A Comparative Study of Quantum and Classical Deletion

Here in this letter, we study the difference between quantum and classical deletion. We point out that the linear mapping deletion operation used in the impossibility proof for quantum systems applies also to classical system. The general classical deletion operation is a combined operation of measurement and transformation, i.e., first read the state and then transfer the state to the standard blank state. Though both quantum information and classical information can be deleted in an open system, quantum information cannot be recovered while classical information can be recovered.     

The Role of Quantum Interference in Quantum Computing

Quantum interference is proposed as a tool to augment Quantum Computation.     

Finite Quantum Tomography and Semidefinite Programming

Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, N-qubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981; Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany (1999); Pegg and Barnett Physical Review A 39 (1989) 1665; Barnett and Pegg Journal of Modern Optics 36 (1989) 7; St. Weigert Acta Physica Slov. 4 (1999) 613). PACs index: 03.65.Ud     

Information Complexity of Quantum Gates

This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate operation in terms of the difference between the entropy of the variables associated with initial and final states of the computation. We argue that the gate operations are irreversible if there is a difference in the accuracy associated with input and output variables. It is shown that under some conditions the gate operation may be associated with unbounded entropy, implying impossibility of implementation. PACS number: 03.65     

“Quantum” Beats in Classical Physics

We present an analysis of (and a classical model for) atomic decays that do (do not) exhibit what has been denoted “quantum beats.” The model shows that the appearance of beats is dependent on implicit (but not necessarily the extent of) phase coherence of the excitation signals. The significance of the existence of this model for arguments on the tenability of neoclassical electromagnetic theory as an alternate theory to quantum electrodynamics is discussed.     

Electron Spins in Quantum Dots as Quantum Bits

The creation, coherent manipulation, and measurement of spins in nanostructures open up completely new possibilities for electronics and information processing, among them quantum computing and quantum communication. We review our theoretical proposal for using electron spins in quantum dots as quantum bits, explaining why this scheme satisfies all the essential requirements for quantum computing. We include a discussion of the recent measurements of surprisingly long spin coherence times in semiconductors. Quantum gate mechanisms in laterally and vertically tunnel-coupled quantum dots and methods for single-spin measurements are introduced. We discuss detection and transport of electronic EPR pairs in normal and superconducting systems.     

Quantum Mechanical Nature in Liquid NMR Quantum Computing

The quantum nature of bulk ensemble NMR quantum computing the center of recent heated debate,is addressed. Concepts of the mixed state and entanglement are examined, and the data in a two-qubit liquid NMRquantum computation are analyzed. The main points in this paper are: i) Density matrix describes the “state“ of anaverage particle in an ensemble. It does not describe the state of an individual particle in an ensemble; ii) Entanglementis a property of the wave function of a microscopic particle (such as a molecule in a liquid NMR sample), and separabilityof the density matrix cannot be used to measure the entanglement of mixed ensemble; iii) The state evolution in bulk-ensemble NMRquantum computation is quantum-mechanical; iv) The coefficient before the effective pure state densitymatrix, e, is a measure of the simultaneity of the molecules in an ensemble. It reflects the intensity of the NMR signaland has no significance in quantifying the entanglement in the bulk ensemble NMR system. The decomposition of thedensity matrix into product states is only an indication that the ensemble can be prepared by an ensemble with theparticles unentangled. We conclude that effective-pure-state NMR quantum computation is genuine, not just classicalsimulations.     

Classical Versus Quantum Probability in Sequential Measurements

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modeled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the “which way” experiments); they are, however, distinguishable in principle.     

Classical and Quantum Coherent States

p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously (V. V. Kisil, p-Mechanics as a physical theory. An Introduction, E-print:arXiv:quant-ph/0212101, 2002; International Journal of Theoretical Physics 41(1), 63–77, 2002). We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allows us to evaluate classical observables at any point of phase space and simultaneously to evaluate quantum probability amplitudes. The example of the forced harmonic oscillator is used to demonstrate these concepts.     

Foundation for Quantum Computing

In this paper we introduce a minimal formal intuitionistic propositional Gentzen sequent calculus for handling quantum types, quantum storage being introduced syntactically along the lines of Girard's of course operator !. The intuitionistic fragment of orthologic is found to be translatable into this calculus by means of a quantum version of the Heyting paradigm. When realized in the category of finite dimensional Hilbert spaces, the familiar qubit arises spontaneously as the irreducible storage capable quantum computational unit, and the necessary involvement of quantum entanglement in the quantum duplication process is plainly and explicitly visible. Quantum computation is modelled by a single extra axiom, and reproduces the standard notion when interpreted in a larger category.     

Foundation for Quantum Computing II

In this continuation of an earlier paper we develop further the theme of quantum logical specification and derive from it some apparently physically viable instantiations of potential quantum computing devices. Specifically, in the case of a one-parameter set of terms (or labels)—read as instants of time—we find, emerging quite naturally from the algebraic setup, the paradigm for a single qubit epitomized by the case of a two-state fermion interacting with an external single mode boson. This covers the cases: cavity QED, trapped ions, and, when the qubits are multiplexed appropriately, NMR based systems. (This case degenerates to one in which only bosons are relevant as in the case of pure bosonic harmonic oscillator models in the “dual rail” representation. Such models fly in the face of the logic itself, thus clearly revealing even at this level their well-known shortcomings as practical quantum computing devices. Here as elsewhere logical constraints apparently dominate physical ones.) In a final section we indicate briefly how this process exactly generalizes, in the case of a manifold of terms more general than the one-parameter case, to yield the notion of holonomic quantum computation. In the course of this investigation we find an interpretation of path integrals as limits of sequences of logical CUTS, thus establishing a link—though still tenuous—between ensembles of acts of quantum computation and Lagrangians.     

Classical Limit of Quantum Dissipative Systems

We discuss the Lindblad equation for the density matrix where the dissipation is linear in the position operator. We consider a potential which is a bounded perturbation of the harmonic oscillator. We show that the perturbation of the potential leads to an analytic perturbation of the Wigner distribution. Then the Wigner distribution of the quantum dissipative system tends (uniformly in time) to the classical phase space distribution of the classical dissipative system (if the initial distribution converges when 0).     

Scalable Arbitrated Quantum Signature of Classical Messages with Multi-Signers

Unconditionally secure signature is an important part of quantum cryptography. Usually, a signature scheme only provides an environment for a single signer. Nevertheless, in real applications, many signers may collaboratively send a message to the verifier and convince the verifier that the message is actually transmitted by them. In this paper, we give a scalable arbitrated signature protocol of classical proved to be secure even with a compromised arbitrator. messages with multi-signers. Its security is analyzed and proved to be secure even with a compromised arbitrator.     

Entanglement and Classical Correlations in the Quantum Frame

The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones. This leads to a frame in which two kinds of correlations emerge: the classical correlation that is coded in the mixed state of the physical system and a new correlation, to be called probabilistic entanglement, which may occur also at pure states. We examine to what extent this characterization of correlations can be applied to quantum mechanics. Explicit calculations on simple examples outline that a same quantum state can show only classical correlations or only entanglement depending on its statistical content; situations may also arise in which the two kinds of correlations compensate each other.     

The Classical Singularity Theorems and Their Quantum Loopholes

The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum violation of the classical energy conditions, and the presence of quantum fluctuations of the spacetime geometry. The possible significance of each is discussed.     

Classical Solutions from Quantum Regime for Barotropic FRW Model

The quantization of gravity coupled to barotropic perfect fluid matter field with a cosmological constant is carried out. The wave function can be determined for any curvature index in the FRW minisuperspace model. The meaning of the existence of the classical solution is discussed in the WKB semiclassical approximation.     

The Distance Between Classical and Quantum Systems

In a recent paper, a “distance” function, , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors for simplicity and clarity. Several specific examples are calculated.     

Duality Computing in Quantum Computers

In this letter, we propose a duality computing mode, which resembles particle-wave duality property when a quantum system such as a quantum computer passes through a double-slit. In this mode, computing operations are not necessarily unitary. The duality mode provides a natural link between classical computing and quantum computing. In addition, the duality mode provides a new tool for quantum algorithm design.     

Energy–Information Coupling From Classical to Quantum Physics

The idea of exploiting a supposedly enhanced information content of superposition states in quantum computation seems to invalidate the classical probabilistic definition of information; but this is not necessarily so.