aiqbench analysis
This paper is a theoretical study of quantum channels: when partial recovery of lost quantum information via the Petz map can be implemented with the same hardware as the forward noise process. Its main results are exact conditions that require time-sensitive control of an ancilla, approximate conditions that drop that requirement, and Lindbladian conditions under a random-time collision model. For quantum computing readers, the practical value lies in knowing when error-recovery operations can be built cheaply from the existing dynamics, but the work is foundational and has no near-term hardware demonstration.
Exact and approximate conditions of tabletop reversibility: when is Petz recovery cost-free?
arXiv:2510.26895v2 Announce Type: replace Abstract: Channels $\mathcal{N}$ that describe open quantum dynamics are inherently irreversible: it is impossible to undo their effect completely, but one can study partial recovery of the information. The Petz recovery map $\hat{\mathcal{N}}_{\gamma}^{(\texttt{P})}$ is a systematic construction that depends only on $\mathcal{N}$ and on a reference state $\gamma$, which will be recovered exactly. If the real input state was different from $\gamma$, the recovery is partial, with a guarantee of near-optimality. Generically, an implementation of the Petz recovery map would look very different from the implementation of the channel. It is natural to study under which conditions the two maps require similar or even identical resources. The noisy forward channel $\mathcal{N}$ is called ``tabletop time-reversible'' for a given $\gamma$ when the corresponding Petz recovery map is realizable in such a way. First, we study the exact tabletop reversibility (TTR) conditions. We show in particular that a time-sensitive control of an ancilla system is needed. Second, we present the approximate TTR conditions, which do not require such a time-sensitive control. Third, we derive Lindbladian TTR conditions under a random-time collision model.
Title:Exact and approximate conditions of tabletop reversibility: when is Petz recovery cost-free?
Abstract:Channels $\mathcal{N}$ that describe open quantum dynamics are inherently irreversible: it is impossible to undo their effect completely, but one can study partial recovery of the information. The Petz recovery map $\hat{\mathcal{N}}_{\gamma}^{(\texttt{P})}$ is a systematic construction that depends only on $\mathcal{N}$ and on a reference state $\gamma$, which will be recovered exactly. If the real input state was different from $\gamma$, the recovery is partial, with a guarantee of near-optimality. Generically, an implementation of the Petz recovery map would look very different from the implementation of the channel. It is natural to study under which conditions the two maps require similar or even identical resources. The noisy forward channel $\mathcal{N}$ is called ``tabletop time-reversible'' for a given $\gamma$ when the corresponding Petz recovery map is realizable in such a way. First, we study the exact tabletop reversibility (TTR) conditions. We show in particular that a time-sensitive control of an ancilla system is needed. Second, we present the approximate TTR conditions, which do not require such a time-sensitive control. Third, we derive Lindbladian TTR conditions under a random-time collision model.
29 pages, 5 figures. Added applications
arXiv:2510.26895 [quant-ph]
(or arXiv:2510.26895v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2510.26895 Focus to learn more arXiv-issued DOI via DataCite
Quantum Sci. Technol. 11 045057 (2026)
https://doi.org/10.1088/2058-9565/aea92d Focus to learn more DOI(s) linking to related resources
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