Randomness in Classical Mechanics and?Quantum Mechanics

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is always positive (non zero).     

Quantum Mechanics and Information Security

After a short review of the background and main theoretical results of quantum key distribution, I shall then introduce the existing problems for secure QKD in practice. Ishall then forus on the security problem of QKD with an imperfect source, in particular, the recently developed theory of the decoy-state method which can help to implement the secure QKD without a single-photon source. Basically, if the single-photon source is replaced by the weak coherent light, the protocol can betotally insecure due to the photon-number-splitting attack given a lossy channel. However, if werandomly change the intensity of each pulses among a few different values （ e. g. , 3 ） we can thenal- most exactly verify the fraction of bits generated by those single-photonpulses. This, together with the prior art theo- retical result, can raise the secure distance of QKD with currently existing technologies from less than 20 kms to more than 120 kms. Experimental implementation of decoy-state QKD have been done.     

Nonadiabatic Geometric Quantum Computation with Asymmetric Superconducting Quantum Interference Device

We propose a method of controlling the dc-SQUID(superconductiong quantum interference device)system by changing the gate voltages,which controls the amplitude of the fictitious magnetic fields Bz,and the externally applied current that produces the piercing magnetic flux Φx for the dc-SQUID system,we have also introduced a physical model for the dc-SQUID system.Using this physical model,one can obtain the non-adiabatic geometric phase gate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the two qubits.It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies an appropriate constraint condition,the charge state evolution can be controlled exactly on a dynamic phase free path.The non-adiabatic evolution of the charge states is given as well.     

Quantum Mechanics as a Simple Generalization of Classical Mechanics

A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices with suitable Hermitian matrices.     

Is Indistinguishability in Quantum Mechanics Conventional?

Darrin Belousek has argued that the indistinguishability of quantum particles is conventional in the Duhemian–Einsteinian sense, in part by critially examining prior arguments given by Redhead and Teller. Belousek's discussion provides a useful occasion to clarify some of those arguments, acknowledge respects in which they were misleading, and comment on how they can be strengthened. We also comment briefly on the relevant sense of conventional.     

Universal Quantum Gates Based on Both Geometric and Dynamic Phases in Quantum Dots

A large-scalable quantum computer model,whose qubits are represented by the subspace subtended by the ground state and he single exciton state on semiconductor quantum dots,is proposed.A universal set of quantum gates in this system may be achieved by a mixed approach,composed of dynamic evolution and nonadiabatic geometric phase.     

Path Integral Formulation for Chern-Simons Quantum Mechanics

Chern-Simons quantum mechanics is studied by using the path integral formulation. We find that the model can be decomposed into two independent oscillators when a set of new coordinate is chosen. The propagator is constructed in this new set of coordinate and the spectra is read off directly from it. The spectra will be divergent when the mass of the particle tends to zero. In order to get a physical result, one must regularize the spectra properly. We afford a new scheme of regularization. Interestingly, our scheme shows that the regularization we proposed amounts to erase one of the oscillators in the new set of coordinate. Physical interpretations for the regularization are given and some ambiguities in the literatures are clarified.     

Is Minkowski Space-Time Compatible with Quantum Mechanics?

In quantum relativistic Hamiltonian dynamics, the time evolution of interacting particles is described by the Hamiltonian with an interaction-dependent term (potential energy). Boost operators are responsible for (Lorentz) transformations of observables between different moving inertial frames of reference. Relativistic invariance requires that interaction-dependent terms (potential boosts) are present also in the boost operators and therefore Lorentz transformations depend on the interaction acting in the system. This fact is ignored in special relativity, which postulates the universality of Lorentz transformations and their independence of interactions. Taking into account potential boosts in Lorentz transformations allows us to resolve the no-interaction paradox formulated by Currie, Jordan, and Sudarshan [Rev. Mod. Phys. 35, 350 (1963)] and to predict a number of potentially observable effects contradicting special relativity. In particular, we demonstrate that the longitudinal electric field (Coulomb potential) of a moving charge propagates instantaneously. We show that this effect as well as superluminal spreading of localized particle states is in full agreement with causality in all inertial frames of reference. Formulas relating time and position of events in interacting systems reduce to the usual Lorentz transformations only in the classical limit (0) and for weak interactions. Therefore, the concept of Minkowski space-time is just an approximation which should be avoided in rigorous theoretical constructions.     

What is Quantum Mechanics? A Minimal Formulation

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called “microscopic theory”, applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen–Specker–Bell theorem and Gleason’s theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.     

Fundamental Equations of Quantum Mechanics in Time-Varying Domain

Fundamental equations of quantum mechanics in time-varying domain are presented. The used method consists in transforming the variable domain into a fixed domain. The transformation has to be covariant in relation to the wavefunction. The new fundamental equations turn out to be a generalization of the classical equations established in a Newtonian space-time. When the time-varying domain becomes stationary, we find again the fundamental equations of the classical quantum mechanics.     

Time Symmetric Quantum Mechanics and Causal Classical Physics ?

A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual “near future” macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.     

The Geometry of¶(Super) Conformal Quantum Mechanics

N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D ^a δ _a whose associated one-form D _a dX ^a is closed. Further, the SL(2,ℝ) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry D ^a I _a ^b δ _b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given. Received: 3 September 1999 / Accepted: 30 January 2000     

Unreasonable and “Unreasonable” in Quantum Mechanics?

The particles of quantum mechanics (QM) are discrete undulatory entities which are described in terms of the complex state vectors of the theory in full agreement with experiment. The wave-particle paradox stems from the fact that undulation and discreteness are inconsistent within the classical theory which was historically the point of departure for the canonical foundation. The author describes his prolonged efforts of anchoring the state vector of QM in experiment rather in obsolete theory.     

On Schrödinger-Hermite Operators in Lattice Quantum Mechanics

Starting from the q-Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties. This happens by algebras of creators and annihilators. Generalized inhomogeneous q-discrete Hermite polynomials occur via their recurrence relations. Within this framework we obtain the special case of an interesting result, proved by Christian Berg in a much larger ge-nerality: The orthogonality measure for q-discrete Hermite polynomials of type II is not uniquely determined on q-exponential lattices.     

Quantum Mechanics Helps in Learning for More Intelligent Robots

A learning algorithm based on the state superposition principle is presented. The theoretical analysis shows that the needed fundamental transformations to realize this algorithm are the same as those needed in the Grover algorithm and are within current state-of-the-art technology. The simulated experiment shows that the quantum learning algorithm can help robots to learn faster and to become more intelligent.     

Is the Epistemic View of Quantum Mechanics Incomplete?

One of the most tantalizing questions about the interpretation of Quantum Theory is the objective vs. subjective meaning of quantum states. Here, by focusing on a typical EPR experiment upon which a selection procedure is performed on one side, we will confront the fully epistemic view of quantum states with its results. Our statement is that such a view cannot be considered complete, although the opposite attitude would also pose well-known problems of interpretation.This paper is dedicated to Prof. Franco Selleri on the occasion of his 70th birthday     

Topos-Theoretic Extension of a Modal Interpretation of Quantum Mechanics

This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained truth-value valuations are investigated. What is taken up is the modal approach based on a determinate lattice , which is a sublattice of the lattice of all quantum propositions and is determined by a quantum state e and a preferred determinate observable R. Topos-theoretic extension is made in the functor category of which base category is determined by R. Each true atom, which determines truth values, true or false, of all propositions in , generates also a multi-valued valuation function of which domain and range are and a Heyting algebra given by the subobject classifier in , respectively. All true propositions in are assigned the top element of the Heyting algebra by the valuation function. False propositions including the null proposition are, however, assigned values larger than the bottom element. This defect can be removed by use of a subobject semi-classifier. Furthermore, in order to treat all possible determinate observables in a unified framework, another valuations are constructed in the functor category . Here, the base category includes all ’s as subcategories. Although has a structure apparently different from , a subobject semi-classifier of gives valuations completely equivalent to those in ’s.     

The End of a Classical Ontology for Quantum Mechanics?

In this paper, I argue that the Shrapnel–Costa no-go theorem undermines the last remaining viability of the view that the fundamental ontology of quantum mechanics is essentially classical: that is, the view that physical reality is underpinned by objectively real, counterfactually definite, uniquely spatiotemporally defined, local, dynamical entities with determinate valued properties, and where typically ‘quantum’ behaviour emerges as a function of our own in-principle ignorance of such entities. Call this view Einstein–Bell realism. One can show that the causally symmetric local hidden variable approach to interpreting quantum theory is the most natural interpretation that follows from Einstein–Bell realism, where causal symmetry plays a significant role in circumventing the nonclassical consequences of the traditional no-go theorems. However, Shrapnel and Costa argue that exotic causal structures, such as causal symmetry, are incapable of explaining quantum behaviour as arising as a result of noncontextual ontological properties of the world. This is particularly worrying for Einstein–Bell realism and classical ontology. In the first instance, the obvious consequence of the theorem is a straightforward rejection of Einstein–Bell realism. However, more than this, I argue that, even where there looks to be a possibility of accounting for contextual ontic variables within a causally symmetric framework, the cost of such an account undermines a key advantage of causal symmetry: that accepting causal symmetry is more economical than rejecting a classical ontology. Either way, it looks like we should give up on classical ontology.     

Quantum Mechanics: An Intelligible Description of Objective Reality?

Jim Cushing emphasized that physical theory should tell us an intelligible and objective story about the world, and concluded that the Bohm theory is to be preferred over the Copenhagen interpretation. We argue here, however, that the Bohm theory is only one member of a wider class of interpretations that can be said to fulfill Cushings desiderata. We discuss how the pictures provided by these interpretations differ from the classical one. In particular, it seems that a rather drastic form of perspectivalism is needed if accordance with special relativity is to be achieved.