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

Information theoretic approach for assessing image fidelity in photon-counting arrays

The method of photon-counting integral imaging has been introduced recently for three-dimensional object sensing, visualization, recognition and classification of scenes under photon-starved conditions. This paper presents an information-theoretic model for the photon-counting imaging (PCI) method, thereby providing a rigorous foundation for the merits of PCI in terms of image fidelity. This, in turn, can facilitate our understanding of the demonstrated success of photon-counting integral imaging in compressive imaging and classification. The mutual information between the source and photon-counted images is derived in a Markov random field setting and normalized by the source-image’s entropy, yielding a fidelity metric that is between zero and unity, which respectively corresponds to complete loss of information and full preservation of information. Calculations suggest that the PCI fidelity metric increases with spatial correlation in source image, from which we infer that the PCI method is particularly effective for source images with high spatial correlation; the metric also increases with the reduction in photon-number uncertainty. As an application to the theory, an image-classification problem is considered showing a congruous relationship between the fidelity metric and classifier’s performance

Free resolutions over short local rings

The structure of minimal free resolutions of finite modules M over commutative local rings (R,m,k) with m^3=0 and rank_k(m^2) < rank_k(m/m^2)is studied. It is proved that over generic R every M has a Koszul syzygy module. Explicit families of Koszul modules are identified. When R is Gorenstein the non-Koszul modules are classified. Structure theorems are established for the graded k-algebra Ext_R(k,k) and its graded module Ext_R(M,k).Comment: 17 pages; number of minor changes. This article will appear in the Journal of the London Math. So

Non-destructive Orthonormal State Discrimination

We provide explicit quantum circuits for the non-destructive deterministic discrimination of Bell states in the Hilbert space $C^{d^{n}}$, where $d$ is qudit dimension. We discuss a method for generalizing this to non-destructive measurements on any set of orthogonal states distributed among $n$ parties. From the practical viewpoint, we show that such non-destructive measurements can help lower quantum communication complexity under certain conditions.Comment: 11 pages, 6 fugure

Phytochemical Screening and In-Vitro Antioxidant Activity of Peristrophe paniculata

Peristrophe paniculata is one of the traditional medicinal plant have been using in treatment of different diseases. The present study was carried out to provide scientific evidence about its medicinal use and phytochemical variation in different parts (stem, leaves and root) of it. Phytochemical studies were carried out for hexane, ethyl acetate and hydro alcoholic extracts using standard test procedures and antioxidant activity was carried on different free radicals i.e., superoxide, hydroxyl and 1, 1- diphenyl-2-picrylhydrazyl (DPPH). Hydroalcoholic, ethyl acetate and hexane extracts of P. paniculata were found to possess concentration dependent free radical scavenging activity on superoxide, hydroxyl and DPPH free radicals. Qualitative phytochemical screening of P. paniculata extracts revealed the presence of diverse in phytochemical constituents like steroids, terpenoids, flavonoids, alkaloids, glycosides, phenols, tannins and carbohydrates. The extracts of different parts gave negative and positive results for the amino acids, oils and saponins. The selected plant extracts showed concentration dependent percentage of inhibition on tested free radicals along with the standard drug ascorbic acid. The hexane extract of all parts of P. paniculata showed lower activity compared to ethyl acetate and hydroalcoholic extracts. Hydroalcoholic extract showed better activity. The variation in the activity and phytochemical constituents in them maybe due to the compounds present in them either as individually or in mixtures. The further research is need to evaluate more pharmacological activities and in isolation of the bioactive compounds from P. paniculata