Dilation,discrimination and Uhlmann's theorem of link products of quantum channels

We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.

Duality theorem for smash coproduct over quantum groupoids

The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.

Quantum Secret Sharing Based on Chinese Remainder Theorem

A novel quantum secret sharing （QSS） scheme is proposed on the basis of Chinese Remainder Theorem （CRT）. In the scheme, the classical messages are mapped to secret sequences according to CRT equations, and distributed to different receivers by different dimensional superdense-coding respectively. CRT＇s secret sharing function, together with high-dimensional superdense-eoding, provide convenience, security, and large capability quantum channel for secret distribution and recovering. Analysis shows the security of the scheme.

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.

Quantum mechanical version of the classical Liouville theorem

In terms of the coherent state evolution in phase space,we present a quantum mechanical version of the classical Liouville theorem.The evolution of the coherent state from ｜z〉to｜sz-rz＊〉 corresponds to the motion from a point z（q,p） to another point sz-rz＊ with ｜s｜2-｜r｜2=1.The evolution is governed by the so-called Fresnel operator U（s,r） that was recently proposed in quantum optics theory,which classically corresponds to the matrix optics law and the optical Fresnel transformation,and obeys group product rules.In other words,we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space,which seems to be a combination of quantum statistics and quantum optics.

Quantum optical ABCD theorem in two-mode case

By introducing the entangled Fresnel operator （EFO） this paper demonstrates that there exists ABCD theorem for two-mode entangled case in quantum optics. The canonical operator method as mapping of ray-transfer ABCD matrix is explicitly shown by EFO＇s normally ordered expansion through the coherent state representation and the technique of integration within an ordered product of operators.

Quantum Group Signature Scheme Based on Chinese Remainder Theorem

A novel quantum group signature scheme is proposed based on Chinese Remainder Theorem (CRT), in order to improve the security of quantum signature. The generation and verification of the signature can be successfully conducted only if all the participants cooperate with each other and with the message owner's and the arbitrator's help. The quantum parallel algorithm is applied to efficiently compare the restored quantum message to the original quantum message. All the operations in signing and verifying phase can be executed in quantum circuits. It has a wide application to E-payment system, Online contract, Online notarization and etc.

The Harmonic Potential Theorem for a Quantum System with Time-Dependent Effective Mass

We investigate the many-body wave function of a quantum system with time-dependent effective mass, confined by a harmonic potential with time-dependent frequency, and perturbed by a time-dependent spatially homogeneous electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schr6dinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the harmonic potential theorem wave function when both the effective mass and frequency are static. An example of application is also given.

Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View

In this paper, we study and answer the following fundamental problems concerning classical equilibrium statistical mechanics: 1): Is the principle of equal a priori probabilities indispensable for equilibrium statistical mechanics? 2): Is the ergodic hypothesis related to equilibrium statistical mechanics? Note that these problems are not yet answered, since there are several opinions for the formulation of equilibrium statistical mechanics. In order to answer the above questions, we first introduce measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics. And we propose the measurement theoretical foundation of equili-brium statistical mechanics, and further, answer the above 1) and 2), that is, 1) is “No”, but, 2) is “Yes”.

A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy

We introduce an ultra high energy combined KAM-Rindler fractal spacetime quantum manifold, which increasingly resembles Einstein’s smooth relativity spacetime, with decreasing energy. That way we derive an effective quantum gravity energy-mass relation and compute a dark energy density in complete agreement with all cosmological measurements, specifically WMAP and type 1a supernova. In particular we find that ordinary measurable energy density is given by E1= mc2 /22 while the dark energy density of the vacuum is given by E2 = mc2 (21/22). The sum of both energies is equal to Einstein’s energy E = mc2. We conclude that E= mc2 makes no distinction between ordinary energy and dark energy. More generally we conclude that the geometry and topology of quantum entanglement create our classical spacetime and glue it together and conversely quantum entanglement is the logical consequence of KAM theorem and zero measure topology of quantum spacetime. Furthermore we show via our version of a Rindler hyperbolic spacetime that Hawking negative vacuum energy, Unruh temperature and dark energy are different sides of the same medal.

Resonant tunneling and quantum fluctuation in a driven triple-well system

The influence of parameters such as the strength and frequency of a periodic driving force on the tunneling dynamics is investigated in a symmetric triple-well potential. It is shown that for some special values of the parameters, tunneling could be enhanced considerably or suppressed completely. Quantum fluctuation during the tunneling is discussed as well and the numerical results are presented and analysed by virtue of Floquet formalism.

Averaging in SU(2) open quantum random walk

We study the average position and the symmetry of the distribution in the SU（2） open quantum random walk （OQRW）. We show that the average position in the central limit theorem （CLT） is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.

An Effective Formulation on Quantum Hadrodynamics at Finite Temperatures and Densities

According to Wick＇s theorem, the second order self-energy corrections of hadrons in the hot and dense nuclear matter are calculated. Furthermore, the Feynman rules are summarized, and an effective formulation on quantum hadrodynamics at finite temperatures and densities is evauated. As the strong couplings between nucleons are considered, the self-consistency of this method is discussed in the framework of relativistic mean-field approximation. Debye screening masses of the scalar and vector mesons in the hot and dense nuclear matter are calculated with this method in the relativistic mean-field approximation. The results are different from those of thermofield dynamics and Brown-Rho conjecture. Moreover, the effective masses of the photon and the nucleon in the hot and dense nuclear matter are discussed.

Simplified Protocol of Quantum Teleportation

A simplified version of the quantum teleportation protocol is presented in here. Its experimental confirmation will have deep implications for a better understanding of Quantum Entanglement with a particular projection on Quantum Communications.

On the Security of Quantum Key Distribution Ping-Pong Protocol

Computational based cryptography might not guarantee long term security if computational algorithms, computers, and so on are made remarkable progress. Therefore, quantum cryptography with unconditionally security attracts attention. In this paper, we consider security of a two-way quantum key distribution protocol, so called Ping-Pong protocol. As a result, we introduce not only robustness but also a different information disturbance theorem, which denotes a trade-off relationship between information gain for an eavesdropper and error rate, from the related works for an attack model.

The Hydrogen Atom Fractal Spectra, the Missing Dark Energy of the Cosmos and Their Hardy Quantum Entanglement

In this letter, I outline the intimate connection between the fractal spectra of the exact solution of the hydrogen atom and the issue of the missing dark energy of the cosmos. A proposal for a dark energy reactor harnessing the dark energy of the Schrodinger wave via a quantum wave nondemolition measurement is also presented.

PROBABILISTIC CLONE-RESEND ATTACK STRATEGY IN QUANTUM KEY DISTRIBUTION

A kind of attack strategy based on a probabilistic cloning machine is proposed in this letter. The security of BB84 and the six-state quantum key distribution protocols under this attack is studied by theoretic analyses and corroborated by simulations. It is concluded that the quantum key distribution protocols still have an asymptotic perfect security even if the eavesdropper adopts the proposed attack strategy.

A New Interpretation of Quantum Mechanics

The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not necessarily desirable. Thus, we propose a new interpretation of measurement theory, which is the linguistic aspect (or, the mathematical generalization) of quantum mechanics. Although this interpretation is superficially similar to a part of so-called Copenhagen interpretation, we show that it has a merit to be applicable to both quantum and classical systems. For example, we say that Bell’s inequality is broken even in classical systems.

Application of Dvoretzky’s Theorem of Measure Concentration in Physics and Cosmology

Using Dvoretzky’s theorem in conjunction with Bohm’s picture of a quantum particle inside a guiding quantum wave akin to De Broglie-Bohm pilot wave we derive Einstein’s famous formula E = mc2 as the sum of two parts E(O) = mc2/22 of the quantum particle and E(D) = m c2 (21/22) of the quantum wave where m is the mass, c is the speed of light and E is the energy. In addition we look at the problem of black holes information in the presence of extra dimensions where it seems initially that extra dimensions would logically lead to a hyper-surface for a black hole and consequently a reduction of the corresponding information density due to the dilution effect of these additional dimensions. The present paper argues that the counterintuitive opposite of the above is what should be expected. Again this surprising result is a consequence of the same well known theorem on measure concentration due to I. Dvoretzky. We conclude that there are only two real applications of the theorem and we expect that many more applications in physics and cosmology will be found in due course.

Testing Bell’s Theorem with Circular Polarization

Bell tests with entangled light have been performed many times in many ways using linear polarizers, but the same tests have never been done with a circular polarizer. Until recently there has never been a true circular polarization beamsplitter—an optical component that separates light directly into left and right handed polarizations. Using a true circular polarization beamsplitter based on birefringent gratings, entangled light has been analyzed with unexpected results.