[quantum-info] IQC Mar 20 Special Seminar - Vlad Gheorghiu

Matthew Fries mfries at uwaterloo.ca
Wed Mar 20 07:23:03 EDT 2013


Seminar

Institute for Quantum Computing

Wednesday, 20 March 2013 at 2:00PM

QNC 1103

Universal Uncertainty Relations

Vlad Gheorghiu

University of Calgary

Uncertainty relations lie at the core of quantum mechanics and are a direct manifestation of the non-commutative structure of the theory. They impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs *entropic measures* to quantify the lack of knowledge associated with measuring non-commuting observables. However there is no fundamental reason for using entropies as quantifiers; any functional relation that characterizes the uncertainty of the measurement outcomes defines an uncertainty relation. Starting from a simple requirement any reasonable measure of uncertainty has to satisfy, we show that Schur-concave functions are the most general uncertainty quantifiers. We then discover a novel fine-grained uncertainty relation written in terms of a majorization relation, which generates an infinite family of distinct scalar uncertainty relations via the application of uncertainty quantifiers. Our relation is universally valid and captures the essence of uncertainty in quantum mechanics.
This work is in collaboration with Gilad Gour (IQST) and Shmuel Friedland (Univ. of Illinois at Chicago)



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