We construct a set of quasi-local measurement operators in 2D CFT, and then
use them to proceed the quantum energy teleportation (QET) protocol and show it
is viable. These measurement operators are constructed out of the projectors
constructed from shadow operators, but further acting on the product of two
spatially separated primary fields. They are equivalently the OPE blocks in the
large central charge limit up to some UV-cutoff dependent normalization but the
associated probabilities of outcomes are UV-cutoff independent. We then adopt
these quantum measurement operators to show that the QET protocol is viable in
general. We also check the CHSH inequality a la OPE blocks.Comment: match the version published on PLB, the main conclusion didn't
change, some techincal details can be found in the previous versio
