Chennai Mathematical Institute


3.30 PM, Seminar Hall
Incompatibility and complementarity in quantum information theory

Prabha Mandayam
Institute of Mathematical Sciences, Chennai.


Heisenberg's celebrated uncertainty principle was the first quantitative expression of the incompatibility of a pair of observables. Recently, entropic uncertainty relations(EURs) have been used to provide a better characterization of incompatibility for any set of measurements. It is known that this measure of incompatibility is maximized when the measurement bases are mutually unbiased. Mutually unbiased bases (MUBs) are thus at the heart of theoretical investigations into complementarity in quantum theory. Familiar examples of MUBs are provided by the eigenbases of the Pauli operators.

Despite the conceptual importance of these ideas in quantum foundations and quantum information theory, the interplay between incompatibility and complementarity is not fully understood even for finite-dimensional quantum systems. In this talk, we present two recent results that make some progress in this regard: (a) an operationally motivated measure of incompatibility that addresses the shortcomings of the EUR formalism (b) a novel construction of unextendible sets of MUBs for n-qubit systems.

Based on : Phys Rev A 87, 042120 (2013); Quant Inf Comp 14, 0823 (2014).