  In classical information theory, channel capacity quantifies the maximum
number of messages that can be reliably transmitted using shared information.
An equivalent concept, termed uncommon information, represents the number of
messages required to be exchanged to completely share all information in
common. However, this equivalence does not extend to quantum information
theory. Specifically, quantum uncommon information is operationally defined as
the minimal amount of entanglement required for the quantum communication task
of quantum state exchange, where two parties exchange quantum states to share
all quantum messages in common. Currently, an analytical closed-form expression
for the quantum uncommon information remains undetermined. In this work, by
investigating underlying characterization of the quantum uncommon information,
we derive improved bounds on it. To obtain these bounds, we develop a subspace
exchange strategy that leverages a common subspace of two parties to identify
the unnecessary qubits for exchange. We also consider a referee-assisted
exchange, wherein a referee aids two parties in efficiently performing the
quantum state exchange. Our bounds provide more precise estimations for the
quantum uncommon information. Furthermore, we demonstrate that the subspace
technique is a versatile tool for characterizing uncommon information not only
in the bipartite scenario but also in various multi-partite ones.
