the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

It has been known since the earliest days of quantum field theory (QFT) that infrared divergences arise in scattering with massless fields. These are manifestations memory effect: At order $1/r$ a generically will not return to same value at late retarded times ($u\ensuremath{\rightarrow}+\ensuremath{\infty}$) as it had early ($u\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$). There...

quantum theory poses itself to be a challenging counterpart to the intelligent design argument. quantum physics founded upon uncertainty, probability and statistics has exerted great influence since its inception on the philosophical thinking of man. the findings of this theory has helped bring about a dramatic transformation in the notion of ‘order in nature.’ in modern physics, it is hardly p...