|| One-Shot Quantum State Redistribution and Quantum Markov Chains
||Anurag Anshu, University of California, Berkeley and Simons Institute for the Theory of Computing, United States; Shima Bab Hadiashar, University of Waterloo, Canada; Rahul Jain, National University of Singapore, Singapore; Ashwin Nayak, University of Waterloo, Canada; Dave Touchette, University of Sherbrooke, Canada|
||D1-S2-T4: Quantum Shannon Theory
||Monday, 12 July, 22:20 - 22:40
||Monday, 12 July, 22:40 - 23:00
We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect one-shot quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution.