Violating the Heisenberg Uncertainty Relation: An Entangled Approach

Since Heisenberg introduced the relation p1 q1 $\sim$ h in 1927, great effort has been made to refine this expression and better understand its meaning. Recent work has shown that the term ``uncertainty'' applies to two different quantum properties. The first pertains to preparation uncertainty, the principle that one cannot prepare a quantum system such that two incompatible observables are arbitrarily well-defined. The second pertains to measurement uncertainty, the principle that the measurement with a certain degree of accuracy of one observable disturbs the subsequent measurement of a second incompatible observable. We review recent experiments showing evidence for a violation of the measurement uncertainty. We illustrate the different relations with examples using spin measurements. We explore how entanglement affects the difference components of the proposed relations.