Relationship Between Quantum Walk and Relativistic Quantum Mechanics

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled form of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schrodinger form. By showing the coin to be a means to make the walk reversible, and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modelled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of quantum walk, maximum speed of the walk propagation and the earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two state system to which the study can be extended.Comment: 12 pages and 1 figure, Published versio

MENTAL MORBIDITY AMONG GRADUATE AND RESEARCH STUDENTS : AN EPIDEMIOLOGICAL STUDY

A cross sectional epidemiological study of mental morbidity among 1160 postgraduate and research students was done by census method. Goldberg's 60 item GHQ was used as screening tool and a person scoring 12 and above was taken as a case. The response rate was 92.5%. A prevalence rate of 16.63 was found. The relationship between mental morbidity and selected socio-demographic, motivational psychological variables; certain life experiences in the campus was studied. The results are discussed. This study is first of its kind in our country

Optimizing the discrete time quantum walk using a SU(2) coin

We present a generalized version of the discrete time quantum walk, using the SU(2) operation as the quantum coin. By varying the coin parameters, the quantum walk can be optimized for maximum variance subject to the functional form $\sigma^2 \approx N^2$ and the probability distribution in the position space can be biased. We also discuss the variation in measurement entropy with the variation of the parameters in the SU(2) coin. Exploiting this we show how quantum walk can be optimized for improving mixing time in an $n$-cycle and for quantum walk search.Comment: 6 pages, 6 figure

Disordered quantum walk-induced localization of a Bose-Einstein condensate

We present an approach to induce localization of a Bose-Einstein condensate in a one-dimensional lattice under the influence of unitary quantum walk evolution using disordered quantum coin operation. We introduce a discrete-time quantum walk model in which the interference effect is modified to diffuse or strongly localize the probability distribution of the particle by assigning a different set of coin parameters picked randomly for each step of the walk, respectively. Spatial localization of the particle/state is explained by comparing the variance of the probability distribution of the quantum walk in position space using disordered coin operation to that of the walk using an identical coin operation for each step. Due to the high degree of control over quantum coin operation and most of the system parameters, ultracold atoms in an optical lattice offer opportunities to implement a disordered quantum walk that is unitary and induces localization. Here we present a scheme to use a Bose-Einstein condensate that can be evolved to the superposition of its internal states in an optical lattice and control the dynamics of atoms to observe localization. This approach can be adopted to any other physical system in which controlled disordered quantum walk can be implemented.Comment: 6 pages, 4 figures, published versio

Generic quantum walk using a coin-embedded shift operator

The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by considering the limiting value of the coin operation parameter in the DTQW, and the coin degree of freedom was shown to be unnecessary [26]. But the coin degree of freedom is an additional resource which can be exploited to control the dynamics of the QW process. In this paper we present a generic quantum walk model using a quantum coin-embedded unitary shift operation $U_{C}$. The standard version of the DTQW and the CTQW can be conveniently retrieved from this generic model, retaining the features of the coin degree of freedom in both variants.Comment: 5 pages, 1 figure, Publishe

Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord

Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate non-classicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly the trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of non-classicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness.Comment: 5 pages with 4 figures, Published Versio

Symmetries and noise in quantum walk

We study some discrete symmetries of unbiased (Hadamard) and biased quantum walk on a line, which are shown to hold even when the quantum walker is subjected to environmental effects. The noise models considered in order to account for these effects are the phase flip, bit flip and generalized amplitude damping channels. The numerical solutions are obtained by evolving the density matrix, but the persistence of the symmetries in the presence of noise is proved using the quantum trajectories approach. We also briefly extend these studies to quantum walk on a cycle. These investigations can be relevant to the implementation of quantum walks in various known physical systems. We discuss the implementation in the case of NMR quantum information processor and ultra cold atoms.Comment: 19 pages, 24 figures : V3 - Revised version to appear in Phys. Rev. A. - new section on quantum walk in a cycle include