Entropic uncertainties for joint quantum measurements

Abstract

We investigate the uncertainty associated with a joint quantum measurement of two components of spin of a spin-1/2 particle and quantify this in terms of entropy. We consider two entropic quantities: the joint entropy and the sum of the marginal entropies, and obtain lower bounds for each of these quantities. For the case of joint measurements where we measure each spin observable equally well, these lower bounds are tight.

13 pages, introduction re-written and extended discussion of results

References in corpus (8)

• Prior information: how to circumvent the standard joint-measurement uncertainty relation
• An optimal entropic uncertainty relation in a two-dimensional Hilbert space
• Coexistence of qubit effects
• Joint measurements of spin, operational locality and uncertainty
• Higher entropic uncertainty relations for anti-commuting observables
• Uncertainty Relations for Positive Operator Valued Measures
• Cloning and Joint Measurements of Incompatible Components of Spin
• Estimating the expectation values of spin 1/2 observables with finite resources

Cited by in corpus (4)

• Duality relations in a two-path interferometer with an asymmetric beam splitter
• Entropic measures of joint uncertainty: effects of lack of majorization
• Approximating incompatible von Neumann measurements simultaneously
• Characterization of measurement uncertainties using the correlations between local outcomes obtained from maximally entangled pairs