Unidirectional acoustic metamaterials based on nonadiabatic holonomic quantum transformations

Nonadiabatic holonomic quantum transformations(NHQTs)have attracted wide attention and have been applied in many aspects of quantum computation,whereas related research is usually limited to the field of quantum physics.Here we bring NHQTs into constructing a unidirectional acoustic metamaterial(UDAM)for shaping classical beams.The UDAM is made up of an array of three-waveguide couplers,where the propagation of acoustic waves mimics the evolution of NHQTs.The excellent agreement among analytical predictions,numerical simulations,and experimental measurements confirms the great applicability of NHQTs in acoustic metamaterial engineering.The present work extends research on NHQTs from quantum physics to the field of classical waves for designing metamaterials with simple structures and may pave a new way to design UDAMs that would be of potential applications in acoustic isolation,communication,and stealth.

Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Classical and Quantum Behavior of Generalized Oscillators in Terms of Linear Canonical Transformations

The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.

Realization of quantum Fourier transform over Z_N

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.

Quantum-Classical Algorithm for an Instantaneous Spectral Analysis of Signals:A Complement to Fourier Theory

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

Applications of quantum Fourier transform in photon-added coherent state

Quantum Fourier transform is realized by the Hadamard gate in a quantum computer, which can also be considered as a Hadamard transform. We introduce the Hadamard transformed photon-added coherent state （HTPACS）, which is obtained by letting the photon-added coherent state （PACS） across the quantum Hadamard gate, from this result. It is found that the HTPACS can be considered as a coordinate-momentum mutual exchanging followed by a squeezing transform of the PACS. In addition, the non-classical statistical properties of HTPACS, such as squeezing coefficient, Mandel parameter, etc., are also discussed.

New 3-mode bosonic operator realization of SU(2) Lie algebra:From the point of view of squeezing

We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.

Three-dimensional quantum wavelet transforms

Wavelet transform is being widely used in the field of information processing.One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms.However,three-dimensional quantum wavelet transforms have not been reported.This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos.Then,we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms,respectively.Next,we design quantum circuits of the two wavelet transforms using iterative methods.Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts.Finally,the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application.Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.

Quantum secret sharing between multiparty and multiparty with entanglement swapping

A quantum secret sharing （QSS） protocol between multiparty and multiparty is proposed, based on Greenberger-Horne- Zeilinger （GHZ） state. The protocol utilizes quantum Fourier transform and entanglement swapping to achieve a high intrinsic efficiency and source capacity. Then, the security of this protocol against some possible eavesdropping strategies has been analyzed. Furthermore, the presented protocol is generalized to the d-level case.

A New Quantum Watermarking Based on Quantum Wavelet Transforms

Quantum watermarking is a technique to embed specific information, usually the owner's identification,into quantum cover data such for copyright protection purposes. In this paper, a new scheme for quantum watermarking based on quantum wavelet transforms is proposed which includes scrambling, embedding and extracting procedures. The invisibility and robustness performances of the proposed watermarking method is confirmed by simulation technique.The invisibility of the scheme is examined by the peak-signal-to-noise ratio(PSNR) and the histogram calculation.Furthermore the robustness of the scheme is analyzed by the Bit Error Rate(BER) and the Correlation Two-Dimensional(Corr 2-D) calculation. The simulation results indicate that the proposed watermarking scheme indicate not only acceptable visual quality but also a good resistance against different types of attack.