  Sensitivity of gravitational-wave detectors (GWDs) is constrained at low
frequencies by quantum radiation-pressure noise, a manifestation of the
measurement's back action. One strategy to mitigate this back action involves
employing variational readout, which entails cross-correlating the measurement
shot noise with radiation-pressure noise. Prior research has demonstrated that
variational readout in GWDs can be accomplished through the use of a filter
cavity. However, current gravitational-wave detectors necessitate filter cavity
lengths on the order of $\sim 100$ meters, with future detectors anticipated to
reach lengths of a few kilometers. This paper introduces a novel approach to
variational readout utilizing principle of quantum teleportation, which
eliminates the need for a filter cavity. *This document will not be published
any journals, since it turned out to be not very useful for the real detectors.
The main reason is that one does not need the EPR entanglement to obtain the
same result, which does not even shows true variational readout. In other
words, both schemes do not exceed the EPR squeezing. Nevertheless this document
will be uploaded to stimulate discussions how to realize "true" back action
evasion, such as variational readout or speed meter, via quantum entanglement.
