We investigate the uncertainty principle for two successive projective measurements in terms of Renyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty relations with a lower optimal bound. We compare our relation with other formulations of the uncertainty principle in two-spin observables measured on a pure quantum state of qubit. It is shown that the low bound of our uncertainty relation has better tightness.
['Jun Zhang', 'Yang Zhang', 'Chang-shui Yu']
Rényi entropy uncertainty relation for successive projective measurements