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

• Published in: New journal of physics Vol. 27; no. 6; pp. 64509 - 64523
• Main Authors: Sone, Akira, Touil, Akram, Maeda, Kenji, Cappellaro, Paola, Deffner, Sebastian
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.06.2025
• Subjects: AdS/CFT; decoherence-free subspace; envariance; Invariance; Physics; shortcuts to adiabaticity; Subspaces; Symmetry
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ade46f

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.