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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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Seminars and Colloquia

Physics

Allowed region and uncertainty relations for angular momentum observable  
 
Thu, Nov 21, 2019,   03:00 PM at Seminar Hall 31, 2nd Floor, Main Building

Dr. Arun
HRI, Allahabad

Abstract: The expectation values of operators drawn from a single quantum state cannot be outside of a particular region, called their allowed region or the joint numerical range of the operators. Basically, the allowed region is an image of the state space under the Born rule. The maximum-eigenvalue-states---of every linear combination of the operators of interest---are sufficient to generate boundary of the allowed region. In this way, we obtain the numerical range of certain Hermitian operators (observables) that are functions of the angular momentum operators. Especially, we consider here three kinds of functions---combinations of powers of the ladder operators, powers of the angular momentum operators and their anticommutators---and discover the allowed regions of different shapes. By defining some specific concave functions on the joint numerical range, we also achieve tight uncertainty relations for the observables. Overall, we demonstrate how the numerical range and uncertainty relations change as the angular momentum quantum number grows. Finally, we apply the quantum de Finetti theorem by taking a multi-qubit system and attain the allowed regions and tight uncertainty relations in the limit where the quantum number goes to infinity. 

Reference: 
J. Phys. A: Math. Theor. in press https://doi.org/10.1088/1751-8121/ab3ca6 
 
 

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