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Helstrom measurement: A nondestructive implementation

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Leuchs,  Gerd
Leuchs Emeritus Group, Emeritus Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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PhysRevA.101.032103.pdf
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Citation

Han, R., Leuchs, G., & Bergou, J. A. (2020). Helstrom measurement: A nondestructive implementation. PHYSICAL REVIEW A, 101(3): 032103. doi:10.1103/PhysRevA.101.032103.


Cite as: https://hdl.handle.net/21.11116/0000-000F-902F-A
Abstract
We discuss an implementation of the minimum error state discrimination measurement, originally introduced by Helstrom [Quantum Detection and Estimation Theory (Academic Press, New York, 1976)]. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first entangled to an ancillary system and the measurement is performed on the ancilla. We show that, by an appropriate choice of the entanglement transformation, the Helstrom bound can be attained. The advantage of this approach is twofold. First, it provides an implementation when the optimal projective measurement cannot be directly performed. For example, in the case of continuous variable states (binary and N phase-shifted coherent signals), the available detection methods, photon counting and homodyning, are insufficient to perform the required cat-state projection. In the case of symmetric states, the square-root measurement is optimal, but it is not easy to perform directly for more than two states. Our approach provides a feasible alternative in both cases. Second, the measurement is nondestructive from the point of view of the original system and one has a certain amount of freedom in designing the post-measurement state, which can then be processed further.