All Dates/Times are Australian Eastern Standard Time (AEST)

# Technical Program

## Paper Detail

 Paper ID D3-S7-T4.4 Paper Title Permutation-invariant quantum coding for quantum deletion channels Authors Yingkai Ouyang, National University of Singapore, Singapore Session D3-S7-T4: Quantum Codes & Channels Chaired Session: Thursday, 15 July, 00:00 - 00:20 Engagement Session: Thursday, 15 July, 00:20 - 00:40 Abstract Quantum deletions, which are harder to correct than erasure errors, occur in many realistic settings. It is therefore pertinent to develop quantum coding schemes for quantum deletion channels. To date, not much is known about which explicit quantum error correction codes can combat quantum deletions. We note that {\em any} permutation-invariant quantum code that has a distance of $t+1$ can correct $t$ quantum deletions for any positive integer $t$ in both the qubit and the qudit setting. Leveraging on coding properties of permutation-invariant quantum codes under erasure errors, we derive corresponding coding bounds for permutation-invariant quantum codes under quantum deletions. We focus our attention on a specific family of $N$-qubit permutation-invariant quantum codes, which we call shifted gnu codes. The main result of this work is that their encoding and decoding algorithms can be performed in $O(N)$ and $O(N^2)$.