  We present the first quantum anonymous notification (QAN) protocol that
introduces anonymity and paves the way for anonymous secure quantum
communication in quantum networks. QAN protocol has applications ranging from
multiparty quantum computation to quantum internet. We utilize the QAN protocol
to propose an anonymous quantum private comparison protocol in an $n$-node
quantum network. This protocol can compare private information of any $2 \leq k
\leq n$ parties with the help of the remaining $n-k$ parties and a semi-honest
third party. These protocols feature a traceless property, i.e., encoding
operations cannot be traced back to their originating sources. Security
analysis shows that this protocol is robust against external adversaries and
malicious participants.
