Noise suppression by quantum control before and after the noise
arXiv:1702.03643 · doi:10.1103/PhysRevA.95.022321
Abstract
We discuss the possibility of protecting the state of a quantum system that goes through noise, by measurements/operations before and after the noise process. The aim is to seek for the optimal protocol that makes the input and output states as close as possible and clarify the role of the measurements therein. We consider two cases, one can perform quantum measurements/operations (i) only after the noise process and (ii) both before and after that. We prove in the two-dimensional Hilbert space that, in the case (i), the noise suppression is essentially impossible for all types of noise and, in the case (ii), the optimal protocol for the depolarizing noise is either the "do nothing" protocol or the "discriminate & reprepare" protocol. These protocols are not "truly quantum" and can be considered as classical. They involve no measurement or only use the measurement outcomes. These results describe the fundamental limitations in quantum mechanics from the viewpoint of control theory. Finally, we conjecture that a statement similar to the case (ii) holds for higher-dimensional Hilbert spaces and present some numerical evidence.
arXiv comment10 pages, 3 figures
References in corpus (14)
- Decoherence Free Subspaces for Quantum Computation
- Dynamical Decoupling of Open Quantum Systems
- Quantum Copying: Beyond the No-Cloning Theorem
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Optimal Cloning of Pure States
- Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
- Decoherence suppression by uncollapsing
- Iterative Optimization of Quantum Error Correcting Codes
- Uncertainty Relation Revisited from Quantum Estimation Theory
- Quantum Control of a Single Qubit
- Feed-forward control for quantum state protection against decoherence
- Suboptimal quantum-error-correcting procedure based on semidefinite programming
- On quantum estimation, quantum cloning and finite quantum de Finetti theorems
- Optimal tracking for pairs of qubit states