Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature. Received 10 August 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Statistical properties of eigenvalues for an operating quantum computer with static imperfections

We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we discuss the quantum chaos border induced by static imperfections by analyzing the statistical properties of the quantum computer eigenvalues. For small imperfection strengths the level spacing statistics is close to the case of quasi-integrable systems while above the border it is described by the random matrix theory. We have found that the border drops exponentially with the number of qubits, both in the ergodic and quasi-integrable dynamical regimes of the map characterized by a complex phase space structure. On the contrary, the regime with integrable map dynamics remains more stable against static imperfections since in this case the border drops only algebraically with the number of qubits. Received 19 June 2002 / Received in final form 30 September 2002 Published online 17 Decembre 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Emergence of Fermi-Dirac thermalization in the quantum computer core

We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with the highest density of states. Above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of eigenstates in an isolated quantum computer. The onset of chaos results in the interaction induced dynamical thermalization and the occupation numbers well described by the Fermi-Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. Received 3 July 2001 and Received in final form 9 September 2001     

Quantum computational gates with radiation free couplings

We examine a generic three level mechanism of quantum computation in which all fundamental single and double qubit quantum logic gates are operating under the effect of adiabatically controllable static (radiation free) bias couplings between the states. Under the time evolution imposed by these bias couplings the quantum state cycles between the two degenerate levels in the ground state and the quantum gates are realized by changing Hamiltonian at certain time intervals when the system collapses to a two state subspace. We propose a physical implementation of the mechanism using Aharonov-Bohm persistent-current loops in crossed electric and magnetic fields, with the output of the loop read out by using a quantum Hall effect aided mechanism. Received 26 March 2002 / Received in final form 8 July 2002 Published online 19 November 2002     

Computational leakage: Grover's algorithm with imperfections

We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that ideal Grover's algorithm operates in a 2-dimensional Hilbert space. The simulation results of this model and Grover's algorithm with imperfections are compared, and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, namely, a diffusion of probability density into the full Hilbert space and a stochastic rotation within the original 2-dimensional Hilbert space. Received 12 August 2002 / Received in final form 14 October 2002 Published online 4 February 2003     

Entanglement purification with noisy apparatus can be used to factor out an eavesdropper

We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information. Received 10 August 2001 and Received in final form 26 October 2001     

Double entanglement and quantum cryptography

We propose a quantum transmission based on bi-photons, which are doubly-entangled both in polarisation and phase. This scheme finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger error on the quantum communication than for a single entangled bi-photon communication, when he steels the same information. Received 23 July 2001 / Received in final form 30 November 2001 Published online 24 September 2002     

Eigenstates of an operating quantum computer: hypersensitivity to static imperfections

We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits n_q, it is shown that the ideal eigenstates become mixed and strongly modified by static imperfections above a certain threshold which drops exponentially with n_q. Above this threshold the quantum eigenstate entropy grows linearly with n_q but the computation remains reliable during a time scale which is polynomial in the imperfection strength and in n_q. Received 7 March 2002/ Received in final form 3 May 2002 Published online 19 July 2002     

Solid-state single photon sources: light collection strategies

We examine the problem of efficiently collecting the photons produced by solid-state single photon sources. The extent of the problem is first established with the aid of simple physical concepts. Several approaches to improving the collection efficiency are then examined and are broadly categorized into two types. First are those based on cavity quantum dynamics, in which the pathways by which the source may emit a photon are restricted, thus channeling emission into one desired mode. Second are those where we try to reshape the free space modes into a target mode in an optimal way, by means of refraction, without fundamentally altering the way in which the source emits. Respectively, we examine a variety of microcavities and solid immersion lenses. Whilst we find that the micropillar microcavities offer the highest collection efficiency (∼70%), choosing this approach may not always be appropriate due to other constraints. Details of the different approaches, their merits and drawbacks are discussed in detail. Received 19 July 2001 and Received in final form 5 October 2001     

Localization of a macroscopic object induced by the factorization of internal adiabatic motion

To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states (such as that of the center-of-mass (CM)) and its inner states based on our recent investigation. Under the adiabatic limit where motion of the CM does not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the CM. Since the adiabatic inner states are factorized with respect to each component of the macroscopic object, this adiabatic separation can induce the quantum decoherence. This observation thus provides us with a possible solution to the Schr?dinger cat paradox. Received 24 October 2000 and Received in final form 8 March 2001     

Quantum computer inverting time arrow for macroscopic systems

Since Boltzmann developed the statistical theory for macroscopic thermodynamics the question has relentlessly been put forward of how time-reversibility at microscopic level is compatible with macroscopic irreversibility. Here we show that a quantum computer can efficiently simulate a macroscopic thermodynamic process with chaotic microscopic dynamics and invert the time arrow even in presence of quantum errors. In contrast, small errors in classical computer simulation of this dynamics grow exponentially with time and rapidly destroy time-reversibility. Received 31 October 2001     

Integrated quantum key distribution system using single sideband detection

We report a new quantum cryptographic system involving single sideband detection and allowing an implementation of the BB84 protocol. The transmitted bits are reliably coded by the phase of a high frequency modulating signal. The principle of operation is described in terms of both classical and quantum optics. The method has been demonstrated experimentally at 1 550 nm using compact and conventional device technology. Single photon interference has been obtained with a fringe visibility greater than 98%, indicating that the system can be used in view of quantum key distribution potentially beyond 50-km-long standard single-mode fiber. Received 13 July 2001 and Received in final form 30 November 2001     

Distribution of local entropy in the Hilbert space of bi-partite quantum systems: origin of Jaynes' principle

For a closed bi-partite quantum system partitioned into system proper and environment we interpret the microcanonical and the canonical condition as constraints for the interaction between those two subsystems. In both cases the possible pure-state trajectories are confined to certain regions in Hilbert space. We show that in a properly defined thermodynamical limit almost all states within those accessible regions represent states of some maximum local entropy. For the microcanonical condition this dominant state still depends on the initial state; for the canonical condition it coincides with that defined by Jaynes' principle. It is these states which thermodynamical systems should generically evolve into. Received 13 June 2002 / Received in final form 14 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: jochen@theol.physik.uni-stuttgart.de     

Infinite chain of different deltas: A simple model for a quantum wire

We present the exact diagonalization of the Schr?dinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced. Received 24 June 2002 Published online 29 November 2002     

Low-energy spectrum and finite temperature properties of quantum rings

Recently it was demonstrated that the rotational and vibrational spectra of quantum rings containing few electrons can be described quantitatively by an effective spin-Hamiltonian combined with rigid center-of-mass rotation and internal vibrations of localized electrons. We use this model Hamiltonian to study the quantum rings at finite temperatures and in presence of a nonzero magnetic field. Total spin, angular momentum and pair correlation show similar phase diagram which can be understood with help of the rotational spectrum of the ring. Received 18 January 2002 Published online 13 August 2002     

Quantum key distribution using quantum-correlated photon sources

Quantum key exchanges using weak coherent (Poissonian) single-photon sources are open to attack by a variety of eavesdropping techniques. Quantum-correlated photon sources provide a means of flagging potentially insecure multiple-photon emissions and thus extending the secure quantum key channel capacity and the secure key distribution range. We present indicative photon-counting statistics for a fully correlated Poissonian multibeam photon source in which the transmitted beam is conditioned by photon number measurements on the remaining beams with non-ideal multiphoton counters. We show that significant rejection of insecure photon pulses from a twin-beam source cannot be obtained with a detector having a realistic quantum efficiency. However quantum-correlated (quadruplet or octuplet) multiplet photon sources conditioned by high efficiency multiphoton counters could provide large improvements in the secure channel capacity and the secure distribution range of high loss systems such as those using the low earth orbit satellite links proposed for global quantum key distribution. Received 14 July and Received in final form 20 November 2001     

Effects of quantum space time foam in the neutrino sector

We discuss violations of CPT and quantum mechanics due to interactions of neutrinos with space-time quantum foam. Neutrinoless double beta decay and oscillations of neutrinos from astrophysical sources (supernovae, active galactic nuclei) are analysed. It is found that the propagation distance is the crucial quantity entering any bounds on EHNS parameters. Thus, while the bounds from neutrinoless double beta decay are not significant, the data of the supernova 1987a imply a bound being several orders of magnitude more stringent than the ones known from the literature. Even more stringent limits may be obtained from the investigation of neutrino oscillations from active galactic nuclei sources, which have an impressive potential for the search of quantum foam interactions in the neutrino sector. Received: 5 June 2000 / Accepted: 12 July 2000     

Ultimate quantum limits for resolution of beam displacements

We compare two high sensitivity techniques which are used to measure very small displacements of physical objects by optical techniques: the interferometric devices, measuring longitudinal phase shifts, and the devices used to monitor transverse displacement of light beams. We detail the differences and the similarities for the quantum limits on the resolution of both systems. In both cases squeezed light can be used to resolve beyond the standard quantum limit and number correlated states allow us to reach the “Heisenberg” limit. Received 12 September 2002 Published online 21 January 2003     

Floating Wigner molecules and possible phase transitions in quantum dots

A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb coupling. Received 12 September 2001 / Received in final form 24 April 2002 Published online 9 July 2002     

Entangled quantum clocks for measuring proper-time difference

We report that entangled pairs of quantum clocks (non-degenerate quantum bits) can be used as a specialized detector for precisely measuring difference of proper-times that each constituent quantum clock experiences. We describe why the proposed scheme would be more precise in the measurement of proper-time difference than a scheme of two-separate-quantum-clocks. We consider possibilities that the proposed scheme can be used in precision test of the relativity theory. Received 7 November 2001