Decoherence dynamics across sub-Planckian to arbitrary scales using kitten states

Environmental decoherence occurs when a quantum system interacts with its surroundings, progressively reducing quantum interference and coherence, complicating the preservation of critical quantum properties over time, especially during experimental implementation. The effect of decoherence varies depending on the phase-space features of quantum states, which are theoretically characterized by the Wigner phase space and appear at different scales. We explore the compass state and its photon-added and photon-subtracted variants, each of which exhibits phase-space features with dimensions beyond the Planck scale, making them suitable for quantum sensing applications. We investigate the interaction of these states with a heat reservoir by employing a range of well-established theoretical techniques, revealing a clear tradeoff between the degree of fineness in the smallest features, such as the sub-Planck structure, and the extent of decoherence. Specifically, increasing the parameters enhances sub-Planck precision in phase space, concomitantly amplifying the fragility of these compass states to undesired decoherence. Our general illustration, validated through these compass states, also applies to any pure quantum state interacting with the considered heat reservoir, exhibiting enhanced sustainability of features at larger phase-space extensions.