Tight state-independent uncertainty relations for qubits

Abstract

The well-known Robertson-Schrödinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit measurements that completely characterise the obtainable uncertainty values. This approach can give such relations for any number of observables, and we do so explicitly for arbitrary pairs and triples of qubit measurements. We show how these relations can be transformed into equivalent tight entropic uncertainty relations. More generally, they can be expressed in terms of any measure of uncertainty that can be written as a function of the expectation value of the observable for a given state.

14 pages, 3 figures

References in corpus (4)

• Entropic Uncertainty Relations and their Applications
• Bloch vectors for qudits
• Stronger uncertainty relations for the sum of variances
• Improved bounds in entropic uncertainty relations

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