arXiv subjects
Publications and source records attributed to Subhash Kak.
This paper introduces the use of decimal sequences in a code division multiple access (CDMA) based watermarking system to hide information for authentication in black and white images. Matlab version 6.5 was used to implement the algorithms discussed in this paper. The advantage of using d-sequences over PN sequences is that one can choose from a variety of prime numbers which provides a more flexible system.
This article considers evidence from physical and biological sciences to show machines are deficient compared to biological systems at incorporating intelligence. Machines fall short on two counts: firstly, unlike brains, machines do not self-organize in a recursive manner; secondly, machines are based on classical logic, whereas Nature's intelligence may depend on quantum mechanics.
This paper considers the realizability of quantum gates from the perspective of information complexity. Since the gate is a physical device that must be controlled classically, it is subject to random error. We define the complexity of gate operation in terms of the difference between the entropy of the variables associated with initial and final states of the computation. We argue that the gate operations are irreversible if there is a difference in the accuracy associated with input and output variables. It is shown that under some conditions the gate operation may be associated with unbounded entropy, implying impossibility of implementation.
The question of the origins of logic as a formal discipline is of special interest to the historian of physics since it represents a turning inward to examine the very nature of reasoning and the relationship between thought and reality. In the West, Aristotle (384-322 BCE) is generally credited with the formalization of the tradition of logic and also with the development of early physics. In India, the Rigveda itself in the hymn 10.129 suggests the beginnings of the representation of reality in terms of various logical divisions that were later represented formally as the four circles of: "A", "not A", ":A and not A", and "not A and not not A''. According to Puranic accounts, Medhatithi Gautama and Aksapada Gautama (or Gotama), which are perhaps two variant names for the author of the early formal text on Indian logic, belonged to about 550 BCE. The Greek and the Indian traditions seem to provide the earliest formal representations of logic, and in this article we ask if they influenced each other. We are also interested in the scope of early logic, since this gives an idea to us of the way early thinkers thought about nature and change. We will show that Greek and Indian logical traditions have much that is distinctive and unique and that they must have emerged independently.
We present a three-stage quantum cryptographic protocol guaranteeing security in which each party uses its own secret key. Unlike the BB84 protocol, where the qubits are transmitted in only one direction and classical information exchanged thereafter, the communication in the proposed protocol remains quantum in each stage. A related system of key distribution is also described.
The golden mean, Phi, has been applied in diverse situations in art, architecture and music, and although some have claimed that it represents a basic aesthetic proportion, others have argued that it is only one of a large number of such ratios. We review its early history, especially its relationship to the Mount Meru of Pingala. We examine the successive divisions of 3, 7, and 22 in Indian music and suggest derivation from variants of Mount Meru. We also speculate on the neurophysiological basis behind the sense that the golden mean is a pleasant proportion.
This note presents reasons why Mendeleev chose Sanskrit names (now superseded) for eight elements in the periodic table.
Historians of science are generally unaware of the contributions of India to physics. The main reason for this is that very little research has been done on the subject in the recent past, a consequence of the fact that there are few history of science departments in Indian universities. The objective of this paper is to present a preliminary outline of early history of physics in India. The schools of Vaisheshika and Samkhya, that were interested in general principles of atomic theory and cosmology, are discussed. In particular, ideas on atoms and molecules, the nature of sound, causality, universals, cosmology, uniform and non-uniform motions are described.
This note is about three interesting 15th and 16th century sightings of comets in Kashmiri chronicles. We provide reasons for their identification as the 1468 S1, 1531 (Halley's), and 1533 M1 comets.
The standard protocol for teleportation of a quantum state requires an entangled pair of particles and the use of two classical bits of information. Here, we present two protocols for teleportation that require only one classical bit. In the first protocol, chained XOR operations are performed on the particles before one of them is removed to the remote location where the state is being teleported. In the second protocol, three entangled particles are used.
The question of the measurements on the Bell states by making use of mode change (from mixed to pure) of one qubit is considered. Such a mode change cannot be taken advantage of for superluminal communication in teleportation, and it may define constraints on the size of the gates.
The commonly used circuit model of quantum computing leaves out the problems of imprecision in the initial state preparation, particle statistics (indistinguishability of particles belonging to the same quantum state), and error correction (current techniques cannot correct all small errors). The initial state in the circuit model computation is obtained by applying potentially imprecise Hadamard gate operations whereas useful quantum computation requires a state with no uncertainty. We review some limitations of the circuit model and speculate on the question if a hierarchy of quantum-type computing models exists.
Associating a physical process with the pure entangled state 1/sqrt 2 (|00> + |11>) is an idealization unless the pair is so prepared using an appropriate quantum gate operating on a known state. Questions related to the reference frame for measurement of the entangled state are considered. Some applications are described.
The notion of quantum information related to the two different perspectives of the global and local states is examined. There is circularity in the definition of quantum information because we can speak only of the information of systems that have been specifically prepared. In particular, we examine the final state obtained by applying unitary transformations on a single qubit that belongs to an entangled pair.
The early Greek and Indian cosmologies are summarized in this paper. The two traditions appear to have developed independently although after the time of Alexander they were consciously aware of each other. The focus and style of the two sciences was different owing to their different cosmologies. Perhaps the only science which worked more or less the same way in the two civilizations was medicine. But even here there was important difference. The reason why the two sciences went their own way in spite of the knowledge of the other was because their worldviews were different. Indian astronomers, for example, never paid any attention to Ptolemy's model with its crystalline spheres that looked restrictive compared to the vast scale of their own conception. On the other hand, the use of enormous time scales of Indian astronomy must have appeared unnecessary to the Greeks.
Did the Indian and Babylonian astronomy evolve in isolation, was there mutual influence, or was one dependent on the other? Scholars have debated these questions for more than two centuries, and opinion has swung one way or the other with time. The similarities between the two systems that have been investigated are: the use of 30 divisions of the lunar month; the 360 divisions of the civil year; the length of the year; and the solar zodiac. Some have wondered if the Babylonian planetary tables might have played a role in the theories of the siddhantas. I shall in this essay go over the essentials of the early Indian and Babylonian astronomy and summarize the latest views on the relationship between them. I shall show that the key ideas found in the Babylonian astronomy of 700 BC are already present in the Vedic texts, which even by the most conservative reckoning are centuries older than this period. I shall also show that the solar zodiac (rashis) was used in Vedic India and I shall present a plausible derivation of the symbols of the solar zodiac from the deities of the lunar segments. This does not mean that the Babylonian astronomy and astrology is derived from the Indian tradition. If at all there was borrowing, that was restricted to the most general ideas only. The nature of Indian and Babylonian astronomical methods is quite different. I propose that it is most likely that Babylonian astronomy emerged independently.
The cyclic model of the universe has an old history in India. It has held the preeminent position regarding the origins of the universe, and it is described in astronomical texts, Puranic encyclopaedias, and philosophical literature. Within the current cycle, which is supposed to have begun several billion years ago, are smaller cycles of pole changes and extinctions on earth. Salient features of the cyclic universe model are presented here.
Error correction, in the standard meaning of the term, implies the ability to correct all small analog errors and some large errors. Examining assumptions at the basis of the recently proposed quantum error-correcting codes, it is pointed out that these codes can correct only a subset of errors, and are unable to correct small phase errors which can have disastrous consequences for a quantum computation. This shortcoming will restrict their usefulness in real applications.