  Built on our observation that entangling surfaces of the boundary field
theory are great co-dimension one spheres in the context of DS/dS
correspondence, we study some information theoretic quantities of the field
theory dual intensively using holographic proposals. We will focus on
entanglement entropy (EE), entanglement of purification (EoP) and complexity.
Several fundamental observations and analysis are provided. For EE, we focus on
its scaling behavior, which indicates the nature of the relevant degrees of
freedom. Moreover, we find that EE provides us with important information of
the energy spectrum in pure dS and it also leads us to the speculation that the
field theory dual is chaotic or non-integrable. For EoP, an interesting
phenomenon we call "Entanglement of Purification Jump" is observed according to
which we propose two puzzles regarding EoP and EE in the context of dS
holography. For complexity, we find that the Complexity=Volume proposal does
not provide a well-defined way to compute complexity for pure dS. However, it
does provide a well-defined way to compute complexity in the
$T\bar{T}+\Lambda_{2}$ deformed case. At the end, we will use the surface/state
correspondence to resolve all the puzzles and hence reach a consistent
information theoretic picture of dS holography. Moreover, we will provide
evidence for our former proposal that the $T\bar{T}+\cdots$ deformations are
operating quantum circuits and study the non-locality of the field theory
algebra suggested by the surface/state correspondence.
