Influence of simultaneous weak measurements in Heisenberg uncertainty relation

Abstract

In quantum mechanics the simultaneous measurement of non-commuter variables has attracted widespread attention. Here we propose a scheme through simultaneously weak measurement to achieve the approximated weak values of two non-commuting variables. It can be observed that the measurement error is better than the Heisenberg uncertainty relation. Furthermore, the effects of free Hamiltonian and higher-order expansion of the time evolution operator are considered.