Quantum key distribution protocols with and without rotational

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We explore the role of rotational symmetry of quantum key distribution
(QKD) protocols in their security. Specifically, in the first part of the
talk, we consider a generalized QKD protocol with discrete rotational
symmetry. Note that, before our work, each QKD protocol seems to have a
different security proof. Given that the techniques of those proofs are
similar, it will be interesting to have a unified proof for QKD protocols
with symmetry (e.g., the BB84 protocol and the SARG04 protocol). This is
exactly what we achieve in our work. We show that rotational symmetry
plays an important role in the unified security proof of QKD protocols
with symmetry, leading to simple and structural security relations. In the
second part, we consider a QKD protocol that does not possess rotational
symmetry and analyze its security. Interestingly, even without any
rotational symmetry, this protocol can still be proven secure. However,
the security relation is not as simple as those in the first part, due to
the lack of symmetry. Therefore, although rotational symmetry is not
required in a QKD protocol to ensure its security, rotational symmetry
does provide significant simplification in the security analysis, leading
to simple security relations.