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Studying the behavior of quantum information scrambling in various quantum systems is an active area of research. Recently, Sharma et al. [K.K. Sharma, V.P Gerdt, Quantum Inf. Process 20, 195 (2021)] have shown the mathematical connection between quantum information scrambling (QIS) and bipartite entanglement in non-thermal states. In the present work, we elegantly generalize this mathematical connection and study such connections in X-states, non-maximally entangled Bell states, and Werner states, Comment: 7

In this article, we focus on tridiagonal Toeplitz Hermitian matrices, which fulfill the requirement of a valid Hamiltonian often used in Quantum Information. We investigate the behavior of such matrices to pursue the dynamics of quantum correlations (entanglement and quantum discord) for bipartite Werner state and maximally entangled mixed states. We have found interesting results that the main diagonal terms in the Toeplitz matrices never affect the quantum correlations in both quantum states. However, super-diagonal and sub-diagonal terms play the important role in the dynamics. We investigate the phenomenon of entanglement sudden death and also observe the presence of quantum discord in the absence of entanglement. Most importantly it is found that MEMS is more sensitive in comparison to the Werner state., Comment: 13 pages, six figures

In this article we investigate the unitary dynamics of squashed entanglement and concurrence measures in Werner state and maximally entangled mixed states (MEMS) under two different Hamiltonians. The aim of the present study is two fold. The first part of the study deals with the dynamics under Heisenberg Hamiltonian and the second part deals under bi-linear bi-quadratic Hamiltonian which is the extension of first Hamiltonian. In both the parts we investigate the dynamical trade off and balancing points for squashed entanglement and concurrence. During the study, we also found the results of entanglement sudden death (ESD) with Heisenberg Hamiltonian in Werner state under concurrence measure. In second part, we investigate the special result for bi-linear bi-quadratic Hamiltonian; it does not disturb squashed entanglement and concurrence in both the states and exhibit the robust character for both of the states., Comment: 12,5

This article reveals the future prospects of quantum algorithms in high energy physics (HEP). Particle identification, knowing their properties and characteristics is a challenging problem in experimental HEP. The key technique to solve these problems is pattern recognition, which is an important application of machine learning and unconditionally used for HEP problems. To execute pattern recognition task for track and vertex reconstruction, the particle physics community vastly use statistical machine learning methods. These methods vary from detector to detector geometry and magnetic field used in the experiment. Here in the present introductory article, we deliver the future possibilities for the lucid application of quantum computation and quantum machine learning in HEP, rather than focusing on deep mathematical structures of techniques arise in this domain., Comment: 8 pages, 2 figures

Investigating the influence of quantum information (QI) scrambling on quantum correlations in a physical system is an interesting problem. In this article we establish the mathematical connections among the quantifiers known as quantum information scrambling, Uhlmann fidelity, Bures metric and bipartite concurrence. We study these relations via four point out-of-time-order correlation (OTOC) function used for quantum information scrambling. Further we study the dynamics of all the quantifiers and investigate the influence of QI scrambling on entanglement in two qubits prepared in Bell states. We also determine the related QI scrambling and entanglement balancing points and investigate that they are periodic in nature for the Ising Hamiltonian., Comment: 9 pages, 5 figures

Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is categorized as a NP optimization problem. Exhaustive search of huge set of features takes huge amount of time on classical computer. In the present paper we discuss the role of quantum adiabatic computation to perform feature selection with bi-quadratic optimization and provide a quantum feature selection algorithm. Our algorithm runs with the quantum adiabatic time complexity bound $O(1/g_{min}^{2})$, which is better than classical approach for bi-quadratic feature selection., Comment: 12 pages,4 figures

In the present article, the robustness of entanglement in two qubits maximally entangled mixed states (MEME) have been studied under quantum decoherence channels. Here we consider bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels. To quantify the entanglement, the concurrence has been used as an entanglement measure. During this study interesting results have been found for sudden death and birth of entanglement under bit flip and bit-phase-flip channels. While amplitude damping channel produces entanglement sudden death and does not allow re-birth of entanglement. On the other hand, two qubits MEMS exhibit the robust character against the phase flip, phase damping and depolarization channels. The elegant behavior of all the quantum channels have been investigated with varying parameter of quantum state MEMS in different cases., Comment: 15 pages, 7 figures

In this article we present milestone developments in the theory and applications of quantum information from historical perspectives. The domain of quantum information is very promising to develop quantum computer, quantum communication and varieties of other applications of quantum technologies. We also give the light on experimental manifestations of major theoretical developments. In addition, we present important no-go theorems frequently used in quantum information along with ideas of their respective mathematical proofs., Comment: 14 pages, 1 figure

In the present paper, we study spin squeezing under decoherence in the superposition of tripartite maximally entangled GHZ and W states. Here we use amplitude damping, phase damping and depolarisation channel. We have investigated the dynamics of spin squeezing with the interplay of superposition and decoherence parameters with different directions of the mean spin vector. We have found the mixture of GHZ and W states is robust against spin squeezing generation for amplitude damping and phase damping channels for certain directions of the mean spin vector. However, the depolarisation channel performs well for spin squeezing generation and generates permanent spin squeezing in the superposition of GHZ and W states., Comment: 6 pages, 3 figures

In this letter we study thermal quantum correlations as quantum discord and entanglement in bipartite system imposed by external magnetic field with Herring-Flicker coupling ie. $J(R)=1.642 e^{-2 R} R^{5/2}+O(R^{2}e^{-2R})$. The Herring-Flicker coupling strength is the function of $R$, which is the distance between spins and systems carry XXX Heisenberg interaction. By tuning the coupling distance $R$, temperature and magnetic field quantum correlations can be scaled in the bipartite system. We find the long sustainable behaviour of quantum discord in comparison to entanglement over the coupling distance $R$. We also investigate the situations, where entanglement totally dies but quantum discord exist in the system. The present findings in the letter may be useful for designing quantum wires, data bus, solid state gates and quantum processors., Comment: 5 pages, 3 figures

We reckon the behaviour of spin squeezing in tripartite unsqueezed maximally entangled Green- berger-Horne-Zeilinger (GHZ) and W states under various decoherence channels with Kitagawa- Ueda (KU) criteria. In order to search spin squeezing sudden death (SSSD) and signatures of spin squeezing production we use bit flip, phase flip, bit-phase-flip, amplitude damping, phase damping and depolarization channels in the present study. In literature, the influence of decoherence has been studied as a destroying element. On the contrary here we investigate the positive aspect of decoherence, which produce spin squeezing in unsqueezed GHZ and W states under certain channels. Our meticulous study shows that GHZ state remain unsqueezed under aforementioned channels except bit-phase-flip and depolarization channels. While all the decoherence channels produce spin squeezing in W state. So we find, GHZ is more robust in comparison to W state in the sense of spin squeezing production under decoherence. Most importantly we find that none of the decoherence channel produce SSSD in any one of the state., Comment: 18 pages, 11 figures, Journal paper

In this article the robustness of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states is investigated against Dzyaloshinskii-Moriya (i.e. DM) interaction. We consider a closed system of three qubits and an environmental qubit. The environmental qubit interacts with any one of the three qubits through DM interaction. The tripartite system is initially prepared in GHZ and W states respectively. The composite four qubits system evolve with unitary dynamics. We detach the environmental qubit by tracing out from four qubits and profound impact of DM interaction is studied on the initial entanglement of the system. As a result we find that the bipartite partitions of W states suffer from entanglement sudden death (i.e. ESD), while tripartite entanglement does not. On the other hand bipartite partitions and tripartite entanglement in GHZ states does not feel any influence of DM interaction. So, we find that GHZ states have robust character than W states. In this work we consider generalised GHZ and W states and three $\pi$ is used as an entanglement measure. This study can be useful in quantum information processing where unwanted DM interaction takes place., Comment: 11 pages, 6 figures in Quantum. Info. Proc. (2016)

In this present paper we study the entanglement dynamics in qubit A-qutrit B pair under x component of Dzyaloshinshkii-Moriya $(D_{x})$ by taking an auxiliary qubit C. Here we consider an entangled qubit-qutrit pair initially prepared in two parameter qubit-qutrit states and one auxiliary qubit prepared in pure state interacts with the qutrit of the pair through DM interaction. We trace away the auxiliary qubit and calculate the reduced dynamics in qubit A-qutrit B pair to study the influence of the state of auxiliary qubit C and $D_{x}$ on entanglement. We find that the state (probability amplitude) of auxiliary qubit does not influence the entanglement, only $D_{x}$ influences the same. The phenomenon of entanglement sudden death (ESD) induced by $D_{x}$ has also been observed. We also present the affected and unaffected two parameter qubit-qutrit states by $D_{x}$., Comment: 8 pages,8 figures, Submitted, Communications in Theoritical physics, 2015

In this paper we study the influence of Dzyaloshinskii-Moriya (DM) interaction on quantum correlations in two qubit Werner states and maximally entangled mixed states (MEMS). We consider our system as a closed system of a qubits pair and one auxiliary qubit which interact with any one of the qubit of the pair through DM interaction. We show that DM interaction, taken along any direction (x or y or z), does not affect two qubit Werner states. On the other hand the MEMS are affected by x and z components of DM interaction and remain unaffected by the y component. Further, we find that the state (i.e probability amplitude) of auxiliary qubit do not affect the quantum correlations in both the states, only DM interaction strength influences the quantum correlations. So one can avoid the intention to prepare the specific state of auxiliary qubit to manipulate the quantum correlations in both the states. We mention here that avoiding the preparation of state can contribute to cost reduction in quantum information processing. We also observe the phenomenon of entanglement sudden death in the present study., Comment: 12 pages, 5 figures (Submitted 12 Sept. 2014), Quantum Information Processing

In the present article we investigate the efficacy of Dzyaloshisnhkii-Moriya (DM) interaction to convert the bound entangled states into free entangled states. Here we consider the tripartite hybrid system as a pair of non interacting two qutrits initially prepared in bound entangled states and one auxiliary qubit. The auxiliary qubit interacts with any one of the qutrit of the pair through DM interaction. It has been found that the DM interaction free the bound entangled states as time advances. In the present work we consider two types of bound entangled states investigated by Horodecki. Further we find that the frequency of free entanglement conversion is same in both the states. We also investigate the phenomenon of entanglement and distillability sudden death and their possibilities. Here the realignment criteria and negativity have been used for detection and quantification of entanglement., Comment: 10 pages, 8 figures

The current work shows the efficacy of Dzyaloshinshkii-Moriya (DM) interaction to free the bound entanglement. Based on the work [Sharma, K.K., Pandey, S.N., Quant. Info. Proc. 15, 1539 (2016)], we present further results in two qutrits bound entangled state proposed by Jurkovaski et al. We consider a closed system of two qutrits and an auxiliary qutrit which interacts with either one of the two qutrits in a closed system. We erase the auxiliary qutrit from the system by doing partial trace operation and open system dynamics has been studied. We have found, the probability amplitude of auxiliary qutrit does not affect the system, while DM interaction plays a major role to govern the dynamics. The realignment and CCNR criteria have been used to detect the bound entanglement in the state, while for quantification of entanglement the negativity has been used. We explored the dynamics with all the possible cases of Jurkowski et al. bound entangled state., Comment: 10 pages, 6 pdf figures

Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equation with point-wise delay or advance, i.e., shift in space. The differential equation involving point-wise delay and advance models the distribution of the time intervals between successive neuronal firings. We construct higher order numerical approximations and discuss their consistency, stability and convergence. The numerical approximations constructed in this paper are consistent, stable under CFL condition, and convergent. We also extend our methods to the higher space dimensions. Some test examples are included to illustrate our approach. These examples verify the theoretical estimates and shows the effect of point-wise delay on the solution., Comment: 15 pages, 8 figures