Allowable Generalized Quantum Gates Using Nonlinear Quantum Optics

In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross- Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.     

广义量子干涉原理及对偶量子计算机

我们综述最近提出的广义量子干涉原理及其在量子计算中的应用。广义量子干涉原理是对狄拉克单光子干涉原理的具体化和多光子推广,不但对像原子这样的紧致的量子力学体系适用,而且适用于几个独立的光子这样的松散量子体系。利用广义量子干涉原理,许多引起争议的问题都可以得到合理的解释,例如两个以上的单光子的干涉等问题。从广义量子干涉原理来看双光子或者多光子的干涉就是双光子和双光子自身的干涉,多光子和多光子自身的干涉。广义量子干涉原理可以利用多组分量子力学体系的广义Feynman积分表示,可以定量地计算。基于这个原理我们提出了一种新的计算机,波粒二象计算机,又称为对偶计算机。在原理上对偶计算机超越了经典的计算机和现有的量子计算机。在对偶计算机中,计算机的波函数被分成若干个子波并使其通过不同的路径,在这些路径上进行不同的量子计算门操作,而后这些子波重新合并产生干涉从而给出计算结果。除了量子计算机具有的量子平行性外,对偶计算机还具有对偶平行性。形象地说,对偶计算机是一台通过多狭缝的运动着的量子计算机,在不同的狭缝进行不同的量子操作,实现对偶平行性。目前已经建立起严格的对偶量子计算机的数学理论,为今后的进一步发展打下了基础。本文着重从物理的角度去综述广义量子干涉原理和对偶计算机。现在的研究已经证明,一台d狭缝的n比特的对偶计算机等同与一个n比特+一个d比特(qudit)的普通量子计算机,证明了对偶计算机具有比量子计算机更强大的能力。这样,我们可以使用一台具有n+log2d个比特的普通量子计算机去模拟一个d狭缝的n比特对偶计算机,省去了研制运动量子计算机的巨大的技术上的障碍。我们把这种量子计算机的运行模式称为对偶计算模式,或简称为对偶模式。利用这一联系反过来可以帮助我们理解广义量子干涉原理,因为在量子计算机中一切计算都是普通的量子力学所允许的量子操作,因此广义量子干涉原理就是普通的量子力学体系所允许的原理,而这个原理只是是在多体量子力学体系中才会表现出来。对偶计算机是一种新式的计算机,里面有许多问题期待研究和发展,同时也充满了机会。在对偶计算机中,除了幺正操作外,还可以允许非幺正操作,几乎包括我们可以想到的任何操作,我们称之为对偶门操作或者广义量子门操作。目前这已经引起了数学家的注意,并给出了广义量子门操作的一些数学性质。此外,利用量子计算机和对偶计算机的联系,可以将许多经典计算机的算法移植到量子计算机中,经过改造成为量子算法。由于对偶计算机中的演化是非幺正的,对偶量子计算机将可能在开放量子力学的体系的研究中起到重要的作用。     

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.     

Allowable Generalized Quantum Gates

In this paper, we give the most general duality gates, or generalized quantum gates in duality quantum computers. Here we show by explicit construction that a n-bit duality quantum computer with d slits can be simulated perfectly with an ordinary quantum computer with n qubits and one auxiliary qudit. Using this model, we give the most general form of duality gates which is of the form ∑i=0^d-1piUi,and the pi ＇s are complex numbers with module less or equal to 1 and constrained by｜∑iPi｜≤1.     

General Quantum Interference Principle and Duality Computer

In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself. A quantum system considered here can be any quantum system: a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented: the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.     

Prime Factorization in the Duality Computer

We give algorithms to factorize large integers in the duality computer.We provide three duality algorithms for factorization based on a naive factorization method,the Shor algorithm in quantum computing,and the Fermat's method in classical computing.All these algorithms may be polynomial in the input size.     

广义量子干涉原理及对偶量子计算机

我们综述最近提出的广义量子干涉原理及其在量子计算中的应用.广义量子干涉原理是对狄拉克单光子干涉原理的具体化和多光子推广,不但对像原子这样的紧致的量子力学体系适用,而且适用于几个独立的光子这样的松散量子体系.利用广义量子干涉原理,许多引起争议的问题都可以得到合理的解释,例如两个以上的单光子的干涉等问题.从广义量子干涉原理来看双光子或者多光子的干涉就是双光子和双光子自身的干涉,多光子和多光子自身的干涉.广义量子干涉原理可以利用多组分量子力学体系的广义Feynman积分表示,可以定量地计算.基于这个原理我们提出了一种新的计算机,波粒二象计算机,又称为对偶计算机.在原理上对偶计算机超越了经典的计算机和现有的量子计算机.在对偶计算机中,计算机的波函数被分成若干个子波并使其通过不同的路径,在这些路径上进行不同的量子计算门操作,而后这些子波重新合并产生干涉从而给出计算结果.除了量子计算机具有的量子平行性外,对偶计算机还具有对偶平行性.形象地说,对偶计算机是一台通过多狭缝的运动着的量子计算机,在不同的狭缝进行不同的量子操作,实现对偶平行性.目前已经建立起严格的对偶量子计算机的数学理论,为今后的进一步发展打下了基础.本文着重从物理的角度去综述广义量子干涉原理和对偶计算机.现在的研究已经证明,一台d狭缝的n比特的对偶计算机等同与一个n比特+一个d比特(qudit)的普通量子计算机,证明了对偶计算机具有比量子计算机更强大的能力.这样,我们可以使用一台具有n+log<,2>d个比特的普通量子计算机去模拟一个d狭缝的n比特对偶计算机,省去了研制运动量子计算机的巨大的技术上的障碍.我们把这种量子计算机的运行模式称为对偶计算模式,或简称为对偶模式.利用这一联系反过来可以帮助我们理解广义量子干涉原理,因为在量子计算机中一切计算都是普通的量子力学所允许的量子操作,因此广义量子干涉原理就是普通的量子力学体系所允许的原理,而这个原理只是是在多体量子力学体系中才会表现出来.对偶计算机是一种新式的计算机,里面有许多问题期待研究和发展,同时也充满了机会.在对偶计算机中,除了幺正操作外.还可以允许非幺正操作,几乎包括我们可以想到的任何操作,我们称之为对偶门操作或者广义量子门操作.目前这已经引起了数学家的注意,并给出了广义量子门操作的一些数学性质.此外,利用量子计算机和对偶计算机的联系,可以将许多经典计算机的算法移植到量子计算机中,经过改造成为量子算法.由于对偶计算机中的演化是非幺正的,对偶量子计算机将可能在开放量子力学的体系的研究中起到重要的作用.     

Study on Duality of Wave and Particle of Turbulence Using CML Models

A family of coupled map lattice （CML） models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.     

Elementary analysis of interferometers for wave-particle duality test and the prospect of going beyond the complementarity principle

A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young＇s two-slit interferometer and the Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern （wave nature） and the which-way information （particle nature） of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave-particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.     

The duality of a single particle with an n-dimensional internal degree of freedom

The wave-particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theo- retically in a Mach-Zehnder interferometer. The famous duality relation D2 ＋ V2 〈 1 is always valid in this situation, where D is the distinguishability and V is the visibility. However, the sum of the particle information and the wave information, D2 V2, can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity D2~ V2 is always equal to one when the internal degree of freedom of the particle is excluded.     

Holographic Insulator/Superconductor Phase Transition in Born–Infeld Electrodynamics

We study holographic insulator/superconductor phase transition in the framework of Born–Infeld electrodynamics both numerically and analytically. First we numerically study the efects of the Born–Infeld electrodynamics on the phase transition, find that when the Born–Infeld parameter increases, the critical chemical potential keeps invariant but the gap frequency becomes larger. Then we employ the variational method for the Sturm–Liouville eigenvalue problem to study the phase transition analytically. The analytical results obtained are found to be consistent with the numerical results.     

Necessary and Sufficient Conditions of Separability for Multipartite Pure States

In this paper we present a necessary and sufficient condition of separability for multipartite pure states and variants of it. These conditions are very simple and calculable, and they do not require Schmidt decomposition （for two subsystems） or tracing out operations. We also give a necessary condition for a local unitary equivalence class for a bipartite system in terms of the determinant of the matrix of amplitudes.     

Coalescence between Cu57 and Cu5s clusters at a room temperature： molecular dynamics simulations

Three coalescence processes of Cu57-Cu57, Cu57-Cu58, and Cu5s Cu58 clusters at 300 K are investigated by employing molecular dynamics simulations. According to the evolutions of mean square displacement and local atom packing, the coalescence process can be separated into three stages including an approaching stage, a coalescing stage, and a coalesced stage. The simulations show that the coalescence processes and the formed products are sensitive to the respective initial structures of, and the relative configuration between, the two coalescing icosahedron-based clusters.     

An Extension of Algorithm on Symbolic Computations of Conserved Densities for High-Dimensional Nonlinear Systems

An improved algorithm for symbolic computations of polynomial-type conservation laws （PCLaws） of a general polynomial nonlinear system is presented. The algorithm is implemented in Maple and can be successfully used for high-dimensional models. Furthermore, the algorithm discards the restriction to evolution equations. The program can also be used to determine the preferences for a given parameterized nonlinear systems. The code is tested on several known nonlinear equations from the soliton theory.     

An Efficient Scheme for Multiparty Multi-particle State Sharing

We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n- 1 auxiliary particles in the initial state ｜0）, applies Hadamard （H） gate and Controlled-Not （CNOT） gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers （i.e., other n - 1 agents）, where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.     

Multiformity of Optical Quantum Coherence Systems with Y and Inverted Y-type Schemes

Y and inverted Y-type four-level schemes for optical quantum coherence systems, which may be intuitively considered to be very simple, have not been studied intensively till now. In this paper, we present the multiformity of these two types of schemes by considering that they can be classified into nine possible level styles as the second-order sub-schemes using laser fields. Further we point out the complexity of their more than one hundred realistic configurations as the third-order four-level sub-schemes that may appear in the optical quantum coherence experiments. Throughout this paper we review which configurations have been studied in some research aspects and which ones not, according to our knowledge, in order to be propitious to next steps of theoretical and experimental investigations, especially for applications in the fields of quantum optics, quantum information science, laser spectroscopy, and so on.     

An indirect approach for quantum-mechanical eigenproblems: duality transforms

We suggest an indirect approach for solving eigenproblems in quantum mechanics. Unlike the usual method, this method is not a technique for solving differential equations. There exists a duality among potentials in quantum mechanics. The first example is the Newton–Hooke duality revealed by Newton in Principia. Potentials that are dual to each other form a duality family consisting of infinite numbers of family members. If one potential in a duality family is solved, the solutions of all other potentials in the family can be obtained by duality transforms. Instead of directly solving the eigenequation of a given potential, we turn to solve one of its dual potentials which is easier to solve. The solution of the given potential can then be obtained from the solution of this dual potential by a duality transform. The approach is as follows: first to construct the duality family of the given potential, then to find a dual potential which is easier to solve in the family and solve it, and finally to obtain the solution of the given potential by the duality transform. In this paper, as examples, we solve exact solutions for general polynomial potentials.     

Entropy of Quantum Dynamical Systems and Sufficient Families in Orthomodular Lattices with Bayessian State

The purpose of the present paper is to study the entropy hs（Ф） of a quantum dynamical systems Ф = （ L, s, Ф）, where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs（ Ф, A） of partition A of a Boolean algebra B with respect to a state s and a state preserving homomorphism Ф, we prove a few results on that, define the entropy of a dynamical system hs（Ф）, and show its invariance. The concept of sufficient families is also given and we establish that hs （Ф） comes out to be equal to the supremum of hs （Ф,A）, where A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system （ L, s, Ф）, which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system （B, s0, Ф）, where B is a Boolean algebra and so is a state on B.