Inseparability of Quantum Parameters

In this work, we show that 'splitting of quantum information' [6] is an impossible task from three different but consistent principles of unitarity of Quantum Mechanics, no-signalling condition and non increase of entanglement under Local Operation and Classical Communication.Comment: 9 pages, Presented in Quantum Computing Back Action in IIT Kanpur (2006). Accepted in International Journal of Theoretical Physic

Quantum information cannot be split into complementary parts

We prove a new impossibility for quantum information (the no-splitting theorem): an unknown quantum bit (qubit) cannot be split into two complementary qubits. This impossibility, together with the no-cloning theorem, demonstrates that an unknown qubit state is a single entity, which cannot be cloned or split. This sheds new light on quantum computation and quantum information.Comment: 9 pages, 1 figur

Self Replication and Signalling

It is known that if one could clone an arbitrary quantum state one could send signal faster than the speed of light. However it remains interesting to see that if one can perfectly self replicate an arbitrary quantum state, does it violate the no signalling principle? Here we see that perfect self replication would also lead to superluminal signalling.Comment: Modified version of quant-ph/0510221, Accepted in International Journal of Theoretical Physic

Rare K-Decays as Crucial Tests for Unified Models with Gauged Baryon Number:

In the grand-unified models based on SU(15) and SU(16) in which the quarks and leptons are un-unified at the intermediate stages, we show that ${\rm BR}\; (K_L \to \mu e) \leq 10^{-14}$ and ${\rm BR}\; (K^+ \to \pi^+\mu e) \leq 10^{-14}$ despite the presence of leptoquark gauge bosons. Thus, the observation of these processes in the ongoing or upcoming experiments will rule out the models.Comment: (7 pages, LATEX, including figures drawn by LATEX) DOE-ER40200-304 CPP-5

Dynamics of two atoms coupled to a cavity field

We investigate the interaction of two two-level atoms with a single mode cavity field. One of the atoms is exactly at resonance with the field, while the other is well far from resonance and hence is treated in the dispersive limit. We find that the presence of the non-resonant atom produces a shift in the Rabi frequency of the resonant atom, as if it was detuned from the field. We focus on the discussion of the evolution of the state purity of each atom.Comment: LaTex, 2 figure

Probing Grand Unification Through Neutrino Oscillations, Leptogenesis, and Proton Decay

Evidence in favor of supersymmetric grand unification including that based on the observed family multiplet-structure, gauge coupling unification, neutrino oscillations, baryogenesis, and certain intriguing features of quark-lepton masses and mixings is noted. It is argued that attempts to understand (a) the tiny neutrino masses (especially Delta m^2 (nu_2 -nu_3)), (b) the baryon asymmetry of the universe (which seems to need leptogenesis), and (c) the observed features of fermion masses such as the ratio m_b/m_tau, the smallness of V_cb and the maximality of theta_{nu_mu-nu_tau}, seem to select out the route to higher unification based on an effective string-unified G(224) = SU(2)_L x SU(2)_R x SU(4)^c or SO(10)-symmetry, operative in 4D, as opposed to other alternatives. A predictive framework based on an effective SO(10) or G(224) symmetry possessing supersymmetry is presented that successfully describes the masses and mixings of all fermions including neutrinos. It also accounts for the observed baryon asymmetry of the universe by utilizing the process of leptogenesis, which is natural to this framework. It is argued that a conservative upper limit on the proton lifetime within this SO(10)/G(224)-framework, which is so far most successful, is given by (1/3-2) x 10^34 years. This in turn strongly suggests that an improvement in the current sensitivity by a factor of five to ten (compared to SuperK) ought to reveal proton decay. Implications of this prediction for the next-generation nucleon decay and neutrino-detector are noted.Comment: 40 page, 3 figures. Conference proceedings from Erice School (Sept 2002), Neutrino Conference (Stony Brook, 2002), PASCOS Conference (Mumbai, 2003) Version 2: New references and some clarifications adde

Fluctuation, time-correlation function and geometric Phase

We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the ``fast'' system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation between the open-path geometric phase, diagonal elements of the quantum metric tensor and the force-force correlation function is provided and the classical limit of the fluctuation-correlation theorem is also discussed.Comment: Latex, 12 pages, no figures, submitted to J. Phys. A: Math & Ge