A Curious Problem in Quantum Channel Capacity
Amolak Kalra | University of Waterloo
In this talk, I will give an overview of the "threshold problem" in quantum channel capacity. The threshold is the maximum error rate below which reliable quantum communication, that is, non-zero quantum capacity is still possible. In classical information theory, Shannon showed that optimal thresholds are achieved by random codes. In the quantum setting, however, the situation is markedly different: explicit codes have been shown to achieve higher thresholds than random stabilizer codes [1,2]. Though there has been much work in the area since this was first realized, determining which explicit codes yield the best threshold remains open, even for fundamental noise models such as the depolarizing channel. We have been thinking about this problem for the last year or so and the goal of the talk is to discuss what we learned.
This talk is based on joint work with Avantika Agarwal, Alan Bu, Debbie Leung, Luke Schaeffer and Graeme Smith.
[1] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters. “Mixed-state entanglement and quantum error correction.” (1996)
[2] P. W. Shor and J. A. Smolin. "Quantum Error-Correcting Codes Need Not Completely Reveal the Error Syndrome." (1996)
Location
- QNC 3206, in-person
- Online on Zoom
- Meeting ID: 946 1908 0927
- Passcode: 853696