Quantum Key Distribution Using Three Basis States

This note presents a method of public key distribution using quantum communication of n photons that simultaneously provides a high probability that the bits have not been tampered. It is a three-state variant of the quantum method of Bennett and Brassard (BB84) where the transmission states have been decreased from 4 to 3 and the detector states have been increased from 2 to 3. Under certain assumptions regarding method of attack, it provides superior performance (in terms of the number of usable key bits) for n < 18 m, where m is the number of key bits used to verify the integrity of the process in the BB84-protocol.Comment: 6 page

Inertial Frames and Clock Rates

This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If inertial frames are explicitly identified by motion with respect to the large scale structure of the universe, it makes it possible to consider the relative inertiality of different frames.Comment: 7 pages, 1 figur

Prime Reciprocal Digit Frequencies and the Euler Zeta Function

Some open questions related to prime reciprocal digit frequencies with potential applications to cryptography are presented.Comment: 6 page

On Quantum Decision Trees

Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some properties of the states obtained in a decision tree structure. How these correlations may be mapped to the decision tree is considered. Classical tree representations and approximations to quantum states are provided.Comment: 9 pages, 7 figure

Probability and the Classical/Quantum Divide

This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being different (Pn). Given three events, Ps/Pn for the classical case, where there are no 3-way coincidences, is one-half whereas for the quantum state it is one-third. For non-maximally entangled objects we find that so long as r < 5.83, we can separate them from classical objects using a probability test. For maximally entangled particles (r = 1), we propose that the value of 5/12 be used for Ps/Pn to separate classical and quantum states when no other information is available and measurements are noisy.Comment: 12 pages; 1 figur

Threshold Quantum Cryptography

Most current research on quantum cryptography requires transmission and reception of single photons that creates severe implementation challenges and limits range. This paper argues for the development of threshold quantum cryptography protocols in which the system is secure so long as the number of photons being exchanged between Alice and Bob is below a specified threshold. We speak of a (p-k-n) threshold system where if the number of photons exchanged is less than p, the system is completely secure, when it is between p and k, the system is partially secure, and when it exceeds k, the system is insecure. The BB84 protocol is (1-1-1) whereas the three-stage protocol appears to be (p-4p-n), where p is the least number of photons necessary to determine the polarization state of identically prepared photons. New quantum cryptography systems should be sought that provide greater flexibility in the choice of p and k.Comment: 10 pages, 4 figures. arXiv admin note: text overlap with arXiv:1206.677

Concepts of Space, Time, and Consciousness in Ancient India

This paper describes Indian ideas of the early-Purana/Mahabharata times (centuries BC) on the nature of space, time and consciousness that would be of interest to the physicist. In order to simplify references, we quote mainly from Yoga-Vasistha (YV), which is representative of that period of Indian thought. YV professes to be a book of instruction on the nature of consciousness but it has many fascinating passages on time, space, matter and cognition. This paper presents a random selection that has parallels with recent speculations in physics. It also presents a brief account of the context in which ideas of YV developed.Comment: 14 pages; with minor corrections and a few additional reference

Thermodynamics, Phase Transition and Quasinormal modes with Weyl corrections

We study charged black holes in D dimensional AdS space, in the presence of four derivative Weyl correction. We obtain the black hole solution perturbatively up to first as well as second order in the Weyl coupling, and show that first law of black hole thermodynamics is satisfied in all dimensions. We study its thermodynamic phase transition and then calculate the quasinormal frequencies of the massless scalar field perturbation. We find that, here too, the quasinormal frequencies capture the essence of black hole phase transition. Few subtleties near the second order critical point are discussed.Comment: 1+26 pages, 16 figure

Probability Reversal and the Disjunction Effect in Reasoning Systems

Data based judgments go into artificial intelligence applications but they undergo paradoxical reversal when seemingly unnecessary additional data is provided. Examples of this are Simpson's reversal and the disjunction effect where the beliefs about the data change once it is presented or aggregated differently. Sometimes the significance of the difference can be evaluated using statistical tests such as Pearson's chi-squared or Fisher's exact test, but this may not be helpful in threshold-based decision systems that operate with incomplete information. To mitigate risks in the use of algorithms in decision-making, we consider the question of modeling of beliefs. We argue that evidence supports that beliefs are not classical statistical variables and they should, in the general case, be considered as superposition states of disjoint or polar outcomes. We analyze the disjunction effect from the perspective of the belief as a quantum vector.Comment: 11 page

On the Mesh Array for Matrix Multiplication

This article presents new properties of the mesh array for matrix multiplication. In contrast to the standard array that requires 3n-2 steps to complete its computation, the mesh array requires only 2n-1 steps. Symmetries of the mesh array computed values are presented which enhance the efficiency of the array for specific applications. In multiplying symmetric matrices, the results are obtained in 3n/2+1 steps. The mesh array is examined for its application as a scrambling system.Comment: 6 page