  It is known that multiphoton states can be protected from decoherence due to
a passive loss channel by applying noiseless attenuation before and noiseless
amplification after the channel. In this work, we propose the combined use of
multiphoton subtraction on four-component cat codes and teleamplification to
effectively suppress errors under detection and environmental losses. The
back-action from multiphoton subtraction modifies the encoded qubit encoded on
cat states by suppressing the higher photon numbers, while simultaneously
ensuring that the original qubit can be recovered effectively through
teleamplification followed by error correction, thus preserving its quantum
information. With realistic photon subtraction and teleamplification-based
scheme followed by optimal error-correcting maps, one can achieve a worst-case
fidelity (over all encoded pure states) of over $93.5\%$ ($82\%$ with only
noisy teleamplification) at a minimum success probability of about $3.42\%$,
under a $10\%$ environmental-loss rate, $95\%$ detector efficiency and
sufficiently large cat states with the coherent-state amplitudes of 2. This
sets a promising standard for combating large passive losses in
quantum-information tasks in the noisy intermediate-scale quantum (NISQ) era,
such as direct quantum communication or the storage of encoded qubits on the
photonic platform.
