  Recently proposed "critical" higher-derivative gravities in $AdS_D$ $D>3$ are
expected to carry logarithmic representation of the Anti de Sitter isometry
group. In this note, we quantize linear fluctuations of these critical
gravities, which are known to be either identical with linear fluctuations of
Einstein's gravity or else satisfy logarithmic boundary conditions at spacial
infinity. We identify the scalar product uniquely defined by the symplectic
structure implied by the classical action, and show that it does not posses
null vectors. Instead, we show that the scalar product between any two Einstein
modes vanishes, while the scalar product of an Einstein mode with a logarithmic
mode is generically nonzero. This is the basic property of logarithmic
representation that makes them neither unitary nor unitarizable.
