Sone, AkiraTouil, AkramMaeda, KenjiCappellaro, PaolaDeffner, Sebastian2025-04-232025-04-232025-03-13https://doi.org/10.48550/arXiv.2503.10400http://hdl.handle.net/11603/38102We elucidate the requirements for quantum operations that achieve environment-assisted invariance (envariance), a symmetry of entanglement. While envariance has traditionally been studied within the framework of local unitary operations, we extend the analysis to consider non-unitary local operations. First, we investigate the conditions imposed on operators acting on pure bipartite entanglement to attain envariance. We show that the local operations must take a direct-sum form in their Kraus operator representations, establishing decoherence-free subspaces. Furthermore, we prove that the unitary operation on the system's subspace uniquely determines the corresponding unitary operator on the environment's subspace. As an immediate consequence, we demonstrate that environment-assisted shortcuts to adiabaticity cannot be achieved through non-unitary operations. In addition, we identify the requirements that local operations must satisfy to ensure that the eternal black hole states remain static in AdS/CFT.11 pagesen-USThis work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.Public Domainhttps://creativecommons.org/publicdomain/mark/1.0/UMBC Quantum Thermodynamics GroupText