arXiv subjects
Publications and source records attributed to Subhash Kak.
This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may be useful in quantum games. It is shown that under certain conditions in a two-party quantum game, the receiver of the states can increase the entropy by adding another pure state.
Two power series models are proposed to represent self-similarity and they are compared to the Zipf and Benford distributions. Since evolution of a social network is associated with replicating self-similarity at many levels, the nature of interconnections can serve as a measure of the optimality of its organization. In contrast with the Zipf distribution where the middle term is the harmonic mean of the adjoining terms, our distribution considers the middle term to be the geometric mean. In one of the power series models, the scaling factor at one level is shown to be the golden ratio. A model for evolution of networks by oscillations between two different self-similarity measures is described.
The value of a social network is generally determined by its size and the connectivity of its nodes. But since some of the nodes may be fake ones and others that are dormant, the question of validating the node counts by statistical tests becomes important. In this paper we propose the use of the Benford's distribution to check on the trustworthiness of the connectivity statistics. Our experiments using statistics of both symmetric and asymmetric networks show that when the accumulation processes are random, the convergence to Benford's law is significantly better, and therefore this fact can be used to distinguish between processes which are randomly generated and those with internal dependencies.
A multiparty computation protocol is described in which the parties can generate different probability events that is based on the sharing of a single anonymized random number, and also perform oblivious transfer. A method to verify the correctness of the procedure, without revealing the random numbers used by the parties, is proposed.
Although random sequences can be used to generate probability events, they come with the risk of cheating in an unsupervised situation. In such cases, the oblivious transfer protocol may be used and this paper presents a variation to the DH key-exchange to serve as this protocol. A method to verify the correctness of the procedure, without revealing the random numbers used by the two parties, is also proposed.
This paper presents a multi-stage, multi-photon quantum key distribution protocol based on the double-lock cryptography. It exploits the asymmetry in the detection strategies between the legitimate users and the eavesdropper. The security analysis of the protocol is presented with coherent states under the intercept-resend attack, the photon number splitting attack, and the man-in-the-middle attack. It is found that the mean photon number can be much larger than one. This complements the recent interest in multi-photon quantum communication protocols that require a pre-shared key between the legitimate users.
This paper investigates randomness properties of sequences derived from Fibonacci and Gopala-Hemachandra sequences modulo m for use in key distribution applications. We show that for sequences modulo a prime a binary random sequence B(n) is obtained based on whether the period is p-1 (or a divisor) or 2p+2 (or a divisor). For the more general case of arbitrary m, we use the property if the period is a multiple of 8 or not. The sequences for prime modulo have much better autocorrelation properties. These are good candidates for key distribution since the generation process is not computationally complex.
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.
The friendship paradox is revisited by considering both local and global averages of friends. How the economics of attention affects the recruitment of friends is examined. Statistical implications of varying individual attentions are investigated and it is argued that this is one reason why the mean of friends is higher than the median in social networks. The distribution of friends skews to the right for two other reasons: (i) the presence of institutional nodes that increase the mean; and (ii) the dormancy of many of the nodes. The difference between friends and friends of friends is a measure of the structural information about the network.
Unary coding is useful but it is redundant in its standard form. Unary coding can also be seen as spatial coding where the value of the number is determined by its place in an array. Motivated by biological finding that several neurons in the vicinity represent the same number, we propose a variant of unary numeration in its spatial form, where each number is represented by several 1s. We call this spread unary coding where the number of 1s used is the spread of the code. Spread unary coding is associated with saturation of the Hamming distance between code words.
The piggy bank idea allows one-way encryption of information that can be accessed only by authorized parties. Here we show how the piggy bank idea can be used to authenticate parties to counter man-in-the-middle (MIM) attack that can jeopardize the double-lock cryptography protocol. We call this method double-signature double lock cryptography and it can be implemented in ways that go beyond hash-based message authentication.
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.
This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement is made by the observer viewed as a quantum system. In interpretations where the system together with the observers is completely described by unitary transformations, the observer cannot make any choices and so measurement is impossible. From the perspective of computability theory, a quantum machine cannot halt and so it cannot observe the computed state, indicating that unitarity alone does not explain all matter processes. Further it is argued that the consideration of information and observation requires an overarching system of knowledge and expectations about outcomes.
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty for a hypothetical oracle machine, the output of which may be verified by a computable function but cannot be simulated on a physical machine. We define a quantum oracle machine for measurements as one that can determine the state by examining a single copy. The complexity of measurement for a realizable machine will then be respect to the number of copies of the state that needs to be examined. A quantum oracle cannot perform simultaneous exact measurement of conjugate variables, although approximate measurement may be performed as circumscribed by the Heisenberg uncertainty relations. When considering the measurement of a variable, there might be residual uncertainty if the number of copies of the variable is limited. Specifically, we examine the quantum measurement complexity of linear polarization of photons that is used in several quantum cryptography schemes and we present a relation using information theoretic arguments. The idea of quantum measurement complexity is likely to find uses in measurements in biological systems.
The premise that consciousness has a quantum mechanical basis or correlate implies that its workings have a nonlocal component. To check whether consciousness as an entity leaves a physical trace, we propose that laboratory searches for such a trace should be for nonlocality, where probabilities do not conform to local expectations. Starting with the idea that nonlocality may be veiled as one of the ways cosmic censorship operates, we further argue that in order to preserve the ordinary objective reality described by local realism and general relativity, veiled nonlocality and cosmic censorship are indispensable operational aspects of the interactions of observers with physical systems. Nevertheless, it may be possible to indirectly detect traces of nonlocality in experiments where humans and other sentient subjects are involved
An explanation is provided for the Inca counting board described by Guaman Poma in 1615. Although the board could have been used in more than one way, we show that based on certain reasonable assumptions regarding non-uniform representation of numbers its most likely use was counting in multiples of 6, 24, and 72. The independent numbers represented on its five rows are 92, 31, 29, 79, and 56 that appear to be astronomically connected to sub-periods within the year and planet periods in a manner similar to Mayan astronomy. Based on these and other considerations we propose that the board fulfilled an astronomical counting function.
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.
This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences have autocorrelation function that is zero everywhere excepting at the origin. These sequences may be used as keys and in other cryptography applications.