No-go theorem for environment-assisted invariance in non-unitary dynamics

• URL: http://arxiv.org/abs/2503.10400v2
• Date: Tue, 01 Apr 2025 17:54:31 GMT
• Title: No-go theorem for environment-assisted invariance in non-unitary dynamics
• Abstract summary: We show that environment-assisted shortcuts to adiabaticity cannot be achieved through non-unitary operations.<n>We also show that the static condition of the eternal black hole in AdS/CFT is violated when the CFTs are coupled to the external baths.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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