Mixed-quantum-state detection with inconclusive results
- Technion-Israel Institute of Technology, Technion City, Haifa 32000 (Israel)
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We show that the design of the optimal detector can be formulated as a semidefinite programming problem, and derive a set of necessary and sufficient conditions for an optimal measurement. We then develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU, respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a reduced size semidefinite programming problem.
- OSTI ID:
- 20633954
- Journal Information:
- Physical Review. A, Vol. 67, Issue 4; Other Information: DOI: 10.1103/PhysRevA.67.042309; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Efficient optimal minimum error discrimination of symmetric quantum states
Complete hierarchies of efficient approximations to problems in entanglement theory