Symmetry and Liouville Space Formulation of Decoherence-Free Subsystems

• URL: http://arxiv.org/abs/2507.15506v1
• Date: Mon, 21 Jul 2025 11:17:32 GMT
• Title: Symmetry and Liouville Space Formulation of Decoherence-Free Subsystems
• Authors: Mi-Jung So, Mahn-Soo Choi,
• Abstract summary: We propose a generic and systematic decoherence-free scheme to encode quantum information into an open quantum system.<n>We primarily concern the permutation symmetry in conjunction with the unitary symmetry.<n>We construct a super-Schur basis, which block-diagonalizes the super-operators that describe the noisy quantum channels.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a generic and systematic decoherence-free scheme to encode quantum information into an open quantum system based focusing on symmetry. Under a given symmetry, the Liouville space is decomposed into invariant subspaces characterized by a tensor-product structure. A decoherence-free subsystem is then identified as a factor of the tensor product. Unlike decoherence-free subspaces, which typically require strong symmetries, decoherence-free systems are permitted under less restrictive weak symmetries. Specifically, we primarily concern the permutation symmetry in conjunction with the unitary symmetry and utilize the Schur-Weyl duality, which facilitates numerous efficient and systematic calculations based on the well-established group representation theory. Employing the isomorphism between the Liouville space and the fictitious Hilbert space, we construct a super-Schur basis, which block-diagonalizes the super-operators that describe the noisy quantum channels, both in the Kraus representation and in terms of the quantum master equation. Each block reveals the tensor-product structure and facilitates the identification of physically relevant decoherence-free subsystems under the specified weak symmetry.

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