Quantum lost and found

Abstract

We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.     

Quantum information with trapped ions at NIST

Abstract

We report experiments on coherent quantum-state synthesis and control of trapped atomic ions. This work has the overall goal of performing large-scale quantum information processing; however, such techniques can also be applied to fundamental tests and demonstrations of quantum mechanical principles, as well as to the improvement of quantum-limited measurements.     

Entangling atoms and ions in dissipative environments

Abstract

Quantum information processing rests on our ability to manipulate quantum superpositions through coherent unitary transformations, and to establish entanglement between constituent quantum components of the processor. The quantum information processor (a linear ion trap, or a cavity confining the radiation field for example) exists in a dissipative environment. We discuss ways in which entanglement can be established within such dissipative environments. We can even make use of a strong interaction of the system with its environment to produce entanglement in a controlled way.     

Nonlinear quantum optical computing via measurement

Abstract

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel (2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM (2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.     

Simple quantum information algorithms in cavity QED

Abstract

Cavity quantum electrodynamics has already proven to be a system capable of demonstrating basic tools in quantum information theory. By combining these tools, we show how simple quantum information protocols could be implemented. We will focus on the examples of the Grover search algorithm and quantum cloning.     

Ground state cooling,quantum state engineering and study of decoherence of ions in Paul traps

Abstract

We investigate single ions of ⁴⁰Ca⁺ in Paul traps for quantum information processing. Superpositions of the S_½ electronic ground state and the metastable D_5/2; state are used to implement a qubit. Laser light on the S_½ ? D_5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.     

Special foundation lecture: A personal view

Abstract

I (try to) review some of my work in theoretical quantum optics done over some 45 years. Highlights include discovery of ?optical solitons‘ as solutions to the nonlinear Maxwell-Bloch (MB) systems of equations as reported at the 1st National QE Conference, also at Owens Park, Manchester, in 1973. Bose-Einstein condensation (BEC) in magnetic traps at temperatures T ～ 10^?9K achieved in 1995 is described by forms of the quantum nonlinear Schrödinger (NLS) equation closely related to the quantized MB equations. It may be possible to see quantum soliton solutions of the quantum attractive NLS equation in one-dimensional (d = 1) magnetic traps holding the Bose condensed metal vapour ⁷Li. More generally such d = 1 quantum solitons may be significant to modern long-distance optical fibre communication, and perhaps to ?quantum information‘.     

Optimal quantum trajectories for discrete measurements

Abstract

Using the method of quantum trajectories we show that a known pure state can be optimally monitored through time when subject to a sequence of discrete measurements. By modifying the way that we extract information from the measurement apparatus we can minimize the average algorithmic information of the measurement record, without changing the unconditional evolution of the measured system. We define an optimal measurement scheme as one which has the lowest average algorithmic information allowed. We also show how it is possible to extract information about system operator averages from the measurement records and their probabilities. The optimal measurement scheme, in the limit of weak coupling, determines the statistics of the variance of the measured variable directly. We discuss the relevance of such measurements for recent experiments in quantum optics.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

Nanostructures,Entanglement and the Physics of Quantum Control

Abstract

Nanostructures might be viewed as solid-state approximations to SU(N) networks, the nodes of which would, in simplest form, be analogous to elementary spins. Owing to interactions with an external light field and coupling between the local nodes these networks allow for single- and multiple-node coherence (entanglement), despite damping. By means of stochastic simulations we demonstrate how such a ‘quantum machinery’ embedded in a qualified environment would look like in terms of measurement protocols. These protocols give evidence for the underlying complex behaviour of the network, a complexity which is based on the non-local information contained in the entanglement and which would not be present in the ‘classical limit’ of using local information only.     

Information Transfer with Two-state Two-particle Quantum Systems

Abstract

Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log₂3 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon, two-mode states spanning the bosonic Bell basis are given.     

Generation of photon number states on demand

Abstract

The widely discussed applications in quantum information and quantum cryptography require radiation sources capable of producing a fixed number of photons. This paper reviews the work performed in our laboratory to produce these fields on demand. Two different methods are discussed. The first is based on the one-atom maser or micromaser operating under the conditions of the so-called trapping states. In this situation the micromaser stabilises to a photon number state. Recently, we also succeeded in determining the Wigner function of a single-photon state. The second device, recently realized in our laboratory, uses a single trapped ion in an optical cavity.     

The information role of entanglement and interference operators in Shor quantum algorithm gate dynamics

Abstract

Shor algorithm dynamics of quantum computation states are analysed from the classical and the quantum information theory points of view. The Shannon entropy is interpreted as the degree of information accessibility through measurement, while the von Neumann entropy is employed to measure the quantum information of entanglement. The intelligence of a state with respect to a subset of qubits is defined. The intelligence of a state is maximal if the gap between the Shannon and the von Neumann entropy for the chosen result qubits is minimal. We prove that the quantum Fourier transform creates maximally intelligent states with respect to the first n qubits for Shor's problem, since it annihilates the gap between the classical and quantum entropies for the first n qubits of every output state.     

Towards photostatistics from photon-number discriminating detectors

Abstract

We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.     

Generation of photon number states on demand

Abstract

Experiments with single atoms have become routine. In this paper two groups of these experiments will be reviewed with special emphasis on applications to study quantum phenomena in the atom-radiation interaction. The first one deals with the one-atom maser and the second one with another cavity quantum electrodynamic device on the basis of trapped ions. The latter device has interesting applications in quantum computing and quantum information.     

Fundamentals and applications of isotope effect in solids

Over the last five decades, the isotope effect in solids has been one of the major researches in solid state science. Most of the physical properties of a solid depend to a greater or lesser degree on its isotopic composition. Scientific interest, technological promise and increased availability of highly enriched isotopes have led to a sharp rise in the number of experimental and theoretical studies with isotopically controlled semiconductor and insulator crystals. A great number of stable isotopes and well-developed methods of their separation have made it possible to date to grow crystals of C, LiH, ZnO, ZnSe, CuCl, GaN, GaAs, CdS, Cu₂O, Si, Ge and α-Sn with a controllable isotopic composition. The use of such objects allows the investigation of not only the isotope effects in lattice dynamics (elastic, thermal and vibrational properties) but also the influence of such effects on the electronic states via electron-phonon coupling (the renormalization of the band-to-band transition energy E_g, the exciton binding energy E_b and the size of the longitudinal-transverse splitting Δ_LT). Capture of thermal neutrons by isotope nuclei followed by nuclear decay produces new elements, resulting in a large number of possibilities for isotope selective doping of solids used in opto-, quantum electronics, fiber optics, etc. The nonlinear dependence of the free exciton luminescence (especially ¹²C_x¹³C_1−x, LiH_xD_1−x) intensity on the excitation density allows us to consider these crystals as potential solid state lasers in the UV part of the spectrum. Isotopic information storage may consist in assigning the information “zero” or “one” to mono-isotopic microislands (or even to a single atom) within a bulk crystalline (or thin film) structure. Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. It shows how the use of quantum physics could revolutionize the way of communication and process information. Although modern computers rely on quantum mechanics to operate, the information itself is still encoded classically. A new approach is to treat information as a quantum concept and to ask what new insights can be gained by encoding this information in an individual quantum system. Isotope information storage and isotope quantum computers are briefly discussed. The review concludes with an outline of the main features of isotope physics in solids, and avenues for future research and applications.     

Quantum network architecture of tight-binding models with substitution sequences

Abstract

We study a two-spin quantum Turing architecture, in which discrete local rotations {α_m} of the Turing head spin alternate with quantum controlled NOT operations. Substitution sequences are known to underlie aperiodic structures. We show that parameter inputs {α_m} described by such sequences can lead here to a quantum dynamics, intermediate between the regular and the chaotic variant. Exponential parameter sensitivity characterizing chaotic quantum Turing machines turns out to be an adequate criterion for induced quantum chaos in a quantum network.     

Reduction of Quantum Entropy by Reversible Extraction of Classical Information

Abstract

We inquire under what conditions some of the information in a quantum signal source, namely a set of pure states ψ_a emitted with probabilities p _a, can be extracted in classical form by a measurement leaving the quantum system with less entropy than it had before, but retaining the ability to regenerate the source state exactly from the classical measurement result and the after-measurement state of the quantum system. We show that this can be done if and only if the source states ψ_a fall into two or more mutually orthogonal subsets.     

High range resolution of ECHO returns from adjacent point targets

Abstract

A new approach to resolve overlapping echoes is proposed. Inverse filtering is performed in a windowed frequency interval to avoid the enhancement of highly distorted signal spectrum. Using the partially inverse filtered signal spectrum as the data base, nonlinear spectral estimation techniques are then applied to resolve the number of overlapping echoes present and to obtain high resolution estimate of the individual echo time delays. Numerical and experimental results verify the effectiveness of the proposed new approach.