Talks

In this talk, I will describe how ideas from geometry and combinatorics can help us understand the mathematical and physical properties of cosmological integrals. From efficiently deriving canonical differential equations to a systematic method for finding a minimal basis for the physical subspace. Time permitting, I will also comment on how geometry and combinatorics control the zeros of cosmological integrands.

I will introduce how to incorporate loop contributions into positivity bounds in a massless scalar theory with shift symmetry. The allowed region of Wilson coefficients is called the EFT-hedron. With loop contributions, the n=4 null constraint, which plays an important role in determining the allowed region for g3–g4 (the Wilson coefficients of dimension-10 and dimension-12 operators, respectively), is modified. This modification of the null constraint reveals new features of the EFT-hedron. We obtained a much stronger bound for g2 (the Wilson coefficient of dimension-8 operators) without using the full unitarity condition. Furthermore, we found a negative g4, which is not possible under the tree-level bound. It would be interesting to generalize our method to more complicated theory and test our results.

Continuous variable (CV) systems play an important role in quantum foundations and quantum information processing, especially because of their quantum optical realization. Gaussian states of CV systems, on the one hand have non-trivial quantum properties, and on the other hand, can be realized in the laboratory.  There are non-Gaussian states which can be obtained from Gaussian states via physically realizable operations and these too can be useful in enhancing  non-classicality and improving the performance of quantum information processing protocols.  In the talk, I will  introduce CV systems and their Gaussian and non-Gaussian states. The violation of Bell-type inequalities using CV systems will be discussed. Quantum key distribution protocols and quantum teleportation schemes using Gaussian and non-Gaussian states will also be taken up.