  Density matrices are the most general descriptions of quantum states,
covering both pure and mixed states. Positive semidefiniteness is a physical
requirement of density matrices, imposing nonnegative probabilities of
measuring physical values. Separately, nonlocality is a property shared by some
bipartite quantum systems, indicating a correlation of the component parts that
cannot be described by local classical variables. In this work, we show that
breaking the positive-semidefinite requirement and allowing states with a
negative minimal eigenvalue arbitrarily close to zero, allows for the
construction of states that are nonlocal under one component labelling but
local when the labelling is interchanged. This is an observer-dependent
nonlocality, showing the connection between nonlocal objectivism and negative
quasi-probabilities.
