Petz recovery map
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In quantum information theory, the Petz recovery map is a quantum map that proposed by Dénes Petz.[1] The Petz recovery map finds applications in various domains, including quantum retrodiction, quantum error correction, and entanglement wedge reconstruction for black hole physics.
Definition
Suppose we have a quantum state which is described by a density operator and a quantum channel , the Petz recovery map is defined as
Notice that is the Hilbert-Schmidt adjoint of .
References
- ^ Petz, Dénes (1986-03-01). "Sufficient subalgebras and the relative entropy of states of a von Neumann algebra" (PDF). Communications in Mathematical Physics. 105 (1): 123–131. doi:10.1007/BF01212345. ISSN 1432-0916.