One- and Two-Photon Interference.- Operational Quantum Mechanics, Quantum Axiomatics and Quantum Structures.- Operator.- Orthodox Interpretation of Quantum Mechanics.- Orthonormal Basis.- Parity.- Particle Physics.- Particle Tracks.- Parton Model.- Paschen-Back Effect.- Pauli Exclusion Principle.- Pauli Spin Matrices.- Photoelectric Effect.- Photon.- Pilot Waves.- Planck's Constant h.- POVM (Positive Operator Value Measure).- Probabilistic Interpretation of Quantum Mechanics.- Probability in Quantum Mechanics.- Projection.- Projection Postulate.- Propensities in Quantum Mechanics.- Protective Measurements.- Pure States.- Quantization (First, Second).- Quantization (Systematic).- Quantum Chaos.- Quantum Chemistry.- Quantum Chromodynamics (QCD).- Quantum Communication.- Quantum Computation.- Quantum Electrodynamics (QED).- Quantum Entropy.- Quantum Eraser.- Quantum Field Theory.- Quantum Gravity (General) and Applications.- Quantum Hall Effect.- Quantum Interrogation.- Quantum Jump Experiments.- Quantum Jumps.- Quantum Logic.- Quantum Mechanics.- Quantum Numbers.- Quantum State Diffusion Theory (QSD).- Quantum State Reconstruction.- Quantum Statistics.- Quantum Theory, 1914-1922.- Quantum Theory, Crisis Period 1923-Early 1925.- Quantum Theory, Early Period (1900-1913).- Quantum Zeno Effect.- Quarks.- Quasi-Classical Limit.- Radioactive Decay Law (Rutherford-Soddy).- Relativistic Quantum Mechanics.- Renormalization.- Rigged Hilbert Spaces in Quantum Physics.- Rigged Hilbert Spaces for the Dirac Formalism of Quantum Mechanics.- Rigged Hilbert Spaces and Time Asymmetric Quantum Theory.- Russell-Saunders Coupling.- Rutherford Atom.- Scattering Experiments.- Schrodinger Equation.- Schrodinger's Cat.- Schrodinger Picture.- Selection Rules.- Self-Adjoint Operator.- Semi-classical Models.- Shor's Algorithm.- Solitons.- Sommerfeld School.- Specific Heats.- Spectral Decomposition.- Spectroscopy.- Spin.- Spin Echo.- Spin Statistics Theorem.- Squeezed States.- Standard Model.- Stark Effect.- States in Quantum Mechanics.- States, Pure and Mixed, and Their Representations.- State Operator.- Statistical Operator.- Stern-Gerlach Experiment.- Superconductivity.- Superfluidity.- Superluminal Communication in Quantum Mechanics.- Superposition Principle (Coherent and Incoherent Superposition).- Superselection Rules.- Symmetry.- Time in Quantum Theory.- Trace.- Transactional Interpretation of Quantum Mechanics.- Tunneling.- Two-State Vector Formalism.- Uncertainty Principle, Indetermincay Relations.- Unitary Operator.- Vector Model.- Wave Function.- Wave Function Collapse.- Wave Mechanics.- Wave Packet.- Wave-Particle Duality: Some History.- Wave-Particle Duality: A Modern View.- Weak Value and Weak Measurements.- Werner States.- Which-Way or Welcher-Weg-Experiments.- Wigner Distribution.- Wigner's Friend.- X-Rays.- Zeeman Effect.- Zero-Point Energy.

Formulation, interpretation and application of non-commutative quantum mechanics

Abstract: In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert?Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on positive operator valued measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non-commutativity are identified.

Minimally Entangled Typical Quantum States at Finite Temperature

Abstract: We introduce a class of states, called minimally entangled typical thermal states, designed to resemble a typical state of a quantum system at finite temperature with a bias towards classical (minimally entangled) properties. These states reveal in an intuitive way properties such as short-range order which may often be hidden. A finite-$T$ density matrix renormalization group algorithm is presented which is only modestly slower than the $T=0$ density matrix renormalization group.

General Paradigm for Distilling Classical Key From Quantum States

Abstract: In this paper, we develop a formalism for distilling a classical key from a quantum state in a systematic way, expanding on our previous work on a secure key from bound entanglement (Horodecki et al, 2005). More detailed proofs, discussion, and examples are provided of the main results. Namely, we demonstrate that all quantum cryptographic protocols can be recast in a way which looks like entanglement theory, with the only change being that instead of distilling Einstein-Podolsky-Rosen (EPR) pairs, the parties distill private states. The form of these general private states are given, and we show that there are a number of useful ways of expressing them. Some of the private states can be approximated by certain states, which are bound entangled. Thus, distillable entanglement is not a requirement for a private key. We find that such bound entangled states are useful for a cryptographic primitive we call a controlled private quantum channel (PQC). We also find a general class of states, which have negative partial transpose (are NPT), but which appear to be bound entangled. The relative entropy distance is shown to be an upper bound on the rate of a key. This allows us to compute the exact value of a distillable key for a certain class of private states.

Thermal Quantum Field Theory: Algebraic Aspects And Applications

Abstract: General Principles: Elements of Thermodynamics Elements of Statistical Mechanics Partition Function and Path Integral Interacting Fields Thermal Field Theory: Thermofield Dynamics (TFD) Thermal Oscillators: Bosons and Fermions Representation of the Thermo-Poincare Group Free Fields at Finite Temperature Thermal Interacting Fields Scattering Processes and Reaction Rates via TFD Applications to Quantum Optics: Thermal Quantum States of Field Mode Non-classical Properties of Thermal States Bipartite Systems and Thermal States Measure of Non-classicality and Temperature SU(2) and SU(1,1) States Thermal Confined Fields: About Confinement and Thermal Theories Casimir Effect for the Electromagnetic Field in Box Casimir Effect for Fermions Superconducting Transition Temperature in Films, Wires and Grains Critical Behavior of Type II Superconducting Films in a Magnetic Field First-Order Phase Transition in Superconducting Films Compactified GrossA-Neveu Model at T=0 Compactified GrossA-Neveu Model at Finite Temperature Applications to Open Systems: TFD, Wigner Functions and Kinetic Theory Schrodinger Approach, TFD and Nonequilibrium Systems Dressed State Approach to the Thermalization Processes.

Signatures of nonclassicality in mixed-state quantum computation

Abstract: We investigate signatures of nonclassicality in quantum states, in particular, those involved in the DQC1 model of mixed-state quantum computation [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)]. To do so, we consider two known nonclassicality criteria. The first quantifies disturbance of a quantum state under locally noneffective unitary operations (LNUs), which are local unitaries acting invariantly on a subsystem. The second quantifies measurement-induced disturbance (MID) in the eigenbasis of the reduced density matrices. We study the role of both figures of nonclassicality in the exponential speedup of the deterministic quantum computation with one qubit (DQC1) model and compare them vis-\`a-vis the interpretation provided in terms of quantum discord. In particular, we prove that a nonzero quantum discord implies a nonzero shift under LNUs. We also use the MID measure to study the locking of classical correlations [D. P. DiVincenzo et al., Phys. Rev. Lett. 92, 067902 (2004)] using two mutually unbiased bases (MUBs). We find the MID measure to exactly correspond to the number of locked bits of correlation. For three or more MUBs, it predicts the possibility of superior locking effects.