Optimal tracking for pairs of qubit states
arXiv:0802.3896 · doi:10.1103/PhysRevA.78.012319
Abstract
In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.
15 pages, 8 figures. Extensive revision of text, optimality results extended, other physical applications included
References in corpus (17)
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Quantum Copying: Beyond the No-Cloning Theorem
- Noncommuting mixed states cannot be broadcast
- Quantum cloning
- Optimal Universal and State-Dependent Quantum Cloning
- Quantum Lost and Found
- Optimum Quantum Error Recovery using Semidefinite Programming
- Iterative Optimization of Quantum Error Correcting Codes
- Optimal Non-Universally Covariant Cloning
- Clean Positive Operator Valued Measures
- Quantum Control of a Single Qubit
- On the existence of physical transformations between sets of quantum states
- Optimizing Completely Positive Maps using Semidefinite Programming
- Robust Quantum Error Correction via Convex Optimization
- Suboptimal quantum-error-correcting procedure based on semidefinite programming
- Computational approach to quantum encoder design for purity optimization
- Comment on "Optimum Quantum Error Recovery using Semidefinite Programming"
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- State protection by quantum control before and after noise
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