A Note on Quantum Errors and Their Correction

This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or phase-flip or both.Comment: 9 page

Observability and Computability in Physical Systems

This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems it is important even where explicit computation is not the goal. Specifically, we examine two problems: observability and computability for quantum computing, and remote measurement of time and frequency.Comment: 8 pages, 1 figur

The Axis and the Perimeter of the Temple

This paper presents textual evidence for an astronomical basis of the dimensions of the axis and perimeter in the plan of the Indian temple.Comment: 13 pages, 7 figures, Kannada Vrinda Seminar Sangama 2005 held at Loyola Marymount University in Los Angeles on November 19, 200

Babylonian and Indian Astronomy: Early Connections

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.Comment: 37 pages; with minor correction

Extended Unary Coding

Extended variants of the recently introduced spread unary coding are described. These schemes, in which the length of the code word is fixed, allow representation of approximately n^2 numbers for n bits, rather than the n numbers of the standard unary coding. In the first of two proposed schemes the spread increases, whereas in the second scheme the spread remains constant.Comment: 5 page

Efficiency of Matrix Multiplication on the Cross-Wired Mesh Array

This note looks at the efficiency of the cross-wired mesh array in the context of matrix multiplication. It is shown that in case of repeated operations, the average number of steps to multiply sets of nxn matrices on a 2D cross-wired mesh array approaches n.Comment: 5 page

The Algebra of Two Dimensional Patterns

The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more efficient than a pixel-wise representation.Comment: 11 pages, 14 figure

The Transactional Nature of Quantum Information

Information, in its communications sense, is a transactional property. If the received signals communicate choices made by the sender of the signals, then information has been transmitter by the sender to the receiver. Given this reality, the potential information in an unknown pure quantum state should be non-zero. We examine transactional quantum information, which unlike von Neumann entropy, depends on the mutuality of the relationship between the sender and the receiver, associating information with an unknown pure state. The information that can be obtained from a pure state in repeated experiments is potentially infinite.Comment: Presented at the 11th International Conference on Squeezed States and Uncertainty Relations and 4th Feynman Festival, Olomouc, Czech Republic, June 22-26, 200

Representation of Entangled States

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.Comment: 7 pages, edited materia

A Key Set Cipher for Wireless Sensor Networks

This paper proposes the use of sets of keys, together with corresponding identifiers, for use in wireless sensor networks and similar resource-constrained applications. A specific cryptographic scheme described in the paper is based on the use of a family of self-inverting matrices derived from the number theoretic Hilbert transform in conjunction with the Blom's scheme. In a randomized version of this scheme, the users change their published IDs at will but the parties can still reach agreement on the key by using individual scaling factors. The random protocol increases the security of the system.Comment: 12 pages, 2 figure