Mutually Unbiased Measurements in Quantum Information Theory

Explore the concept of mutually unbiased measurements in quantum theory through this 57-minute colloquium presented by Dr Máté Farkas from ICFO Barcelona. Delve into the complementary nature of mutually unbiased bases (MUBs) and their significance in quantum information processing tasks. Examine examples such as photon polarisation and spin measurements, and understand their applications in quantum state tomography, communication, Bell inequalities, and cryptography. Investigate the characteristics of mutually unbiased measurements (MUMs), comparing their similarities and differences with MUBs. Learn about Bell nonlocality, device-independent quantum key distribution, and optimization techniques for lower and upper bounds. Gain insights into the fundamental principles of quantum measurements and their practical implications in the field of quantum information.

Intro
Measurements in quantum information theory
General case: density operators and POVMs
Mutually unbiased bases (MUBs)
MUBS in quantum information
MUBs and complementarity
Mutually unbiased measurements (MUMs)
MUM characterisation
Similarities between MUBs and MUMS
Differences between MUBs and MUMS
Witnessing Bell nonlocality: Bell inequalities
Bell inequalities for d-outcome MUMS
Device-independent quantum key distribution
Lower bounds: heuristic optimisation
Summary
Upper bounds: Moroder hierarchy