  An experimental verification of the maximally entangled state ensures that
the constructed state is close to the maximally entangled state, but it does
not guarantee that the state is exactly the same as the maximally entangled
state. Further, the entanglement structure is not uniquely determined in
general probabilistic theories even if we impose that the local subsystems are
fully equal to quantum systems. Therefore, the existence of the maximally
entangled state depends on whether the standard entanglement structure is
valid. To examine this issue, we introduce pseudo standard entanglement
structure as a structure of quantum composite system under natural assumptions
based on the existence of projective measurements and the existence of
approximations of all maximally entangled standard states. Surprisingly, there
exist infinitely many pseudo standard entanglement structures different from
the standard entanglement structure. In our setting, any maximally entangled
state can be arbitrarily approximated by an entangled state that belongs to our
obtained pseudo standard entanglement structure. That is, experimental
verification does not exclude the possibility of our obtained pseudo standard
entanglement structure that is different from the standard entanglement
structure. On the other hand, such pseudo structures never possess global
unitary symmetry, i.e., global unitary symmetry is essential condition for the
standard entanglement structure.
