No-go theorem for environment-assisted invariance in non-unitary dynamics
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Sone, Akira, Akram Touil, Kenji Maeda, Paola Cappellaro, and Sebastian Deffner. “No-Go Theorem for Environment-Assisted Invariance in Non-Unitary Dynamics.” New Journal of Physics 27, no. 6 (2025): 064509. https://doi.org/10.1088/1367-2630/ade46f.
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This 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.
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Abstract
We 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 this also holds for the multipartite scenario. As an immediate consequence, we demonstrate that environment-assisted shortcuts to adiabaticity cannot be achieved through non-unitary operations. In addition, we show that the static condition of the eternal black hole in AdS/CFT is violated when the CFTs are coupled to the external baths.