The Physics of Communication

CONTRIBUTORS TO THE PROCEEDINGS OF THE XXII SOLVAY CONFERENCE ON PHYSICS

ADMINISTRATIVE COUNCIL OF THE INTERNATIONAL INSTITUTES FOR PHYSICS AND CHEMISTRY, FOUNDED BY E. SOLVAY A.S.B.I.

SCIENTIFIC COMMITTEE OF PHYSICS OF THE INTERNATIONAL INSTITUTES FOR PHYSICS AND CHEMISTRY, FOUNDED BY E. SOLVAY A.S.B.I.

HONORARY COMMITTEE

HELLENIC SCIENTIFIC COMMITTEE AND LOCAL ORGANISING COMMITTEE

THE SOLVAY CONFERENCES ON PHYSICS

PREFACE

PROLOGUE by Minister E. Venizelos

PHOTO OF FIRST SOLVAY CONFERENCE

OPENING ADDRESS BY J. SOLVAY

OPENING REMARKS BY I. PRIGOGINE

CHALLENGES IN AMBIENT INTELLIGENCE (A TRIBUTE TO CLAUDE SHANNON AND MICHAEL DERTOUZOS)

CONTENTS

In recent years, we have introduced a new type of transformation operator Λ, leading to irreversible kinetic equations from dynamics, both classical and quantum. In our approach we have no loss of information, since the Λ transformation is invertible. In this paper we consider classical mechanics. Our transformation is obtained by an extension of the canonical (unitary) transformation operator U that eliminates interactions. While U can be constructed for integrable systems in the sense of Poincaré, for nonintegrable systems there appear divergences in the perturbation expansion, due resonances. The removal of divergences leads to the Λ transformation. This transformation is “star-unitary”. Star-unitarity for non-integrable systems is an extension of unitarity for integrable systems. In addition, Λ is non-distributive with respect to products of dynamical variables. This gives fluctuations usually associated with noise in phenomenological equations such as the Langevin equation.

The recently developed Irreversible Quantum Mechanics formalism describes physical reality both at the statistical and the particle levels and voices have been heard suggesting that it be used in fundamental physics. Two examples are sketched in which similar steps were taken and proved to be terrible errors: Aristotle’s rejection of the vacuum because “nature does not tolerate it”, replacing it by a law of force linear in velocity and Chew’s rejection of Quantum Field Theory because “it is not unitary off-mass-shell”. In Particle Physics, I suggest using the new representation as an “effective” picture without abandoning the canonical background.

We review the ENS experiments performed with circular Rydberg atoms interacting, one at a time, with a high-quality superconducting cavity. The atom-cavity interaction makes it possible to engineer and manipulate complex entangled states. It also allows for an in-depth experimental exploration of basic quantum mechanics concepts, such as complementarity.

It is widely believed that quantum information devices like quantum computers will be built from solid-state qubits. Making functioning networks of these will pose formidable challenges coming from decoherence, which is usually very strong in the solid state. Here I review theoretical progress in understanding the decoherence mechanisms in superconductors and magnetic systems, wherein we believe decoherence can be made extremely small, and for which experiments reporting large-scale coherence already exist. Our microscopic understanding of superconducting and magnetic qubits is reviewed – the way in which one arrives at a low-energy effective Hamiltonian is explained in detail for a magnetic system. The way in which decoherence enters the dynamics of solid-state qubits is then discussed, along with the connection to experiment. Finally, I discuss ways in which decoherence can be further suppressed, using for example applied transverse fields.

A pure quantum state is a projection on into linear space of quantum mechanics. But this may become, through a quantum stochastic map, a convex sum of projections (and hence an impure state) by decoherence. This is not a superposition. To get superposition we need to restore phase relations and that involves a fiducal projector. As this projector varies the various possible coherent combinations of the components of the mixture may be obtained. By a further application of this method the quantum entanglement between two subsystems can be restored. These methods can be used to maintain long term phase relations by the state being repeatedly processed by purification with possible applications to storage and processing information in quantum computing. In particular from separable or partially separable states we can obtain a purely entangled state.

The problem of decoherence in a system of a particle coupled with a field is studied by applying the Complex Spectral Representation of the Liouvillian that gives a rigorous approach to the irreversible processes without relying upon any anthropomorphic principle such as coarse-graining. We focus the time evolution of the field, which is commonly neglected in phenomenological approaches to the decoherence problem. In contrast to the usual hypothesis, our result shows that there is a non-negligible time evolution of the field. The decoherence in the field is an important consequence of the irreversible processes that leads dynamically to a mixed state from a pure state through a secular effect due to the resonance effect between the particle and the field.

It is shown that a slight modification of one axiom of Quantum Mechanics eliminates the conflicts between the standard mathematical theory and the phenomenological description of resonance scattering and decay. In addition, this modification leads to a quantum theory that incorporates time asymmetry in the quantum mechanical time evolution.

In the state-of-the-art strain induced InAs/GaAs quantum dots, the polaron lifetime due to the anharmonic LO-TA phonons interaction was recently estimated numerically to be several picoseconds. This time, treated as the upper limit for the decoherence of orbital degrees of freedom in quantum dots, is too short for successful application of the error correction procedures necessary to create a scalable optically driven quantum computer in self-assembled dot technology, even when using ultrafast, of femtosecond scale, information processing. In the present report, we rediscuss the polaron relaxation in a quantum dot using the Davydov diagonalization method; we show that the previous estimations were too sever and argue that the relevant relaxation channel is slower by one order of magnitude. The increase of the estimation results from taking into account the coherent renormalization of the appropriate anharmonic term. We give also the explanation of the strong enhancement of the electron-LO phonon interaction for electrons confined in the dot, which can be expressed via renormalization of the Fröhlich constant.

The stimulated emission from an atom interacting with radiation in a non-equilibrium state is considered. The stochastic limit, applied to the non-relativistic QED Hamiltonian, shows that the state of the atom, driven by a non-equilibrium state of the field, approaches a stationary state which can continuously emit photons, unlike the case with an equilibrium state. Non equilibrium states of the radiation field are characterized by a single function of the energy. The Gibbs states are precisely those for which this function is linear. The nonlinearity of the generalized (inverse) temperature function can account for effects previously attributed to so–called “negative temperatures”. It also allows to deduce a nonlinear, non-equilibrium, generalization of Einstein’s formula describing the detailed balance of the radiation at each frequency in an equilibrium state. We conclude the present paper with the introduction of a general notion of “local KMS condition” as a characterization of local equilibrium states and with the proof of the fact that the non equilibrium states (both for field and atom) considered in the first part of the paper satisfy this condition.

We model the quantum computer hardware as a two-dimensional lattice of qubits with static imperfections, i.e. fluctuations in individual qubit energies and residual short-range inter-qubit couplings. We show that these imperfections can lead to the emergence of quantum chaos and dynamical thermalization also in a quantum computer ideally decoupled from the environment. We discuss their effect on the stability of (i) the quantum computer hardware and (ii) an efficient quantum algorithm simulating a physical model with rich and complex dynamics described by the quantum sawtooth map.

We indicate some of the lessons learned from our work on coherence and decoherence in various fields and mention some recent work with solid state devices as elements of the “quantum computer”, including the realization of simple logic gates controlled by adiabatic processes. We correct a commonly held misconception concerning decoherence for a free particle.

We discuss the algorithmic information approach to the analysis of the observational data on the Universe. Kolmogorov complexity is proposed as a descriptor of the Cosmic Microwave Background (CMB) radiation maps. An algorithm of computation of the complexity is described, applied, first, to toy models and then, to the data of the Boomerang experiment. The sky maps obtained via the summing of two independent Boomerang channels reveal threshold independent behavior of the mean ellipticity of the anisotropies, thus indicating correlations present in the sky signal and possibly carrying crucial information on the curvature and the non-Friedmannian, i.e. accelerated expansion of the Universe. Similar effect has been detected for COBE-DMR 4 year maps. Finally, as another application of these concepts, we consider the possible link between the CMB properties, curvature of the Universe and arrows of time.

We report the first observation of the Quantum Zeno effect (QZE) and Anti-Zeno effect (AZE) in an unstable system. These effects are the inhibition or enhancement of decay by frequent measurement during the non-exponential time. The experiment builds on our earlier observation of short-time deviations from exponential decay in the tunneling of atoms from accelerating lattices. Recent improvements in the experiment and development of the measurement method have now allowed us to observe both the QZE and the AZE.

No abstract received.

The quantum Zeno evolution of a quantum system takes place in a proper subspace of the total Hilbert space. The physical and mathematical features of the “Zeno subspaces” depend on the measuring apparatus: when this is included in the quantum description, the Zeno effect becomes a mere consequence of the dynamics and, remarkably, can be cast in terms of an adiabatic theorem, with a dynamical superselection rule. We look at several examples and focus on quantum computation and decoherence-free subspaces.

Conceptual tensions between the three pillars of physics consisting of quantum mechanics, relativity, and statistical mechanics, will be reviewed. Relativity is not violated by our earlier experiments showing that quantum tunneling is superluminal, nor by the recent observations of faster-than-c group velocities, including the recent Princeton NEC experiments, nor by our electronic circuit experiments, which demonstrate the existence of negative group delays. In fact, relativity does not forbid the group velocity in transparent optical media from exceeding c, nor the occurrence of seemingly anti-causal negative group delays in any other linear-response media. We have observed such counter-intuitive behaviors in electronic circuits, in particular, the occurrence of negative group delays of analytic signals, in which the peak of an output pulse leaves the exit port of the circuit before the peak of the input pulse enters the input port. Moreover, we predict that similar negative group delays will occur for atomic wavepackets incident at low energies on an atomic BEC. Some applications of these counter-intuitive effects, including the speeding up of computers, will be discussed.

We review the recent work on producing a transparent, linear, anomalously dispersive medium. Experimentally, a light pulse propagating through the atomic vapor cell has its peak reaching the exit side before entering it, resulting in a negative transit time, and negative group velocity. We further review a recently proposed operational definition of the velocity of information transport based on a close analysis of quantum fluctuations.

In recent years it has become possible to carry optical diffraction experiments over to atoms and molecules, in particular diffraction by double slits and transmission gratings. However, small deviations from the usual wave-optical theory occur, and a fully quantum mechanical theory yields new surprising insights on the interaction of atoms with surfaces and on the size of molecules.

Photonic tunneling permits superluminal group velocity. The principle of causality is not violated but the time duration between cause and effect can be shortened compared with an interaction exchange with velocity of light. This outstanding property can be applied to speed-up photonic modulation and transmission as well as to improve micro-electronic devices. Superluminal photonic pulse transmission has been presented at microwave and infrared frequencies already. Presumably superluminal photonic and electronic devices can become reality having in mind the experimental evidence of the universal tunneling time of photons and of electrons.

Nonlocal variables are briefly reviewed and it is shown that all nonlocal variables related to two or more separate sites can be measured instantaneously, provided we restrict ourselves to verification measurements. The method is based on quantum teleportation.

We study kinetics of the formation, quantum fluctuations, and decoherence of Bose-Einstein condensate (BEC) in a weakly interacting Bose gas. These processes determine, in particular, the properties of the atom lasing and quantum information processing based on BEC. We develop the method of the canonical ensemble quasiparticles in the theory of interacting Bose gases that solves the problem of uncontrollable particle-number non-conservation of the standard grand canonical ensemble approximations, e.g., Bogoliubov-Popov approximation. It yields a solution to the problem of the non-Gaussian anomalously large fluctuations of the ground state occupation in a condensed interacting Bose gas at all temperatures below the critical value.

This method allows us also to derive a time-dependent equation for a coherent order parameter in a partially condensed weakly interacting Bose gas, i.e., a generalized Gross-Pitaevskii equation, that takes a form of a nonlocal nonlinear Schrodinger equation coupled to the equation for the noncondensate excitations via nonlocal inhomogeneous source term responsible for an exchange of particles between condensate and noncondensate. In this way we make gapless approximations particle-number-conserving and provide a well-grounded basis for the analysis of the formation and decoherence of a coherent condensate due to coupling with an incoherent noncondensate.

A microscopic dynamical entropy (or function) for a two-level atom interacting with a field is introduced. The excitation process of the atom due to the resonance scattering of a wave packet is discussed. Three stages of scattering process (before, during and after the collision) are described in terms of entropy production and entropy flow. The excitation of the atom may be considered as the construction of a non-equilibrium structure due to entropy flow. The emission of photons distributes the energy of the unstable state among the field modes, leading to an increase of microscopic entropy. In this process, instability in dynamics associated with resonances plays a central role. The function is constructed outside the Hilbert space, which allows strictly irreversible time evolution, avoiding probabilistic arguments associated with ignorance.

The problem of relativistic causality in atom-radiation interacting systems is investigated. The excitation transfer in the Fermi problem is considered and it is shown that, independently from the initial state of the two atoms, it is causal, as well as the propagation of the electromagnetic field emitted by an excited atom. Nonlocal interatomic correlations and nonlocal spatial field correlations however appear in the evolution of the systems considered. These nonlocal correlations are shown to be compatible with relativistic causality. Our results are discussed with reference to questions recently raised in the literature about possible violations of relativistic causality.

The advent of lasers and novel experimental techniques have made it possible to conduct experiments on the already solved but ever “intriguing” problem of the “superluminal velocity of light pulses” ^1,2 in various experimental situations (see review ³): anomalous dispersion near an absorption line ⁴, linear gain spectral lines ^5–11, and tunneling barriers ^12,13. In essence, these experiments have only confirmed the usefulness of the five different kinds of wave velocity, namely, the phase velocity, the group velocity, the energy velocity, the “signal ”velocity, and the “front” velocity, introduced by L. Brillouin ² for absorptive dispersion media. In this connection, I would like to return to the discussion of this problem for the interesting case of propagation of a short laser pulse in a nonlinear (saturable) amplifying medium in the wider context of propagation of instability autowaves in an active nonlinear medium.

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 the micromaser operating under the conditions of the so-called trapping states. In this situation the micromaser stabilises to a photon number state. The second device uses a single ion in an optical cavity. The latter setup was recently realised in our laboratory.

Coherent quantum solitons show a characteristic evolution when propagating through an optical fiber, unlike their classical counterparts which are stable solutions to the nonlinear Schrödinger equation. The dynamical properties of quantum solitons as well as their use in quantum interferometry and in high-bit rate, long distance and secure optical communication are discussed.

The generation and detection of maximally-entangled two-particle states, ‘Bell states’, are crucial tasks in many quantum information protocols such as cryptography, teleportation, and dense coding. Unfortunately, they require strong inter-particle interactions lacking in optics. For this reason, it has not previously been possible to perform complete Bell state determination in optical systems. In this work, we show how a recently developed quantum interference technique for enhancing optical nonlinearities can make efficient Bell state measurement possible. We also discuss weaknesses of the scheme including why it cannot be used for unconditional quantum teleportation.

When a single photon is split by a beam splitter, its two “halves” can entangle two distant atoms into an EPR pair. We discuss a time-reversed analogue of this experiment where two distant sources cooperate so as to emit a single photon. The two “half photons,” having interacted with two atoms, can entangle these atoms into an EPR pair once they are detected as a single photon. Entanglement occurs by creating indistinguishabilility between the two mutually exclusive histories of the photon. This indistinguishabilility can be created either at the end of the two histories (by “erasing” the single photon’s path) or at their beginning (by “erasing” the two atoms’ positions).

We develop a Floquet scattering matrix to describe quantum mechanical behavior of an electron which scatters from an atomic core in the presence of an intense laser field. As the laser intensity is increased, the underlying classical scattering process becomes chaotic. This underlying chaos appears to manifest itself in an interesting form of level repulsion among the eigenphases of the Floquet scattering matrix.

We give a brief overview of work on extending present two-party quantum communication protocols to three-party and multi-party protocols. In particular we discuss the case of three-party protocols and entanglement-assisted transformations between inequivalent classes of three-particle entangled states (GHZ-states and W-states) which are non-interchangeable under local transformations. We furthermore review possible applications of three-party entangled states.

Recent experimental and theoretical results demonstrate that both populations and coherence in a system of nuclear spins in solids can be controlled by a laser field with high efficiency. Nearly 100% nuclear polarization can be achieved on a submicrosecond time scale. Both a high speed of the optical excitation of nuclear polarization and long storage times can be achieved simultaneously. The most promising candidates are rare-earth and possibly transition-metal impurities with a large constant of hyperfine interaction.

Trojan horse attacking strategy on quantum cryptography is investigated, three aspects are involved. First, the mechanism for the Trojan horse attacking strategy on quantum cryptography as well as classic cryptography is studied. Then the fragility of the quantum cryptographic algorithm employing EPR pairs as key against the Trojan horse attacking strategy is analyzed. To prevent the Trojan horse attacking strategy, an improvement scheme which makes use of non-orthogonal entangled states is proposed, results show the improvement scheme is robust to the Trojan horse attacking strategy without reducing the security on other kinds of attacking strategies.

In the past 20 years quantum probability has challenged the widespread belief that classical macroscopic systems cannot, by local independent choices, produce sequences of data whose correlations violate Bell’s inequality. The possibility of such a violation is not a matter of interpretation, but of fact: “local independent choices” means that two separated and non communicating experimenters make measurements but one does not know what the other measures (or even if the other one measures something); correlations are evaluated by means of standard procedures. The present experiment shows that this is not the case: in no way the EPR correlations and related experiments can be considered as a support of the incompatibility of quantum theory with local realistic theories, in particular relativity.

Although formal discussions of quantum computation and communication involve abstract unitary transformations in Hilbert space, implementations of quantum logic require attention to the dynamical processes of particular physical systems. In the Quantum Optics Group at Caltech, we are attempting to lay the foundations for quantum information science by way of advances on several fronts in optical physics, including cavity quantum electrodynamics.

In the ion trap quantum computer the internal states of trapped ions serve as quantum bits and laser induced collective vibrations of the ions serve to couple the ions and to perform gate operations. We have developed a method to perform gates on different ions by illuminating the ions with bichromatic light. Here, we display a geometric representation of this operation which enables us to extend the method to implement trigonometric functions of operators on the quantum register and to produce gates which may involve a large number of bits in a single operation.

Much of the Bell Theory for quantum mechanics may be placed within a general operator trigonometry which I developed independently about 35 years ago. From that mathematical viewpoint, certain issues in the Bell theory are seen as “just geometry”.

No abstract received.

Communication channels are physical systems that transfer information from one place to another. Like all physical systems, communication channels are governed by the laws of quantum mechanics. Quantum mechanics is known to bound the capacity of bosonic channels such as optical fibers or free-space electromagnetic communication: a single transverse mode of the electromagnetic field can communicate a number of bits per second proportional to the square root of the power invested in communication. This paper investigates the capacity of a variety of quantum channels, and shows that enhancements in channel capacity can be obtained by coupling together the information degrees of freedom in quantum channels. So, for example, by coupling together modes in a multimode optical fiber, one can in principle obtain a significant enhancement of the capacity of the fiber for fixed power over the same fiber with uncoupled modes.

We discuss the average kinetic energy of N non-interacting quantum particles in its dependence on N. For a peculiar entangled state, the kinetic energy increases quadratically with N, in contrast to its behavior in simple thermodynamics.

We show how one can use atomic ensembles in order to construct quantum repeaters. This may allow for quantum communication over long distances.

An implementation method of a gate in a quantum computer is studied in terms of a finite number of steps evolving in time according to a finite number of basic Hamiltonians, which are controlled by on-off switches. As a working example, the case of a particular implementation of the two qubit computer employing a simple system of two coupled Josephson junctions is considered.

I will review the relationship between error-correction codes and certain mathematical models of spin glasses. I will show that there is a one to one relationship between error correcting codes and spin glass models. Minimum error probability decoding is equivalent to finding the magnetisation of the corresponding spin system. Convolutional codes correspond to one-dimensional spin systems and Viterbi’s decoding algorithm to the transfer matrix algorithm of Statistical Mechanics.

I will also show how the recently discovered (or rediscovered) capacity approaching codes (turbo codes and low density parity check codes) can be analysed using statistical mechanics. Turbo codes correspond to two coupled spin chains, while low density parity check codes are spin models on a diluted random graph. It is possible to show, using statistical mechanics, that these codes allow error-free communication for signal to noise ratio above a certain threshold. This threshold, which corresponds to a phase transition in the spin model, depends on the particular code, and can be computed analytically in many cases.

After playing a significant role in the development of the foundations of quantum mechanics, entanglement has been recently rediscovered as a new physical resource with potential commercial applications, ranging from quantum cryptography to very precise frequency standards. Thus, the detection of quantum entanglement is vital in the experimental context. We present a direct method of detecting the presence of entanglement and we put it in the context of quantum information science.

A connection between the theory of neural networks and cryptography is presented. A new phenomenon, namely synchronization of neural networks, is leading to a new method of exchange of secret messages. Two artificial networks being trained by the Hebbian learning rule on their mutual outputs develop an antiparallel state of their synaptic weights. The synchronized weights are used to construct an ephemeral key exchange protocol for the secure transmission of secret data. The complexity of the generation of the secure channel is linear with the size of the network. An attacker who knows the protocol and all details of any transmission of the data finds it difficult to decrypt the secret message.