International Journal of Quantum Information

To explore the multi-directional quantum communication in a three-dimensional (3D) system, 13- and $(2n+1)$-qutrit entangled states are constructed by 3D Hadamard gates and 3D controlled NOT gates in this paper. Then we propose a novel theoretical scheme to fulfill four-party double-direction cyclic controlled quantum teleportation (QT) by using a 13-qutrit entangled state as the quantum channel. In this scheme, each observer can teleport two different arbitrary unknown single-qutrit states to the other two observers under the control of the supervisor, respectively and synchronously, which realizes cyclic controlled QT in both clockwise and counterclockwise directions simultaneously. Each observer performs two 3D Bell basis measurements and the supervisor carries out a single-qutrit measurement in the 3D $Z$-basis. After hearing the measurement results from the other two observers and the supervisor, each observer can restore the target states by utilizing suitable 3D Weyl operators. Based on the $(4n+1)$-qutrit entangled channel that we construct, we exhibit in detail how to extend the presented four-party double-direction cyclic controlled QT scheme to the situation with $n$ ($n>3$) observers. Analysis shows that the success probability of both the proposed four-party and $(n+1)$-party schemes can reach 1, and these two schemes are expected to be realized experimentally in the near future. Through detailed discussion, we find that the security of our schemes and the control power of the supervisor can be guaranteed, and the intrinsic efficiency of the proposed schemes is relatively high.

A new transistor-less field-coupled nanocomputing (FCN) method for ultra-scale “nanochip” integration is called quantum-dot cellular automata (QCA). Electrostatic repulsion between electrons and the electron tunneling process in quantum dots is employed in QCA to depict digital circuitry. QCA technology is able to achieve higher clock speed, lower occupied chip area, and more energy efficiency than traditional complementary metal-oxide semiconductor (CMOS) technology. Irreversible majority gates are commonly utilized as the main building blocks in the development of QCA circuits. In order to create highly energy-efficient QCA circuits, some research has recently presented digital image processing design strategies that use majority gates as the primary building block. Image processing, which encompasses picture analysis, enhancement, and correction, is used to extract information from images and improve their quality. Among the primary methods for processing images are picture enhancement, restoration, compression, object recognition, and machine vision applications. However, morphological procedures such as dilation and erosion constitute the fundamental component of image processing and are widely applied in practical applications. In this study, QCA-optimized nanostructures are presented for applications in mathematical morphology, serving as erosion and dilation operators. The completed circuit comprises 33 cells and exhibits a temporal delay of approximately 0.75 during each clock cycle. A comparison with the best equivalent nano-architecture demonstrates a significant improvement in cell performance, scalability, and latency.

Quantum secret sharing (QSS) is a fundamental primitive in quantum cryptography. The existing QSS protocols are either $(n,n)$-threshold or $(t,n)$-threshold access structure, where $n$ denotes the number of players and $t$ denotes the threshold number of players. Here, we introduce a novel verifiable QSS scheme that executes a restricted hyperstar access structure by using entangled states. Our method involves encoding selected quantum states and their corresponding measurements to yield outcomes of either $+1$ or $-1$. Furthermore, we give the validation of the scheme through the system of equations derived from the measurements, which then guarantees the honesty of the participants. At last, we also analyze the security of our scheme in two primary quantum attacks, such as external attacks and internal attacks.

Considerable evidence supports the existence of many-body localization (MBL) phase transitions, although accurately determining the critical disorder intensity remains challenging due to significant instabilities in system size within the examined parameters. In this study, we employ the global quantum discord (GQD) to investigate MBL phase transitions and identify the critical points of the quantum Ising spin chain subjected to both disordered interacting and disordered external fields. Our analysis of GQD demonstrates its effectiveness in identifying the critical points between the thermal and the MBL phases. We further utilize the temporal evolution of GQD to comprehensively explore the characteristics of MBL phase transitions in the disordered quantum Ising spin chain. Our findings suggest that MBL phase transitions adhere to the same generality category based on the scaling analysis. Additionally, we investigate the effects of these examined parameters on the GQD and its dynamics and use them to estimate the critical points.

In this paper, we present a new and algebraically simple algorithm that prepares any pure three-qubit state using only local gates and at most three controlled-$Z$ gates. In 2008, Znidaric et al. already showed that three is the optimal number of controlled-$Z$ gates required for the preparation of three-qubit states if in addition to those gates only local gates are used. If we restrict the local gates to $R_y(𝜃)$ gates, our algorithm provides a way to prepare any pure three-qubit state $|\varphi 〉$ with real amplitudes using at most four controlled-$Z$ gates when its hyperdeterminant is negative and three or fewer controlled-$Z$ gates otherwise. We conjecture the existence of three-qubit states with real amplitudes that cannot be prepared using only $R_y(𝜃)$ gates and less than four controlled-$Z$ gates.

This paper investigates the regularity properties of quantum master equations with unbounded coefficients within the space of square-integrable complex-valued Bernoulli functionals. Initially, we demonstrate the existence of a unique regular solution to the linear stochastic Schrödinger equation driven by cylindrical Brownian motions. Subsequently, we establish the existence of regular solutions for the autonomous linear quantum master equation and provide a probabilistic representation of this solution in terms of the stochastic Schrödinger equation. Finally, by taking the expectation of some observables with respect to the solution of the quantum master equation, we derive a system of differential equations that describe the evolution of the mean values of certain quantum observables.