Quantum Cramér–Rao bound
The quantum Cramér–Rao bound is the quantum analogue of the classical Cramér–Rao bound. It bounds the achievable precision in parameter estimation with a quantum system:
where is the number of independent repetitions, and is the quantum Fisher information.[1][2]
Here, is the state of the system and is the Hamiltonian of the system. We consider a unitary dynamics of the type
where is the initial state of the system. Here, is the parameter to be estimated based on measurements on
References[]
- ^ Braunstein, Samuel L.; Caves, Carlton M. (1994-05-30). "Statistical distance and the geometry of quantum states". Physical Review Letters. American Physical Society (APS). 72 (22): 3439–3443. doi:10.1103/physrevlett.72.3439. ISSN 0031-9007. PMID 10056200.
- ^ Braunstein, Samuel L.; Caves, Carlton M.; Milburn, G.J. (April 1996). "Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance". Annals of Physics. 247 (1): 135–173. doi:10.1006/aphy.1996.0040.
Categories:
- Quantum information science
- Quantum mechanics
- Quantum optics