arXiv subjects
Publications and source records attributed to D. Gangopadhyay.
Based on the Schmidt decomposition new convenient thumbrules are obtained to test entanglement of wavefunctions for bipartite qubit and qutrit systems. For the qubit system there is an underlying SU(2) algebra , while the same for a qutrit system is SU(3).
Violation of the Leggett-Garg inequality (LGI) implies quantum phenomena. In this light we establish that the Moreva \textit{et al.} \cite{moreva} experiment demonstrating the Page-Wootter's mechanism \cite{wootters} falls in the quantum domain. An observer outside a 2-photons world does not detect any change in the $2-$photons state,i.e. there is no time parameter for the outside observer. But an observer attached to one of the photons sees the other photon evolving and this means there is an "internal" time. The LGI is violated for the clock photon whose state evolves with the internal time as measured by the system photon. Conditional probabilities in this 2-photons system are computed for both sharp and unsharp measurements. The conditional probability increases for entangled states as obtained by Page and Wootters for both ideal and also unsharp measurements. We discuss how the conditional probabilities can be used to distinguish between massless and massive gravitons. This is important in the context of gravitational waves.
We re-analyse the Bužek-Hillery Universal Quantum Cloning machine protocol and show that it allows better values for fidelity and Hilbert-Schmidt norm than hitherto reported. This higher value for the fidelity is identical to the maximum fidelity of phase covariant quantum cloning of Bruß-Cinchetti-D'Ariano-Macchiavello. This value of fidelity has also been obtained by Niu and Griffiths in their work without machine states. This is the maximum possible fidelity obtainable in $1\rightarrow 2$ qubits cloning. We then describe a different and new state dependent cloning protocol with four machine states where all non-exact copies of input states are taken into account in the output and we use the Hessian method of determining extrema of multivariate functions. The fidelity for the best overall quantum cloning in this protocol is $\bar{F}=0.847$ with an associated von-Neumann entropy of $\bar{S}=0.825$.
The Leggett-Garg inequality (LGI) as a temporal analogue of Bell's inequality, derived using the notion of realism, is applied in a hitherto unexplored context involving the weak interaction induced two-state oscillations of decaying neutral kaons and neutrinos. The maximum violation of LGI obtained from the quantum mechanical results is significantly higher for the oscillating neutrinos compared to that for the kaons. Interestingly, the effect of CP non-invariance for the kaon oscillation is to enhance this violation while, for neutrinos, it is sensitive to the value of the mixing parameter.
We consider the evolution of primordial black holes in a generalyzed Jordan-Brans-Dicke cosmological model where both the Brans-Dicke scalar field and its coupling to gravity are dynamical functions determined from the evolution equations. The evaporation rate for the black holes changes compared to that in standard cosmology. We show that accretion of radiation can proceed effectively in the radiation dominated era. The black hole lifetime shortens for low initial mass, but increases for high initial mass, and is thus considerably modified compared to the case of standard cosmology. We derive a cut-off value for the initial black hole mass, below which primordial black holes evaporate out in the radiation dominated era, and above which they survive beyond the present era.
The general version of the bosonic harmonic oscillator realisation of bosonic q-oscillators is given. It is shown that the currently known realisation is a special case of our general solution. The investigation has been performed at the Laboratory of theoretical Physics,JINR.
We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization scheme.
We find a non-invertible matrix representation for Van der Waerden's colouring theorem for two distinct colours in a one dimensional periodic lattice. Using this,an infinite one dimensional antiferromagnetic Ising system is mapped to a pseudo-ferromagnetic one, thereby relating the couplings. All this is reminiscent of renormalisation group.