  Cat states, with their unique phase-space interference properties, are ideal
candidates for understanding fundamental principles of quantum mechanics and
performing key quantum information processing tasks. However, they are highly
susceptible to photon loss, which inevitably diminishes their quantum
non-Gaussian features. Here, we protect these non-Gaussian features against
photon loss by compressing the phase-space distribution of a cat state. We
achieve this compression with a deterministic technique based on the echo
conditional displacement operation in a circuit QED device. We present a
versatile technique for creating robust non-Gaussian continuous-variable
resource states in a highly linear bosonic mode and manipulating their
phase-space distribution to achieve enhanced resilience against photon loss.
Compressed cat states offer an attractive avenue for obtaining new insights
into quantum foundations and quantum metrology, and for developing inherently
more protected bosonic codewords for quantum error correction.
