Inferred-variance uncertainty relations in the presence of quantum entanglement

Abstract

Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum entanglement on uncertainty relations was not probed. Berta et al. [Nat. Phys. 6, 659 (2010)] removed this gap by deriving a conditional-entropic uncertainty relation in the presence of quantum entanglement. In the same spirit, using inferred-variance, we formulate uncertainty relations in the presence of entanglement for general two-qubit systems and arbitrary observables. We derive lower bounds for the sum and product inferred-variance uncertainty relations. Strikingly, we can write the lower bounds of these inferred-variance uncertainty relations in terms of measures of entanglement of two-qubit states, as characterized by concurrence, or $G$ function. The presence of entanglement in the lower bound of inferred-variance uncertainty relation is quite distinctive. We also explore the violation of local uncertainty relations in this context and an interference experiment. Furthermore, we discuss possible applications of these uncertainty relations.