  Schmidt rank of bipartite pure state serves as a testimony of entanglement.
It is a monotone under local operation + classical communications (LOCC) and
puts restrictions in LOCC convertibility of quantum states. Identifying the
Schmidt rank of an unknown quantum state therefore seek importance from
information theoretic perspective. In this work it is shown that a modified
version of Hardy's argument, which reveals the contradiction of quantum theory
with local realism, turns out to be useful for inspecting the minimal Schmidt
rank of the unknown state and hence also the minimal dimension of the system.
Use of Hardy's test in such task provides a practical advantage: the Schmidt
rank can be determined without knowing the detailed functioning of the
experimental devices i.e., Hardy's test suffices to be a device independent
Schmidt rank witness.
