Petz recovery maps for qudit quantum channels
arXiv:2305.11658 · doi:10.1016/j.physleta.2024.129583
Abstract
This study delves into the efficacy of the Petz recovery map within the context of two paradigmatic quantum channels: dephasing and amplitude-damping. While prior investigations have predominantly focused on qubits, our research extends this inquiry to higher-dimensional systems. We introduce a novel, state-independent framework based on the Choi-Jamiołkowski isomorphism to evaluate the performance of the Petz map. By analyzing different channels and the (non-)unital nature of these processes, we emphasize the pivotal role of the reference state selection in determining the map's effectiveness. Furthermore, our analysis underscores the considerable impact of suboptimal choices on performance, prompting a broader consideration of factors such as system dimensionality.
10 pages, 10 figures, V2
References in corpus (20)
- Advances in High Dimensional Quantum Entanglement
- The Bloch Vector for N-Level Systems
- Bloch vectors for qudits
- Entanglement Certification From Theory to Experiment
- Reversing quantum dynamics with near-optimal quantum and classical fidelity
- Quantum Steering Ellipsoids
- Randomized Benchmarking with Confidence
- Monotonicity of quantum relative entropy revisited
- Average fidelity between random quantum states
- Universal recovery maps and approximate sufficiency of quantum relative entropy
- Quantum algorithm for Petz recovery channels and pretty good measurements
- Fluctuation theorems from Bayesian retrodiction
- Experimental simulation of decoherence in photonics qudits
- Quantum capacity analysis of multi-level amplitude damping channels
- Reversing Lindblad Dynamics via Continuous Petz Recovery Map
- Axioms for retrodiction: achieving time-reversal symmetry with a prior
- An Invitation to Quantum Channels
- State retrieval beyond Bayes' retrodiction
- Measure of not-completely-positive qubit maps: the general case
- Fluctuation Theorems with Retrodiction rather than Reverse Processes