In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for unimodular Kac algebras with biprojections and prove Hardy's uncertainty principle in terms of minimizers. 1 Introduction Uncertainty principles for locally compact abelian groups were studied by Hardy [15], Hirschman [16], Beckner [2], Donoho and Stark [9], Smith [23], Tao [24] etc. In 2008, Alagic and Russell [1] proved Donoho-Stark uncertainty principle for compact groups. In 2004,Özaydm and Przebinda [21] characterized the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for locally compact abelian groups.Kac algebras were introduced independently by L.I Vainerman and G.I. Kac [27,28,29] and by Enock and Nest [10,11,12], which generalized locally compact groups and their duals. Furthermore, J. Kustermans and S. Vaes introduced locally compact quantum groups [18]. Recently Crann and Kalantar proved Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for unimodular locally compact quantum groups [7].Subfactor theory also provides a natural framework to study quantum symmetry. The group symmetry is captured by the subfactor arisen from the group crossed product construction. Ocneanu first pointed out the one-to-one correspondence between finite dimensional Kac algebras and finiteindex, depth-two, irreducible subfactors. This correspondence was proved by W. Szymanski [22]. Enock and Nest generalized the correspondence to infinite dimensional compact (or discrete) type Kac algebras and infinite-index, depth-two, irreducible subfactors [14]. In general, a subfactor provides a pair of non-commutative spaces dual to each other and a Fourier transform F between them. It appears to be natural to study Fourier analysis for subfactors.