Device-independent security of quantum cryptography against collective attacks

We present the optimal collective attack on a quantum key distribution protocol in the "device-independent" security scenario, where no assumptions are made about the way the quantum key distribution devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.     

Characterizations of classical and quantum logics

In classical logic (Boolean algebras) probability systems involving correlations are fully characterized by the system of generalized Bell inequalities. On the other hand, probability systems with pairwise correlations on orthomodular lattices (OML) representing quantum logics are so general that the only inequalities that hold universally are the trivial inequalities 0p _i1, 0p _ijmin {p _i,p _j}. In this paper it is shown that every correlation sequence p=(p₁,...,p _n,...,P _ij,...) satisfying the above inequalities can be represented by a probability measure on an orthomodular latticeL admitting a full set of {0,1}-valued probability measures with the additional property that isL ortho-Arguesian.     

Separating the classical and quantum information via quantum cloning

An application of quantum cloning to optimally interface a quantum system with a classical observer is presented; in particular, we describe a procedure to perform a minimal disturbance measurement on a single qubit by adopting a 1-->2 cloning machine followed by a generalized measurement on a single clone and the anticlone or on the two clones. Such a scheme can be applied to enhance the transmission fidelity over a lossy quantum channel.     

Integrable classical systems in higher dimensions

A general method for the construction of the second constant of motion (up to second order) for higher-dimensional classical systems is carried out. Correspondingly, the first- and the second-order potential equations are obtained whose solutions can directly provide the integrable systems.     

Experimental tests of extra dimensions

Spherically symmetric solutions of general relativity in higher dimensions are tested. We find that the existence of extra dimensions is compatible with the classical tests of general relativity, which place almost no restrictions on the parameters involved. The models studied fail to explain the geological data concerning the apparent variability of the gravitational constant with the distance.     

Superposition in quantum and classical mechanics

Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.Dedicated to the Memory of Charles H. Randall.     

Connecting the quantum and classical worlds

By considering (non‐relativistic) quantum mechanics as it is done in practice in particular in condensed‐matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope, leaving a lot of room for embedding the quantum‐classical transition into our current theories without recurring to difficult‐to‐accept interpretations of quantum mechanics. Nonunitary projections to initial and final states, the breaking of time‐reversal symmetry, a change of Hilbert space, and the introduction of classical concepts such as external potentials or localized atomic nuclei are widespread in quantum mechanical calculations. Furthermore, quantum systems require classical environments that enable the symmetry breaking that is necessary for creating the atomic configurations of molecules and crystals. This paper argues that such classical environments are provided by finite‐temperature macroscopic systems in which the range of quantum correlations and entanglement is limited. This leads to classical behavior on larger scales, and to collapse‐like events in all dynamical processes that become coupled to the thermalized degrees of freedom.

     

On classical and quantum relativistic dynamics

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added.     

Relation between classical and quantum mechanics

Expressions for the Lie derivatives of functions of non-commuting variables are derived and used to reformulate classical mechanics. This is possible only if the phase space variables commute, or if they satisfy Heisenberg's commutation relations.This work was supported in part by the National Science Foundation Grant Number NSF GP-14803, and by the Air Force Office of Scientific Research, contract number AFOSR 68-1524.     

Aspects of classical and quantum Nambu mechanics

We present recent developments in the theory of Nambu mechanics, which include new examples of Nambu-Poisson manifolds with linear Nambu brackets and new representations of Nambu-Heisenberg commutation relations.     

Problems of classical and quantum gravitational collapse

An exact solution of Einstein's equations is obtained in the case of a spherically symmetric distribution of a perfect fluid with maximally hard equation of state. A sufficient condition of halting of the collapse of charged dust is obtained. The dynamics and statics of a vector massive configuration with massless source are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–12, September, 1977.We are very grateful to N. V. Pavlov and K. A. Bronnikov for valuable discussions and helpful comments.     

量子谐振子与经典谐振子的比较

运用广义线性量子变换的普遍理论求解了量子谐振子,同经典谐振子比较给出了量子谐振子趋近于经典极限的条件,并得出相干态是最理想的经典极限态．     

Device-independent certification of entangled measurements

We present a device-independent protocol to test if a given black-box measurement device is entangled, that is, has entangled eigenstates. Our scheme involves three parties and is inspired by entanglement swapping; the test uses the Clauser-Horne-Shimony-Holt Bell inequality, checked between each pair of parties. In the case where all particles are qubits, we characterize quantitatively the deviation of the measurement device from a perfect Bell-state measurement.     

Self-interaction and regularization of classical electrodynamics in higher dimensions

The classical electrodynamic system of a field and a single point-like source is considered in even-dimensional spacetime. The problem of self-interaction is discussed. It is manifestly shown that all singular terms appearing in these equations can be regularized. Relations between formulas for radiation and radiation friction are discussed. The text was submitted by the author in English.     

Tomographic quantum cryptography: equivalence of quantum and classical key distillation

The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.     

Anomalous low-field classical magnetoresistance in two dimensions

The magnetoresistance of classical two-dimensional electrons scattered by randomly distributed impurities is investigated by numerical simulation. At low magnetic fields, we find for the first time a negative magnetoresistance proportional to |B|. This unexpected behavior is shown to be due to a memory effect specific for backscattering events, which was not considered previously.     

The classical nucleation rate in two dimensions

In many systems in condensed matter physics and quantum field theory, first order phase transitions are initiated by the nucleation of bubbles of the stable phase. In homogeneous nucleation theory the nucleation rate can be written in the form of the Arrhenius law: . Here is the energy of the critical bubble, and the prefactor can be expressed in terms of the determinant of the operator of fluctuations near the critical bubble state. In general it is not possible to find explicit expressions for and . If the difference between the energies of the stable and metastable vacua is small, the constant can be determined within the leading approximation in , which is an extension of the ”thin wall approximation”. We have done this calculation for the case of a model with a real-valued order parameter in two dimensions. Received: 11 September 2002 / Revised version: 30 October 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: munsteg@uni-muenster.de RID="b" ID="b" e-mail: rut@ifttp.bas-net.by ^* Present address: Universit?t Essen, Fachbereich 7 - Physik, Universit?tsstr. 5, 45117 Essen, Germany     

Interaction between classical and quantum systems and the measurement of quantum observables

Quantum mechanics presumes classical measuring instruments with which they interact. The problem of measurement interaction between classical and quantum systems is posed and solved. The restriction to compatible measurements comes about naturally as the condition for the integrity of the classical system. A technical device is the perspective on classical mechanics as quantum mechanics with essentially hidden dynamical variables. Work supported in part by U.S. Atomic Energy Commission, ERDA.