# The min-entropy of classical quantum combs and some applications

### APA

Smith, I. (2023). The min-entropy of classical quantum combs and some applications. Perimeter Institute. https://pirsa.org/23060052

### MLA

Smith, Isaac. The min-entropy of classical quantum combs and some applications. Perimeter Institute, Jun. 08, 2023, https://pirsa.org/23060052

### BibTex

@misc{ pirsa_PIRSA:23060052, doi = {10.48660/23060052}, url = {https://pirsa.org/23060052}, author = {Smith, Isaac}, keywords = {Quantum Foundations}, language = {en}, title = {The min-entropy of classical quantum combs and some applications}, publisher = {Perimeter Institute}, year = {2023}, month = {jun}, note = {PIRSA:23060052 see, \url{https://pirsa.org}} }

Isaac Smith Leopold-Franzens Universität Innsbruck

## Abstract

It is often the case that interaction with a quantum system does not simply occur between an initial point in time and a final one, but rather over many time steps. In such cases, an interaction at a given time step can have an influence on the dynamics of the system at a much later time. Just as quantum channels model dynamics between two time steps, quantum combs model the more general multi-time dynamics described above, and have accordingly found application in such fields as open quantum systems and quantum cryptography. In this talk, we will consider ensembles of combs indexed by a random variable, dubbed classical-quantum combs, and discuss how much can be learnt about said variable through interacting with the system. We characterise the amount of information gain using the comb min-entropy, an extension of the analogous entropic quantity for quantum states. With combs and the min-entropy in our toolbox, we turn to a number of applications largely inspired by Measurement-Based Quantum Computing (MBQC), including the security analysis of a specific Blind Quantum Computing protocol and some comments regarding learning causal structure.

Zoom Link: https://pitp.zoom.us/j/98315660866?pwd=cWU3RzB6SG9DOGIza1BqV1lqNklvQT09