arXiv subjects

K R Parthasarathy

Publications and source records attributed to K R Parthasarathy.

3 recordsLinked to original sources

arXiv2021

Computation of sandwiched relative alpha-entropy of two n-mode gaussian states

A formula for the sandwiched relative $α$-entropy $\widetilde{D}_α(ρ\vert\vertσ)=\frac{1}{α-1}\, \ln\,{\rm Tr}\, \left(σ^{\frac{1-α}{2α}}\,ρ\,σ^{\frac{1-α}{2α}}\right)^α$ for $0 < α< 1$, of two $n$ mode gaussian states $ρ$, $σ$ in the boson Fock space $Γ(\mathbb{C}^n)$ is presented. This computation extensively employs the $\mathcal{E}_2$-parametrization of gaussian states in $Γ(\mathbb{C}^n)$ introduced in J. Math. Phys. {\bf 62} (2021), 022102.

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arXiv2021

A pedagogical note on the computation of relative entropy of two $n$-mode gaussian states

We present a formula for the relative entropy S(rho||sigma) of two n mode gaussian states rho, sigma in the boson Fock space. It is shown that the relative entropy has a classical and a quantum part: The classical part consists of a weighted linear combination of relative Shannon entropies of n pairs of Bernouli trials arising from the thermal state composition of the gaussian states rho and sigma. The quantum part has a sum of n terms, that are functions of the annihilation means and the covariance matrices of 1-mode marginals of the gaussian state $ρ'$, which is equivalent to ρunder a disentangling unitary gaussian symmetry operation of the state $σ$. A generalized formula for the Petz-Renyi relative entropy S_alpha(rho||sigma) for gaussian states ρ, σis also presented. Furthermore it is shown that the Petz-Renyi relative entropy converges to the limit S(rho||sigma) as alpha increases to 1.

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arXiv2001

An Entropic Uncertainty Principle for Quantum Measurements

The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result includes not only the case of projectivmeasurements (or equivalently, observables) exhibiting degeneracy but also an uncertainty principle for a single measurement.

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