Berlin 2001 – scientific programme
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Q: Quantenoptik
Q 4: Quantum Information I
Q 4.5: Talk
Monday, April 2, 2001, 16:45–17:00, Audimax
Self-learning measurement of a quantum mechanical two-state system — •Th. Hannemann, Ch. Balzer, D. Reiss, W. Neuhauser, P. E. Toschek, and Ch. Wunderlich — Institut für Laser-Physik, Universität Hamburg, Jungiusstr. 9, 20355 Hamburg
The measurement of a quantum system’s state is of fundamental importance. In particular, determining an arbitrary state of a quantum mechanical two-state system (a qubit) is relevant in the context of quantum information processing [1]. The exact determination of a qubit state would require infinitely many measurements on identically prepared qubits. If a finite number, N of qubits is available, an optimal estimate of the quantum state can be obtained by a simultaneous measurement on all N qubits [2]. We have performed sequential measurements on arbitrary but identically prepared states of a single qubit, the ground state hyperfine levels of electrodynamically trapped 171Yb+, in order to estimate the state of this qubit more economically. The base of measurement is varied during a sequence of N measurements conditioned on the results of previous measurements in this sequence. We compare the experimental efficiency and fidelity of such a self-learning measurement [3] with strategies where the measurement base is either a predetermined orthonormal one or is randomly chosen during a sequence of N measurements.
[1] Special issue of J. Mod. Opt. 44, no. 11 and 12, (1997) on State Preparation and Measurement eds. W. P. Schleich and M. G. Raymer.
[2] A. Peres and W. K. Wootters, Phys. Rev. Lett. 66, 1119 (1991)
[3] D. G. Fischer, S. H. Kienle, and M. Freyberger, Phys. Rev. A 61, 032306-1 (2000).