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Authors:V. S. Indrajith, R. Muthuganesan, R. Sankaranarayanan Abstract: International Journal of Quantum Information, Ahead of Print. Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this paper, we propose fidelity-based valid measure of purity and coherence monotone, and establish a relationship between them. This formulation of coherence is extended to quantum correlation relative to measurement. It is shown that under the measurement process, purity decreases and reaches a saturation. Citation: International Journal of Quantum Information PubDate: 2022-06-23T07:00:00Z DOI: 10.1142/S0219749922500162
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Authors:Qi Han, Yaxin Kou, Ning Bai, Huan Wang Abstract: International Journal of Quantum Information, Ahead of Print. In this paper, continuous-time quantum walk is discussed based on the view of quantum probability, i.e. the quantum decomposition of the adjacency matrix A of graph. Regard adjacency matrix A as Hamiltonian which is a real symmetric matrix with elements 0 or 1, so we regard [math] as an unbiased evolution operator, which is related to the calculation of probability amplitude. Combining the quantum decomposition and spectral distribution [math] of adjacency matrix A, we calculate the probability amplitude reaching each stratum in continuous-time quantum walk on complete bipartite graphs, finite two-dimensional lattices, binary tree, [math]-ary tree and [math]-fold star power [math]. Of course, this method is also suitable for studying some other graphs, such as growing graphs, hypercube graphs and so on, in addition, the applicability of this method is also explained. Citation: International Journal of Quantum Information PubDate: 2022-05-28T07:00:00Z DOI: 10.1142/S0219749922500150
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Authors:Cheng-Yang Zhang, Pu Wang, Li-Hua Bai, Zhi-Hua Guo, Huai-Xin Cao Abstract: International Journal of Quantum Information, Ahead of Print. Quantum coherence is one of the most fundamental and striking features in quantum physics. Considered the standard coherence (SC), the partial coherence (PC) and the block coherence (BC) as variance of quantum states under some quantum channels (QCs) [math], we propose the concept of channel-based coherence of quantum states, called [math]-coherence for short, which contains the SC, PC and BC, but does not contain the positive operator-valued measure (POVM)-based coherence. By our definition, a state [math] is said to be [math]-incoherent if it is a fixed point of a QC [math], otherwise, it is said to be [math]-coherent. First, we find the set [math] of all [math]-incoherent states for some given channels [math] and prove that the set [math] forms a nonempty compact convex set for any channel [math]. Second, we define [math]-incoherent operations ([math]-IOs) and prove that the set of all [math]-IOs is a nonempty convex set. We also establish some characterizations of a [math]-IO in terms of its Kraus operators. Lastly, we discuss the problem of quantifying [math]-coherence and prove some related properties. Citation: International Journal of Quantum Information PubDate: 2022-05-27T07:00:00Z DOI: 10.1142/S0219749922500149
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Authors:Chusei Kiumi Abstract: International Journal of Quantum Information, Ahead of Print. There is a property called localization, which is essential for applications of quantum walks. From a mathematical point of view, the occurrence of localization is known to be equivalent to the existence of eigenvalues of the time evolution operators, which are defined by coin matrices. A previous study proposed an approach to the eigenvalue problem for space-inhomogeneous models using transfer matrices. However, the approach was restricted to models whose coin matrices are the same in positions sufficiently far to the left and right, respectively. This study shows that the method can be applied to extended models with periodically arranged coin matrices. Moreover, we investigate localization by performing the eigenvalue analysis and deriving their time-averaged limit distribution. Citation: International Journal of Quantum Information PubDate: 2022-05-21T07:00:00Z DOI: 10.1142/S0219749922500137
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Authors:Georgios D. Varsamis, Ioannis G. Karafyllidis Abstract: International Journal of Quantum Information, Ahead of Print. Finding or estimating the lowest eigenstate of quantum system Hamiltonians is an important problem for quantum computing, quantum physics, quantum chemistry, and material science. Several quantum computing approaches have been developed to address this problem. The most frequently used method is variational quantum eigensolver (VQE). Many quantum systems, and especially nanomaterials, are described using tight-binding Hamiltonians, but until now no quantum computation method has been developed to find the lowest eigenvalue of these specific, but very important, Hamiltonians. We address the problem of finding the lowest eigenstate of tight-binding Hamiltonians using quantum walks. Quantum walks is a universal model of quantum computation equivalent to the quantum gate model. Furthermore, quantum walks can be mapped to quantum circuits comprising qubits, quantum registers, and quantum gates and, consequently, executed on quantum computers. In our approach, probability distributions, derived from wave function probability amplitudes, enter our quantum algorithm as potential distributions in the space where the quantum walk evolves. Our results showed the quantum walker localization in the case of the lowest eigenvalue is distinctive and characteristic of this state. Our approach will be a valuable computation tool for studying quantum systems described by tight-binding Hamiltonians. Citation: International Journal of Quantum Information PubDate: 2022-04-25T07:00:00Z DOI: 10.1142/S0219749922500125
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Authors:Y. Ben-Aryeh, A. Mann Abstract: International Journal of Quantum Information, Ahead of Print. Using the Hilbert–Schmidt (HS) decomposition we suggest new possible choices of Bell operators and entanglement witnesses (EWs) for [math] ([math]) qubits systems for (full/bi) separability. The latter give upper bounds for (full/bi) separability. Also using the HS decomposition, we find explicitly (full/bi) separable forms for some qubits states which give lower bounds for (full/bi) separability. When the lower bounds and upper bounds coincide it means that the EW is optimal. In the case of full separability, the positive transpose method can sometimes give optimal results. As concrete examples, we give results for the GHZ(3), [math] and cluster [math] states. Citation: International Journal of Quantum Information PubDate: 2022-04-11T07:00:00Z DOI: 10.1142/S0219749922500113
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Authors:Xue-Ting Feng, Jun-Yang Song, Chuan Wang Abstract: International Journal of Quantum Information, Ahead of Print. The concept of quantum secure direct communication (QSDC) is to distribute secure message directly between distant users securely, which is an important branch of quantum information science. The purpose of QSDC is to investigate the large capacity of quantum channels and fast speed of information transmission. However, the fidelity of qubits and the efficiency of QSDC will inevitably be affected by the channel noise and the decoherence of the quantum system. In this work, we focus on the performance of QSDC under different noisy channels, and investigate the evolution of quantum states. By numerically studying the performance for two QSDC protocols, we show the efficiency of information transmission over different noisy channel models. Citation: International Journal of Quantum Information PubDate: 2022-04-09T07:00:00Z DOI: 10.1142/S0219749922500101
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Authors:Antonín Hoskovec, Igor Jex Abstract: International Journal of Quantum Information, Ahead of Print. Perfect State Transfer is known to be possible on complex next-to-nearest-neighbor structures of qubits. The complexity of these networks coupled with the pervasive imperfections of the real world can lead to shortcomings in their practical construction. We analyze several realistic categories of flaws in the networks and show that they can have a harsh effect on the network’s performance. Dynamical decoupling is a known quantum error correction algorithm that can be used for partial or complete mitigation of undesired artefacts in quantum systems. We show here that dynamical decoupling can, in principle, also be used to stabilize the complex next-to-nearest-neighbor networks of qubits. We compare the proposed dynamical decoupling schemes with a baseline of dynamical decoupling scheme that eliminates all but one path to quantum state transfer on the network, thus effectively transforming it to a nearest-neighbor chain. Citation: International Journal of Quantum Information PubDate: 2022-03-30T07:00:00Z DOI: 10.1142/S0219749922500095
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