  Here we show that, if we insert context dependent unitary evolutions (which
can be achieved via post selection) into spatial (i.e., normal) Bell-CHSH test,
then it is possible to violate space-time Bell-CHSH inequality maximally (i.e.,
up to $4$). However this does not contradict Tsirelson quantum bound
($2\sqrt{2}$), as the latter has been derived without taking into consideration
context dependent unitary evolutions and/or post selection. As an important
application, this leads to a more efficient quantum key distribution protocol.
