Orthonormal Basis States Research Articles

Quantum Multi-Image Encryption Based on Iteration Arnold Transform with Parameters and Image Correlation Decomposition

A novel quantum multi-image encryption algorithm based on iteration Arnold transform with parameters and image correlation decomposition is proposed, and a quantum realization of the iteration Arnold transform with parameters is designed. The corresponding low frequency images are obtained by performing 2-D discrete wavelet transform on each image respectively, and then the corresponding low frequency images are spliced randomly to one image. The new image is scrambled by the iteration Arnold transform with parameters, and the gray-level information of the scrambled image is encoded by quantum image correlation decomposition. For the encryption algorithm, the keys are iterative times, added parameters, classical binary and orthonormal basis states. The key space, the security and the computational complexity are analyzed, and all of the analyses show that the proposed encryption algorithm could encrypt multiple images simultaneously with lower computational complexity compared with its classical counterparts.

Entangled bases with fixed Schmidt number

An entangled basis with a fixed Schmidt number k (EBk) is a set of orthonormal basis states with the same Schmidt number k in a product Hilbert space . It is a generalization of both the product basis and the maximally entangled basis. We show here that for any , EBk exists in for any d and d′. Consequently, general methods of constructing SEBk (EBk with the same Schmidt coefficients) and EBk (but not SEBk) are proposed. Moreover, we extend the concept of EBk to multipartite cases and find out that the multipartite EBk can be constructed similarly.

Quantum Image Encryption Algorithm Based on Image Correlation Decomposition

A novel quantum gray-level image encryption and decryption algorithm based on image correlation decomposition is proposed. The correlation among image pixels is established by utilizing the superposition and measurement principle of quantum states. And a whole quantum image is divided into a series of sub-images. These sub-images are stored into a complete binary tree array constructed previously and then randomly performed by one of the operations of quantum random-phase gate, quantum revolving gate and Hadamard transform. The encrypted image can be obtained by superimposing the resulting sub-images with the superposition principle of quantum states. For the encryption algorithm, the keys are the parameters of random phase gate, rotation angle, binary sequence and orthonormal basis states. The security and the computational complexity of the proposed algorithm are analyzed. The proposed encryption algorithm can resist brute force attack due to its very large key space and has lower computational complexity than its classical counterparts.

Schemes to generate and distinguish a type of genuine four-qubit entangled states in a cavity QED system

We propose a scheme to generate a type of genuine four-qubit entangled states, which were firstly introduced by Yeo et al. [Y. Yeo, W. K. Chua, Phys. Rev. Lett. 96 (2006) 060502]. These states have many interesting entanglement properties and possess possible applications in quantum information processing and in fundamental tests of quantum physics. We show that such a type of 16 orthonormal basis states can be deterministically distinguished by a cavity QED system.

Quantal computation of tonality in music

Each independent scale interval structure with N semitones and M notes contains a multiplet of N scales (for example, the major scale has the interval structure 2212221; and its twelve multiplet members are: C‐major, D flat‐major,..., B‐major scales). Operators that step through these multiplet members (by sharping or flatting the notes of the multiplet members) are identical with those of N‐level finite state quantum mechanics. It is possible to construct orthonormal basis states which represent the multiplet members of a given interval structure. A musical score can then be expressed as a mixture of various tonalities, using the density matrix formalism of quantum mechanics. Several examples help illustrate this quantitative approach.

A New Formulation of a Many-Level Shell Model: A Method of Constructing Orthonormal Basis States Analytically

We propose an analytic representation of completely antisymmetric basis states and the Hamiltonian matrix in a many-level shell model.

Generalized Coherent States and Phase-Space-Interface in Multi-Mode Systems

The Hilbert space of a single mode quantum system is spanned by a countable set of orthonormal basis states denoted |n〉 for n = 0, 1, 2, … Such a basis can be used to define quasi-probability distributions over a two-dimensional quantum phase plane. Multi-mode quantum systems are spanned by orthonormal product states |n1,…nk〉 = |n1〉 ⊗ … ⊗ |nk〉 which can be used to define quasiprobability distributions over a 2k-dimensional phase volume. However, this multi-mode basis set is also countable and can be uniquely specified by a single integer label. This labeling allows us to define new collective operators and generalized coherent states to construct probability distributions over a new two-dimensional phase plane. These distributions represent the system's 2k-dimensional phase volume with perfect fidelity, and allow us to apply phase space interference (PSI) approaches to multi-mode quantum systems.

An approximate analytical treatment of the T⊗(ε⊕τ2) Jahn-Teller effect

The octahedral Jahn-Teller system T(X)( epsilon g(+) tau 2g) is considered, in which the epsilon g and tau 2g modes correspond to the same frequency and are equally coupled to the electronic state T. A correspondence is drawn between the energy matrix for the J=1 states of this system and the energy matrix for the m=0 states of a three-dimensional harmonic oscillator displaced along the z axis. It is shown that the two sets of matrix elements become asymptotically proportional to each other as one proceeds towards the far interior of each infinite matrix. This permits a perturbation procedure to be set up for the Jahn-Teller system. Orthonormal basis states are established and a number of relations involving Laguerre polynomials are exploited to calculate to first order the energies of the J=1 levels, the Ham reduction factors and the intensities for the vibronic structure of the transition s to p. Analytic expressions are obtained for these quantities as a function of the coupling strength, and good agreement is obtained with the numerical calculations that are available at present.