Showing papers on "Quantum state published in 2005"
TL;DR: In this paper, the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments.
Abstract: Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.
4,218 citations
TL;DR: This work reports a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent, and shows that non-trivial quantum computations at EPG’s of as low as one per cent could be implemented.
Abstract: In theory, quantum computers offer a means of solving problems that would be intractable on conventional computers. Assuming that a quantum computer could be constructed, it would in practice be required to function with noisy devices called 'gates'. These gates cause decoherence of the fragile quantum states that are central to the computer's operation. The goal of so-called 'fault-tolerant quantum computing' is therefore to compute accurately even when the error probability per gate (EPG) is high. Here we report a simple architecture for fault-tolerant quantum computing, providing evidence that accurate quantum computing is possible for EPGs as high as three per cent. Such EPGs have been experimentally demonstrated, but to avoid excessive resource overheads required by the necessary architecture, lower EPGs are needed. Assuming the availability of quantum resources comparable to the digital resources available in today's computers, we show that non-trivial quantum computations at EPGs of as high as one per cent could be implemented.
1,030 citations
TL;DR: A key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling is described, which stems from violation of a Bell inequality.
Abstract: Standard quantum key distribution protocols are provably secure against eavesdropping attacks, if quantum theory is correct It is theoretically interesting to know if we need to assume the validity of quantum theory to prove the security of quantum key distribution, or whether its security can be based on other physical principles The question would also be of practical interest if quantum mechanics were ever to fail in some regime, because a scientifically and technologically advanced eavesdropper could perhaps use postquantum physics to extract information from quantum communications without necessarily causing the quantum state disturbances on which existing security proofs rely Here we describe a key distribution scheme provably secure against general attacks by a postquantum eavesdropper limited only by the impossibility of superluminal signaling Its security stems from violation of a Bell inequality
875 citations
TL;DR: A coding theorem is proved to achieve the ‘wire–tapper’ bound, the difference of the mutual information Alice–Bob and that of Alice–Eve, for so–called classical–quantum-quantum–correlations, via one–way public communication, which yields information–theoretic formulae for the distillable secret key.
Abstract: We study and solve the problem of distilling a secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via oneway public discussion: we...
794 citations
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01 Jan 2005
TL;DR: In this article, a path integral and holomorphic formalism for quantum mechanics is proposed, where path integrals are fermions and quantization is performed by path integral in phase space.
Abstract: 1. Gaussian integrals 2. Path integral in quantum mechanics 3. Partition function and spectrum 4. Classical and quantum statistical physics 5. Path integrals and quantization 6. Path integral and holomorphic formalism 7. Path integrals: fermions 8. Barrier penetration: semi-classical approximation 9. Quantum evolution and scattering matrix 10. Path integrals in phase space QUANTUM MECHANICS: MINIMAL BACKGROUND A1 Hilbert space and operators A2 Quantum evolution, symmetries and density matrix A3 Position and momentum. Scrodinger equation
736 citations
TL;DR: In this paper, a single photon is generated from a cold atomic ensemble at one site 1, and is directed to another site through 100 metres of optical fibre, then converted into a single collective atomic excitation using a dark-state polariton approach.
Abstract: Two groups this week report a significant step on the long road to quantum computing: the storage and retrieval of single photons onto and from atomic quantum memories. Chaneliere et al. produced single photons from an atomic quantum memory in one lab, transported them through a 100-metre-long optical fibre and stored them for a time in a second memory. The atomic excitation was then converted back into a single photon. Previously, weak coherent laser pulses have been stopped and retrieved in atomic media, but single photons are ideal for realizing quantum bits. Eisaman et al. report a similar approach, using the coherent control technique known as electromagnetically induced transparency for the generation, transmission and storage of single photons. A third paper reports progress in another technology critical for quantum communication and computation: the storage and distribution of entangled quantum states. Chou et al. have achieved entanglement between two samples of atoms separated by 2.8 metres that jointly store one quantum bit of information. An elementary quantum network operation involves storing a qubit state in an atomic quantum memory node, and then retrieving and transporting the information through a single photon excitation to a remote quantum memory node for further storage or analysis. Implementations of quantum network operations are thus conditioned on the ability to realize matter-to-light and/or light-to-matter quantum state mappings. Here we report the generation, transmission, storage and retrieval of single quanta using two remote atomic ensembles. A single photon is generated from a cold atomic ensemble at one site 1, and is directed to another site through 100 metres of optical fibre. The photon is then converted into a single collective atomic excitation using a dark-state polariton approach2. After a programmable storage time, the atomic excitation is converted back into a single photon. This is demonstrated experimentally, for a storage time of 0.5 microseconds, by measurement of an anti-correlation parameter. Storage times exceeding ten microseconds are observed by intensity cross-correlation measurements. This storage period is two orders of magnitude longer than the time required to achieve conversion between photonic and atomic quanta. The controlled transfer of single quanta between remote quantum memories constitutes an important step towards distributed quantum networks.
638 citations
TL;DR: This work demonstrates the use of EIT for the controllable generation, transmission and storage of single photons with tunable frequency, timing and bandwidth and probes the spectral and quantum statistical properties of narrow-bandwidth single-photon pulses, revealing that their quantum nature is preserved under EIT propagation and storage.
Abstract: Techniques to facilitate controlled interactions between single photons and atoms are now being actively explored. These techniques are important for the practical realization of quantum networks, in which multiple memory nodes that utilize atoms for generation, storage and processing of quantum states are connected by single-photon transmission in optical fibres. One promising avenue for the realization of quantum networks involves the manipulation of quantum pulses of light in optically dense atomic ensembles using electromagnetically induced transparency (EIT, refs 8, 9). EIT is a coherent control technique that is widely used for controlling the propagation of classical, multi-photon light pulses in applications such as efficient nonlinear optics. Here we demonstrate the use of EIT for the controllable generation, transmission and storage of single photons with tunable frequency, timing and bandwidth. We study the interaction of single photons produced in a 'source' ensemble of 87Rb atoms at room temperature with another 'target' ensemble. This allows us to simultaneously probe the spectral and quantum statistical properties of narrow-bandwidth single-photon pulses, revealing that their quantum nature is preserved under EIT propagation and storage. We measure the time delay associated with the reduced group velocity of the single-photon pulses and report observations of their storage and retrieval.
602 citations
TL;DR: Observations of entanglement between two atomic ensembles located in distinct, spatially separated set-ups are reported, representing significant progress in the ability to distribute and store entangled quantum states.
Abstract: A critical requirement for diverse applications in quantum information science is the capability to disseminate quantum resources over complex quantum networks. For example, the coherent distribution of entangled quantum states together with quantum memory (for storing the states) can enable scalable architectures for quantum computation, communication and metrology. Here we report observations of entanglement between two atomic ensembles located in distinct, spatially separated set-ups. Quantum interference in the detection of a photon emitted by one of the samples projects the otherwise independent ensembles into an entangled state with one joint excitation stored remotely in 10(5) atoms at each site. After a programmable delay, we confirm entanglement by mapping the state of the atoms to optical fields and measuring mutual coherences and photon statistics for these fields. We thereby determine a quantitative lower bound for the entanglement of the joint state of the ensembles. Our observations represent significant progress in the ability to distribute and store entangled quantum states.
459 citations
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TL;DR: A comprehensive review of quantum cloning machines can be found in this paper, where the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning.
Abstract: The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional and for continuous-variable quantum systems); in addition, it presents the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning.
402 citations
TL;DR: In this paper, an approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi-and multipartite quantum states of arbitrary finite dimension is developed. But this approach is limited to the case where the state of the system is incoherent.
374 citations
TL;DR: In this paper, the theory of ideal tomography is presented and the full experimental realization (measurement, electronics, error correction, numerical analysis, measurement choice, and estimation of uncertainties) of a tomographic system applied to polarized photonic qubits is described.
Abstract: Quantum state tomography is the process by which an identical ensemble of unknown quantum states is completely characterized. A sequence of identical measurements within a series of different bases allow the reconstruction of a complete quantum wavefunction. This article reviews state representation and notation, lays out the theory of ideal tomography, and details the full experimental realization (measurement, electronics, error correction, numerical analysis, measurement choice, and estimation of uncertainties) of a tomographic system applied to polarized photonic qubits.
TL;DR: The use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems are explored and the possibility of stabilizing one outcome of a quantum measurement with unit probability is demonstrated.
Abstract: Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
TL;DR: An analysis of the equilibrium limits of the two most widely used approaches for simulating the dynamics of molecular systems that combine both quantum and classical degrees of freedom and shows that the self-consistent-field (Ehrenfest) method deviates substantially from Boltzmann.
Abstract: We present an analysis of the equilibrium limits of the two most widely used approaches for simulating the dynamics of molecular systems that combine both quantum and classical degrees of freedom. For a two-level quantum system connected to an infinite number of classical particles, we derive a simple analytical expression for the equilibrium mean energy attained by the self-consistent-field (Ehrenfest) method and show that it deviates substantially from Boltzmann. By contrast, “fewest switches” surface hopping achieves Boltzmann quantum state populations. We verify these analytical results with simulations.
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TL;DR: In this paper, the theory of stabilizer codes over finite fields is described and bounds on the maximal length of maximum distance separable stabilizer code are given, and a discussion of open problems is given.
Abstract: One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been derived as binary stabilizer codes. Fault-tolerant quantum computation prompted the study of nonbinary quantum codes, but the theory of such codes is not as advanced as that of binary quantum codes. This paper describes the basic theory of stabilizer codes over finite fields. The relation between stabilizer codes and general quantum codes is clarified by introducing a Galois theory for these objects. A characterization of nonbinary stabilizer codes over GF(q) in terms of classical codes over GF(q^2) is provided that generalizes the well-known notion of additive codes over GF(4) of the binary case. This paper derives lower and upper bounds on the minimum distance of stabilizer codes, gives several code constructions, and derives numerous families of stabilizer codes, including quantum Hamming codes, quadratic residue codes, quantum Melas codes, quantum BCH codes, and quantum character codes. The puncturing theory by Rains is generalized to additive codes that are not necessarily pure. Bounds on the maximal length of maximum distance separable stabilizer codes are given. A discussion of open problems concludes this paper.
TL;DR: In this paper, the authors reported the observation of coherent spin-changing collisions in a gas of spin-1 bosons and demonstrated coherent control of the evolution of the system by applying differential phase shifts to the spin states using magnetic fields.
Abstract: Collisions in a thermal gas are perceived as random or incoherent as a consequence of the large numbers of initial and final quantum states accessible to the system In a quantum gas, for example, a Bose–Einstein condensate or a degenerate Fermi gas, the phase space accessible to low-energy collisions is so restricted that collisions become coherent and reversible Here, we report the observation of coherent spin-changing collisions in a gas of spin-1 bosons Starting with condensates occupying two spin states, a condensate in the third spin state is coherently and reversibly created by atomic collisions The observed dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter–wave four-wave mixing The spin-dependent scattering length is determined from these oscillations to be −145(32) bohr Finally, we demonstrate coherent control of the evolution of the system by applying differential phase shifts to the spin states using magnetic fields
TL;DR: The conditions are formulated as an infinite series of inequalities for the moments of the state under study and the violation of any inequality of this series is a sufficient condition for entanglement.
Abstract: We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under study. The violation of any inequality of this series is a sufficient condition for entanglement. Previously known entanglement conditions are shown to be special cases of our approach.
TL;DR: An original approach is developed for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension and the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglements measure, concurrence.
Abstract: We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.
TL;DR: An analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension is derived relating concurrence, the Peres-Horodecki criterion, and the realignment criterion and is demonstrated that it is exact for some mixed quantum states.
Abstract: We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.
TL;DR: In this paper, the authors considered a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay, and showed that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified.
TL;DR: In this article, the authors considered the low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by quenched disorder.
Abstract: We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperatute $T$ does not exceed some finite value $T_c$. At the same time, it can be also proven that at high enough $T$ the conductivity is finite. These two statements imply that the system undergoes a finite temperature Metal-to-Insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries. We formulate the effective Hamiltonian description of the system at low energies (of the order of the level spacing in the single-particle localization volume). In the metallic phase quantum Boltzmann equation is valid, allowing to find the kinetic coefficients. In the insulating phase, $T
Patent•
28 Mar 2005TL;DR: In this article, a method for computing using a quantum system (1540) comprising a plurality of superconducting qubits is provided, in which the plurality of qubits are arranged with respect to one another, with a predetermined number of couplings between respective pairs of qubit pairs.
Abstract: A method for computing using a quantum system (1540) comprising a plurality of superconducting qubits is provided. Quantum system (1540) can be in any one of at least two configurations including (i) an initialization Hamiltonian Ho and (ii) a problem Hamiltonian Hp. The plurality of superconducting qubits are arranged with respect to one another, with a predetermined number of couplings between respective pairs of superconducting qubits in the plurality of qubits, such that the plurality of superconducting qubits, coupled by the predetermined number of couplings, collectively define a computational problem to be solved. In the method, quantum system (1540) is initialized to the initialization Hamiltonian Ho. Quantum system (1540) is then adiabatically changed until it is described by the ground state of the problem Hamiltonian Hp. The quantum state of quantum system (1540) is then readout thereby solving the computational problem to be solved.
TL;DR: In this paper, the authors give a complete classification of indecomposable apparatuses (for discrete spectrum) by providing different necessary and sufficient conditions for extremality of POVMs, along with a simple general algorithm for the decomposition of a POVM into extremals.
Abstract: Similarly to quantum states, also quantum measurements can be ‘mixed’, corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely classical nature. It is then natural to ask which apparatuses are indecomposable, i.e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies give optimal apparatuses that are indecomposable. Mathematically the problem is posed describing each measuring apparatus by a positive operator-valued measure (POVM), which gives the statistics of the outcomes for any input state. The POVMs form a convex set, and in this language the indecomposable apparatuses are represented by extremal points—the analogous of ‘pure states’ in the convex set of states. Differently from the case of states, however, indecomposable POVMs are not necessarily rank-one, e.g. von Neumann measurements. In this paper we give a complete classification of indecomposable apparatuses (for discrete spectrum), by providing different necessary and sufficient conditions for extremality of POVMs, along with a simple general algorithm for the decomposition of a POVM into extremals. As an interesting application, ‘informationally complete’ measurements are analysed in this respect. The convex set of POVMs is fully characterized by determining its border in terms of simple algebraic properties of the corresponding POVMs.
TL;DR: Generalizations of concurrence are proposed for multipartite quantum systems that can distinguish qualitatively distinct quantum correlations and all introduced quantities can be evaluated efficiently for arbitrary mixed sates.
Abstract: We propose generalizations of concurrence for multipartite quantum systems that can distinguish qualitatively distinct quantum correlations. All introduced quantities can be evaluated efficiently for arbitrary mixed sates.
TL;DR: In this article, a Laughlin quasiparticle interferometer with fractional statistics is presented, where interference fringes are observed as conductance oscillations as a function of magnetic flux, similar to the Aharonov-Bohm effect.
Abstract: In two dimensions, the laws of physics permit existence of anyons, particles with fractional statistics which is neither Fermi nor Bose. That is, upon exchange of two such particles, the quantum state of a system acquires a phase which is neither 0 nor \pi, but can be any value. The elementary excitations (Laughlin quasiparticles) of a fractional quantum Hall fluid have fractional electric charge and are expected to obey fractional statistics. Here we report experimental realization of a novel Laughlin quasiparticle interferometer, where quasiparticles of the 1/3 fluid execute a closed path around an island of the 2/5 fluid and thus acquire statistical phase. Interference fringes are observed as conductance oscillations as a function of magnetic flux, similar to the Aharonov-Bohm effect. We observe the interference shift by one fringe upon introduction of five magnetic flux quanta (5h/e) into the island. The corresponding 2e charge period is confirmed directly in calibrated gate experiments. These results constitute direct observation of fractional statistics of Laughlin quasiparticles.
TL;DR: In this article, it was shown that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain and the key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate.
Abstract: Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions that display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics, any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at an arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.
TL;DR: In this article, a position-sensitive neutron detector with an extra-high spatial resolution of ∼ 2 µm was developed and tested for this particular experiment, to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states.
Abstract: We have studied neutron quantum states in the potential well formed by the earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in the two lowest quantum states correspond to expectations with an experimental accuracy. A position-sensitive neutron detector with an extra-high spatial resolution of ∼ 2 µm was developed and tested for this particular experiment, to be used to measure the spatial density distribution in a standing neutron wave above a mirror for a set of some of the lowest quantum states. The present experiment can be used to set an upper limit for an additional short-range fundamental force. We studied methodological uncertainties as well as the feasibility of improving further the accuracy of this experiment.
TL;DR: In this paper, the spectral absorption profile of a material such as a rare-earth-ion-doped crystal can be manipulated to efficiently absorb and subsequently reemit a wave-packet, in a photon echo-like process.
TL;DR: A general renormalization-group transformation on quantum states, independent of any Hamiltonian dynamics of the system, is constructed and illustrated for translational invariant matrix product states in one dimension.
Abstract: We construct a general renormalization-group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show that product, Greenberger-Horne-Zeilinger, W, and domain wall states are special cases of an emerging classification of the fixed points of this coarse-graining transformation.
12 Jan 2005
TL;DR: The syntax, operational semantics and type system of CQP are formally defined, and it is proved that the semantics preserves typing, and that typing guarantees that each qubit is owned by a unique process within a system.
Abstract: We define a language CQP (Communicating Quantum Processes) for modelling systems which combine quantum and classical communication and computation. CQP combines the communication primitives of the pi-calculus with primitives for measurement and transformation of quantum state; in particular, quantum bits (qubits) can be transmitted from process to process along communication channels. CQP has a static type system which classifies channels, distinguishes between quantum and classical data, and controls the use of quantum state. We formally define the syntax, operational semantics and type system of CQP, prove that the semantics preserves typing, and prove that typing guarantees that each qubit is owned by a unique process within a system. We illustrate CQP by defining models of several quantum communication systems, and outline our plans for using CQP as the foundation for formal analysis and verification of combined quantum and classical systems.
TL;DR: The Heisenberg uncertainty relation sets a fundamental limit for quantum measurement of incompatible observables as mentioned in this paper, and the standard form derived by Weyl and Robertson is of purely quantum nature when the state is pure and the variance involving a mixed state is a hybrid of classical and quantum uncertainty.
Abstract: The Heisenberg uncertainty relation sets a fundamental limit for quantum measurement of incompatible observables Its standard form derived by Weyl and Robertson is of purely quantum nature when the state is pure However, for mixed states, because the variance involving a mixed state is a hybrid of classical and quantum uncertainty, the conventional uncertainty relation is of a ``mixed'' flavor It is desirable to seek some decomposition of variance into classical and quantum parts and to cast the Heisenberg uncertainty relation for mixed states in a more quantum form By use of the skew information introduced by Wigner and Yanase in 1963, we make such an attempt and establish a different uncertainty relation which is stronger than the conventional one