BELT: Block Encoding of Linear Transformation on Density Matrices

• URL: http://arxiv.org/abs/2508.12858v1
• Date: Mon, 18 Aug 2025 11:54:40 GMT
• Title: BELT: Block Encoding of Linear Transformation on Density Matrices
• Authors: Fuchuan Wei, Rundi Lu, Yuguo Shao, Junfeng Li, Jin-Peng Liu, Zhengwei Liu,
• Abstract summary: We introduce Block.<n>$ of Linear Transformation (BELT), a systematic protocol that simulates arbitrary linear maps.<n>BELT allows the manipulation and extraction of information about $mathcalN(rho)$ through coherent quantum evolution.<n>BELT finds applications in entanglement detection, quantum channel inversion, and pseudo-differential operators.
• Score: 6.803593864509459
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Linear maps that are not completely positive play a crucial role in the study of quantum information, yet their non-completely positive nature renders them challenging to realize physically. The core difficulty lies in the fact that when acting such a map $\mathcal{N}$ on a state $\rho$, $\mathcal{N}(\rho)$ may not correspond to a valid density matrix, making it difficult to prepare directly in a physical system. We introduce Block Encoding of Linear Transformation (BELT), a systematic protocol that simulates arbitrary linear maps by embedding the output $\mathcal{N}(\rho)$ into a block of a unitary operator. BELT enables the manipulation and extraction of information about $\mathcal{N}(\rho)$ through coherent quantum evolution. Notably, BELT accommodates maps that fall outside the scope of quantum singular value transformation, such as the transpose map. BELT finds applications in entanglement detection, quantum channel inversion, and simulating pseudo-differential operators, and demonstrates improved sample complexity compared to protocols based on Hermitian-preserving map exponentiation.

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