  Superposed photon-added and photon-subtracted squeezed-vacuum states exhibit
sub-Planck phase-space structures and metrological potential similar to the
original compass states (superposition of four coherent states), but are more
closely tied to modern experiments. Here, we observe that these compasslike
states are highly susceptible to loss of quantum coherence when placed in
contact with a thermal reservoir; that is, the interaction with the thermal
reservoir causes decoherence, which progressively suppresses the capacity of
these states to exhibit interference traits. We focus on the sub-Planck
structures of these states and find that decoherence effects on these features
are stronger with increasing the average thermal photon number of the
reservoir, the squeezing parameter, or the quantity of added (or subtracted)
photons to the squeezed-vacuum states. Furthermore, we observe that the
sub-Planck structures of the photon-subtracted case survive comparatively
longer in the thermal reservoir than their counterparts in the photon-added
case, and prolonged contact with the thermal reservoir converts these
compasslike states into a classical state.
