Southwest Quantum Information and Technology

Recoverability in quantum information theory

Presenting Author: Mark Wilde, (Louisiana)

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Furthermore, the recovery operation has an explicit form and is universal, in the sense that it depends only on the channel and the state which can be perfectly recovered. Our proof method relies on complex interpolation and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This submission is based on the following two papers: [1] Mark M. Wilde. "Recoverability in quantum information theory," Proceedings of the Royal Society A, vol. 471, no. 2182, page 20150338 October 2015 [2] Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, Andreas Winter. "Universal recovery from a decrease of quantum relative entropy", arXiv:1509.07127.

(Session 9c : Friday from 4:00 pm - 4:30 pm)