Geometric Bloch Vector Solution to Minimum Error Discriminations of Mixed Qubit States
arXiv:2108.12299 · doi:10.1007/s11128-023-04080-4
Abstract
We investigate minimum-error (ME) discrimination for mixed qubit states using a geometric approach. By analyzing positive operator-valued measure (POVM) solutions and introducing Lagrange operator , we develop a four-step structured instruction to find for mixed qubit states. Our method covers optimal solutions for two, three, and four mixed qubit states, including a novel result for four qubit states. We introduce geometric-based POVM classes and non-decomposable subsets for constructing optimal solutions, enabling us to find all possible answers for the general problem of minimum-error discrimination for mixed qubit states with arbitrary a priori probabilities.
References in corpus (18)
- Quantum Cryptography
- Unambiguous Discrimination Between Linearly-Independent Quantum States
- Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
- Maximum Confidence Quantum Measurements
- Minimum-error discrimination between three mirror-symmetric states
- Optimal quantum detectors for unambiguous detection of mixed states
- On the conditions for discrimination between quantum states with minimum error
- State discrimination with error margin and its locality
- A family of generalized `pretty good' measurements and the minimal-error pure-state discrimination problems for which they are optimal
- Discrimination with error margin between two states - Case of general occurrence probabilities -
- Measurement does not always aid state discrimination
- Qubit State Discrimination
- Minimum error discrimination problem for pure qubit states
- Optimal discrimination of single-qubit mixed states
- Results in Optimal Discrimination
- New general lower and upper bounds under minimum-error quantum state discrimination
- Parametrization of quantum states and the quantum state discrimination problem
- Minimum-error discrimination of thermal states