Showing papers on "Quantum state published in 2007"
TL;DR: The freedom in representations with and without translation symmetry are determined, derive respective canonical forms and provide efficient methods for obtaining them.
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.
942 citations
Journal Article•
TL;DR: The experimental realization of single electron spin rotations in a double quantum dot is reported, demonstrating the feasibility of operating single-electron spins in a quantum dot as quantum bits.
Abstract: The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.
865 citations
TL;DR: The toy theory of as discussed by the authors states that the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge.
Abstract: We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.
726 citations
TL;DR: An efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t is presented in terms of a procedure for computing the matrix entries of H.
Abstract: We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log*n)t1+1/2k) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.
626 citations
TL;DR: A conceptually new regime of cavity QED is achieved, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation, which opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.
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
462 citations
TL;DR: A spin chain is a permanently coupled 1D system of spins as discussed by the authors, which can be used to connect quantum registers without resorting to optics, and it has been shown that it is possible to achieve perfect quantum state transfer through spin chains.
Abstract: We present an introductory overview of the use of spin chains as quantum wires, which has recently developed into a topic of lively interest. The principal motivation is in connecting quantum registers without resorting to optics. A spin chain is a permanently coupled 1D system of spins. When one places a quantum state on one end of it, the state will be dynamically transmitted to the other end with some efficiency if the spins are coupled by an exchange interaction. No external modulations or measurements on the body of the chain, except perhaps at the very ends, is required for this purpose. For the simplest (uniformly coupled) chain and the simplest encoding (single qubit encoding), however, dispersion reduces the quality of transfer. We present a variety of alternatives proposed by various groups to achieve perfect quantum state transfer through spin chains. We conclude with a brief discussion of the various directions in which the topic is developing.
439 citations
TL;DR: In this article, the authors employ a new physics of objective reduction, which appeals to a form of quantum gravity to provide a useful description of fundamental processes at the quantum/classical borderline.
Abstract: What is consciousness? Some philosophers have contended that "qualia," or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being comprised of "occasions of experience." To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to terms with the physics of space-time--as is described by Einstein's general theory of relativity--and its relation to the fundamental theory of matter--as described by quantum theory. This leads us to employ a new physics of objective reduction: " OR" which appeals to a form of quantum gravity to provide a useful description of fundamental processes at the quantum/classical borderline (Penrose, 1994; 1996). Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific "objective" criterion (a threshold related to quantum gravity) is reached; the coherent system then self-reduces (objective reduction: OR). We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness. OR is taken as an instantaneous event--the climax of a self-organizing process in fundamental space-time--and a candidate for a conscious Whitehead "occasion" of experience. How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate an OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons (Penrose and Hameroff, 1995; Hameroff and Penrose, 1995; 1996). In this model, quantum-superposed states develop in microtubule subunit proteins ("tubulins"), remain coherent and recruit more superposed tubulins until a mass-time-energy threshold (related to quantum gravity) is reached. At that point, self-collapse, or objective reduction (OR) abruptly occurs. We equate the pre-reduction, coherent superposition ("quantum computing") phase with pre-conscious processes, and each instantaneous (and non-computable) OR, or self-collapse, with a discrete conscious event. Sequences of OR events give rise to a "stream" of consciousness. Microtubule-associated-proteins can "tune" the quantum oscillations of the coherent superposed states; the OR is thus self-organized, or "orchestrated" ("Orch OR"). Each Orch OR event selects (non-computably) microtubule subunit states which regulate synaptic/neural functions using classical signaling. The quantum gravity threshold for self-collapse is relevant to consciousness, according to our arguments, because macroscopic superposed quantum states each have their own space-time geometries (Penrose, 1994; 1996). These geometries are also superposed, and in some way "separated," but when sufficiently separated, the superposition of space-time geometries becomes significantly unstable, and reduce to a single universe state. Quantum gravity determines the limits of the instability; we contend that the actual choice of state made by Nature is non-computable. Thus each Orch OR event is a self-selection of space-time geometry, coupled to the brain through microtubules and other biomolecules. If conscious experience is intimately connected with the very physics underlying space-time structure, then Orch OR in microtubules indeed provides us with a completely new and uniquely promising perspective on the hard problem of consciousness.
436 citations
TL;DR: In this article, the authors show that the full content of the uncertainty principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted.
398 citations
01 Feb 2007
TL;DR: In this paper, the authors proposed a method for the measurement of continuous variables of light states using the Optical Kerr Effect (O Glockl et al. 2003) and the optical Kerr effect (V Josse et al., 2003).
Abstract: Bipartite and Multipartite Entanglement of Gaussian States (G Adesso & F Illuminati) Gaussian Quantum Channels (J Eisert & M M Wolf) Entanglement in Systems of Interacting Harmonic Oscillators (K M R Audenaert et al.) Continuous-Variable Quantum Key Distribution (F Grosshans et al.) Gaussian Quantum Cellular Automata (O Kruger & R F Werner) Distillation of Continuous-Variable Entanglement (J Fiura'ek et al.) Loophole-Free Test of Quantum Nonlocality with Continuous Variables of Light (R Garcia-Patron et al.) Homodyne Tomography and the Reconstruction of Quantum States of Light (G M D'Ariano et al.) Schrodinger Cat States for Quantum Information Processing (H Jeong & T C Ralph) Polarization Squeezing and Entanglement (N Korolkova) Type-II Optical Parametric Oscillator: A Versatile Source of Quantum Correlations and Entanglement (J Laurat et al.) Accessing the Phase Quadrature of Intense Non-Classical Light State (O Glockl et al.) Experimental Polarization Squeezing and Continuous Variable Entanglement via the Optical Kerr Effect (V Josse et al.) High-Fidelity Quantum Teleportation and a Quantum Teleportation Network (N Takei et al.) Quantum State Sharing with Continuous Variables (T Tyc et al.) Experimental Quantum Cloning with Continuous Variables (U L Andersen et al.) Quantum Imaging Techniques for Improving Information Extraction from Images (C Fabre et al.) Squeezed Light for Gravitational Wave Detectors (R Schnabel) Continuous Variables for Single Photons (L Zhang et al.) Experimental Non-Gaussian Manipulation of Continuous Variables (J Wenger et al.) Continuous-Variable Quantum-State Tomography of Optical Fields and Photons (A I Lvovsky & M G Raymer) Gaussian Description of Continuous Measurements on Continuous Variable Quantum Systems (L B Madsen & K Molmer) Quantum State Preparation of Spin Ensembles by Continuous Measurement and Feedback (R van Handel et al.) Real-Time Quantum Feedback Control with Cold Alkali Atoms (J M Geremia) Deterministic Quantum Interface Between Light and Atomic Ensembles (K Hammerer et al.) Long Distance Quantum Communication with Atomic Ensembles (C W Chou et al.) Decoherence and Decoherence Suppression in Ensemble-Based Quantum Memories for Photons (M Fleischhauer & C Mewes).
365 citations
TL;DR: This Letter shows that criticality is not a sufficient condition to ensure superextensive divergence of the geometric tensor, and state the conditions under which this is possible.
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.
360 citations
TL;DR: Results show how atom–atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble, and enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.
Abstract: Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source, highlighting the importance of two-photon correlations and stimulating the development of modern quantum optics. The quantum interpretation of bunching relies on the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterization of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect (a tendency to avoid each other). Antibunching of fermions is associated with destructive two-particle interference, and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: (3)He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom-atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.
TL;DR: This experiment demonstrates the reversible mapping of a coherent state of light with a mean photon number approximately equal to 1.1 to and from the hyperfine states of an atom trapped within the mode of a high-finesse optical cavity.
Abstract: We demonstrate the reversible mapping of a coherent state of light with a mean photon number (-)n approximately equal to 1.1 to and from the hyperfine states of an atom trapped within the mode of a high-finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step toward the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network.
TL;DR: In this paper, the transport properties of multiple-particle quantum states in a class of one-dimensional systems with a single quantum impurity were investigated, and an exact theoretical approach based on real-space equations of motion and the Bethe ansatz was proposed to construct the full scattering matrix for these systems.
Abstract: We consider the transport properties of multiple-particle quantum states in a class of one-dimensional systems with a single quantum impurity. In these systems, the local interaction at the quantum impurity induces strong and nontrivial correlations between the multiparticles. We outline an exact theoretical approach, based upon real-space equations of motion and the Bethe ansatz, that allows one to construct the full scattering matrix ($S$ matrix) for these systems. In particular, we emphasize the need for a completeness check upon the eigenstates of the $S$ matrix, when these states obtained from Bethe ansatz are used for describing the scattering properties. As a detailed example of our approach, we solve the transport properties of two photons incident on a single two-level atom, when the photons are restricted to a one-dimensional system such as a photonic crystal waveguide. Our approach predicts a number of nonlinear effects involving only two photons, including background fluorescence, spatial attraction and repulsion between the photons, as well as the emergence of a two-photon bound state.
01 Jan 2007
TL;DR: In this paper, the quantum spin Hall effect was observed in HgTe/(Hg,Cd)Te quantum wells with well width d63 nanometers, where the residual conductance was independent of the sample width, indicating that it is caused by edge states.
Abstract: Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime For thin quantum wells with well width d63 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature However, for thicker quantum wells (d63 nanometers), the nominally insulating regime showed a plateau of residua conductance close to 2e2/h, where e is the electron charge and h is Planck's constant The residual conductance was independent of the sample width, indicating that it is caused by edge states Furthermore, the residual conductance was destroyed by a small external magnetic field The quantum phase transition at the critical thickness, d =63 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition These observations provide experimental evidence of the quantum spin Hall effect
TL;DR: In this paper, the authors proposed a secure quantum key distribution network following the ideas in quantum dense coding, where the server of the network provides the service for preparing and measuring the Bell states, and the users encodes the states with local unitary operations.
Abstract: We propose a theoretical scheme for secure quantum key distribution network following the ideas in quantum dense coding. In this scheme, the server of the network provides the service for preparing and measuring the Bell states, and the users encodes the states with local unitary operations. For preventing the server from eavesdropping, we design a decoy when the particle is transmitted between the users. It has high capacity as one particle carries two bits of information and its efficiency for qubits approaches 100%. Moreover, it is not necessary for the users to store the quantum states, which makes this scheme more convenient for application than others.
TL;DR: All these tests—based on the very same data—give rise to quantitative estimates in terms of entanglement measures, and if a test is strongly violated, one can also infer that the state was quantitatively very much entangled, in the bipartite and multipartite setting.
Abstract: Entanglement witnesses provide tools to detect entanglement in experimental situations without the need of having full tomographic knowledge about the state. If one estimates in an experiment an expectation value smaller than zero, one can directly infer that the state has been entangled, or specifically multi-partite entangled, in the first place. In this paper, we emphasize that all these tests—based on the very same data—give rise to quantitative estimates in terms of entanglement measures: 'If a test is strongly violated, one can also infer that the state was quantitatively very much entangled'. We consider various measures of entanglement, including the negativity, the entanglement of formation, and the robustness of entanglement, in the bipartite and multipartite setting. As examples, we discuss several experiments in the context of quantum state preparation that have recently been performed.
TL;DR: In this article, a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements is proposed, which is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum likelihood state.
Abstract: We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive procedure that ensures likelihood increase in every iteration and convergence to the maximum-likelihood state. We apply the algorithm to homodyne tomography of optical states and quantum tomography of entangled spin states of trapped ions and investigate its convergence properties.
TL;DR: In this article, the authors introduced a measure of entanglement in the space of operators and showed, for a transverse Ising spin-$1∕2$ chain, that the simulation of observables is efficient for initial local operators.
Abstract: The efficiency of time-dependent density matrix renormalization group methods is intrinsically connected to the rate of entanglement growth. We introduce a measure of entanglement in the space of operators and show, for a transverse Ising spin-$1∕2$ chain, that the simulation of observables, contrary to the simulation of typical pure quantum states, is efficient for initial local operators. For initial operators with a finite index in Majorana representation, the operator space entanglement entropy saturates with time to a level which is calculated analytically, while for initial operators with infinite index the growth of operator space entanglement entropy is shown to be logarithmic.
TL;DR: In this article, a linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated, using Bloch-Messiah reduction, using off-line squeezers and beam splitters.
Abstract: The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. First, using Bloch-Messiah reduction, we show how to achieve canonical cluster-state generation, otherwise based on pairwise acting quantum nondemolition gates, by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful. Hence we propose a systematic way to create a whole family of cluster-type states, including potentially cheaper states. Any given cluster (or graph) state can be realized this way. As an example, we consider a protocol in which a single-mode quantum state propagates through a multiple-rail cluster. Such a redundant encoding may reduce errors due to finite squeezing.
TL;DR: The results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory and demonstrate the analogies of the color superconducting and baryonic phases in QCD.
Abstract: We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, $Ul0$. Using a variational calculation for equal color densities and small couplings, $|U|l|{U}_{C}|$, a color superfluid state emerges with a tendency to domain formation. For $|U|g|{U}_{C}|$, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.
TL;DR: In this paper, the information-spectrum analysis made by Han for classical hypothesis testing for simple hypotheses is extended to a unifying framework including both classical and quantum hypothesis testing, and the results are also applied to fixed-length source coding when loosening the normalizing condition for probability distributions and for quantum states.
Abstract: The information-spectrum analysis made by Han for classical hypothesis testing for simple hypotheses is extended to a unifying framework including both classical and quantum hypothesis testing. The results are also applied to fixed-length source coding when loosening the normalizing condition for probability distributions and for quantum states. We establish general formulas for several quantities relating to the asymptotic optimality of tests/codes in terms of classical and quantum information spectra
TL;DR: Using cavity-enhanced non-degenerate parametric down-conversion, a frequency tunable source of heralded single photons with a narrow bandwidth of 8 MHz is built, making it compatible with atomic quantum memories and revealing a clearly negative Wigner function.
Abstract: Using cavity-enhanced non-degenerate parametric down-conversion, we have built a frequency tunable source of heralded single photons with a narrow bandwidth of 8 MHz, making it compatible with atomic quantum memories. The photon state is 70% pure single photon as characterized by a tomographic measurement and reconstruction of the quantum state, revealing a clearly negative Wigner function. Furthermore, it has a spectral brightness of ~1,500 photons/s per MHz bandwidth, making it one of the brightest single photon sources available. We also investigate the correlation function of the down-converted fields using a combination of two very distinct detection methods; photon counting and homodyne measurement.
TL;DR: This work delineate the reliability domain of dynamical decoupling used for quantum state preservation, in a general setting for a single qubit, using as a key tool a renormalization transformation of the effective system-bath coupling Hamiltonian.
Abstract: Dynamical decoupling can be used to preserve arbitrary quantum states despite undesired interactions with the environment, using control Hamiltonians affecting the system only. We present a system-independent analysis of dynamical decoupling based on leading order decoupling error estimates, valid for bounded-strength environments. Using as a key tool a renormalization transformation of the effective system-bath coupling Hamiltonian, we delineate the reliability domain of dynamical decoupling used for quantum state preservation, in a general setting for a single qubit. We specifically analyze and compare two deterministic dynamical decoupling schemes\char22{}periodic and concatenated\char22{}and distinguish between two limiting cases of fast versus slow environments. We prove that concatenated decoupling outperforms periodic decoupling over a wide range of parameters. These results are obtained for both ``ideal'' (zero-width) and realistic (finite-width) pulses This work extends and generalizes our earlier work [Phys. Rev. Lett. 95, 180501 (2005)].
TL;DR: An unknown mixed quantum state's entanglement is quantified by suitable, local parity measurements on its twofold copy by identifying the associated observable as a generalized entanglements witness.
Abstract: We quantify an unknown mixed quantum state's entanglement by suitable, local parity measurements on its twofold copy The associated observable qualifies as a generalized entanglement witness
TL;DR: In this paper, it was shown that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime.
Abstract: We present a proof that quantum Yang-Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang-Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensure conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators.
Book•
01 Jan 2007
TL;DR: Two-photon interference in parametric down-conversion has been studied in this paper, where the phase independent interference between a two-phase state and a coherent state has been investigated.
Abstract: Two-Photon Interference.- Historical Background and General Remarks.- Quantum State from Parametric Down-Conversion.- Hong-Ou-Mandel Interferometer.- Phase-Independent Two-Photon Interference.- Phase-Dependent Two-Photon Interference: Two-Photon Interferometry.- Interference between a Two-Photon State and~a Coherent State.- Quantum Interference of More Than Two Photons.- Coherence and Multiple Pair Production in~Parametric Down-Conversion.- Quantum Interference with Two Pairs of~Down-Converted Photons.- Temporal Distinguishability of a Multi-Photon State.- Homodyne of a Single-Photon State: A Special Multi-Photon Interference.
TL;DR: In this paper, a general scheme for computing effective equations perturbatively in a Hamiltonian formalism is proposed, which is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive.
Abstract: Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type, which correct the classical equations by modified coefficients and higher derivative terms. In gravity, for instance, one expects terms with higher powers of curvature. Such higher derivative formulations are discussed here with an emphasis on the role of degrees of freedom and on differences between Lagrangian and Hamiltonian treatments. A general scheme is then provided which allows one to compute effective equations perturbatively in a Hamiltonian formalism. Here, one can expand effective equations around any quantum state and not just a perturbative vacuum. This is particularly useful in situations of quantum gravity or cosmology where perturbations only around vacuum states would be too restrictive. The discussion also demonstrates the number of free parameters expected in effective equations, used to determine the physical situation being approximated, as well as the role of classical symmetries such as Lorentz transformation properties in effective equations. An appendix collects information on effective correction terms expected from loop quantum gravity and string theory.
TL;DR: In this paper, a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state is proposed to evaluate the non-gaussianity of some relevant single-mode and multimode quantum states.
Abstract: We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in detail the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single-mode and multimode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily computable for any state of a bosonic system and allows one to define a corresponding measure for the non-Gaussian character of a quantum operation.
TL;DR: This work constructs a local model for the case in which rho is maximally entangled and p is at or below a certain bound, and extends the model to arbitrary rho, providing bounds on the resistance to noise of the nonlocal correlations of entangled states.
Abstract: We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state rho of two d-dimensional systems and completely depolarized noise, with respective weights p and 1-p. We first construct a local model for the case in which rho is maximally entangled and p at or below a certain bound. We then extend the model to arbitrary rho. Our results provide bounds on the resistance to noise of the nonlocal correlations of entangled states. For projective measurements, the critical value of the noise parameter p for which the state becomes local is at least asymptotically log(d) larger than the critical value for separability.
TL;DR: In this paper, an efficient quantum cryptography network protocol with d-dimension polarized photons is proposed without resorting to entanglement and quantum memory, which does not require the servers and the users to store the quantum state and almost all of the single photons can be used for carrying the information.
Abstract: An efficient quantum cryptography network protocol is proposed with d-dimension polarized photons, without resorting to entanglement and quantum memory. A server on the network, say Alice, provides the service for preparing and measuring single photons whose initial state are |0>. The users code the information on the single photons with some unitary operations. For preventing the untrustworthy server Alice from eavesdropping the quantum lines, a nonorthogonal-coding technique (decoy-photon technique) is used in the process that the quantum signal is transmitted between the users. This protocol does not require the servers and the users to store the quantum state and almost all of the single photons can be used for carrying the information, which makes it more convenient for application than others with present technology. We also discuss the case with a faint laser pulse.