Local asymptotic normality for qubit states
- University of Nijmegen, Toernooiveld 1, Postbus 9010, 6500 GL Nijmegen (Netherlands)
- Universite Paris-Sud 11, Departement de Mathematiques, Bat 425, 91405 Orsay Cedex (France)
We consider n identically prepared qubits and study the asymptotic properties of the joint state {rho}{sup xn}. We show that for all individual states, {rho} situated in a local neighborhood of size 1/{radical}(n) of a fixed state {rho}{sup 0}, the joint state converges to a displaced thermal equilibrium state of a quantum harmonic oscillator. The precise meaning of the convergence is that there exists physical transformations T{sub n} (trace preserving quantum channels) which map the qubits states asymptotically close to their corresponding oscillator state, uniformly over all states in the local neighborhood. A few consequences of the main result are derived. We show that the optimal joint measurement in the Bayesian setup is also optimal within the point-wise approach. Moreover, this measurement converges to the heterodyne measurement which is the optimal joint measurement of position and momentum for the quantum oscillator. A problem of local state discrimination is solved using local asymptotic normality.
- OSTI ID:
- 20787208
- Journal Information:
- Physical Review. A, Vol. 73, Issue 5; Other Information: DOI: 10.1103/PhysRevA.73.052108; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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