Related papers: Connecting Quantum Tomography and Quantum Retrodiction

Connecting Quantum Tomography and Quantum Retrodiction

URL: http://arxiv.org/abs/2606.23777v1
Date: Mon, 22 Jun 2026 18:00:00 GMT
Title: Connecting Quantum Tomography and Quantum Retrodiction
Abstract summary: We show that tomography reconstructs quantum states from measurement data, whereas retrodiction infers past quantum states from observed outcomes.<n>We prove that the Petz recovery map associated with a measurement channel is precisely the gradient update of the log-likelihood used in maximum-likelihood tomography.
Score: 0.20999222360659606
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks: tomography reconstructs quantum states from measurement data, whereas retrodiction infers past quantum states from observed outcomes. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map associated with a measurement channel is precisely the gradient update of the log-likelihood used in maximum-likelihood tomography. Consequently, repeated applications of the Petz map monotonically increase the likelihood. Extending beyond measurement channels, we derive a noncommutative generalization of the Petz map from the gradient of a generalized likelihood for arbitrary quantum channels. The resulting iterative procedure maximizes the likelihood and provides a general framework for quantum tomography, establishing a direct bridge between retrodiction, recovery maps, and statistical inference.

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