Universal recoverability of quantum states in tracial von-Neumann algebras

2025/12/09 by Bhattacharya, Saptak
Computer Science · Physics and Astronomy · #46L52 #81P17 #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems

paper · doi:10.48550/arxiv.2512.08418

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss a refinement of quantum data processing inequality for the sandwiched quasi-relative entropy S₂ on a tracial von-Neumann algebra. The main result is a universal recoverability bound with the Petz recovery map, which was previously obtained in the finite dimensional setup.

Citations

• Approximate recoverability and the quantum data processing inequality
• Sufficient statistic and recoverability via Quantum Fisher Information metrics
• Approximate recoverability and relative entropy II: 2-positive channels\n of general v. Neumann algebras
• Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras
• Approximate recovery and relative entropy I. general von Neumann subalgebras
• Recovery map stability for the Data Processing Inequality
• Bures Contractive Channels on Operator Algebras
• Completely positive maps and entropy inequalities

Related

• Approximate recoverability and the quantum data processing inequality
• Approximate recoverability and the quantum data processing inequality
• Approximate recoverability and relative entropy II: 2-positive channels\n of general v. Neumann algebras
• Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras
• Approximate recovery and relative entropy I. general von Neumann subalgebras