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Scheme for implementing dichotomic quantum measurements through non-ideal Stern–Gerlach setup

A Correction to this article was published on 25 June 2018

This article has been updated


Positive operator-valued measures (POVMs) are the most general class of quantum measurements. There has been significant interest in the theory and possible implementations of generalized measurement in the form of POVMs. Such measurements are useful in the context of cryptography, state discrimination, preparation of arbitrary states and for monitoring quantum dynamics. As argued by Busch (Phys. Rev. D 33(8):2253–2261, 1986), the most general dichotomic POVMs are characterized by two real parameters known as sharpness and biasedness of measurements. Unbiased unsharp measurements have been demonstrated experimentally, for example using the quantum feedback stabilization of number of photons in a microwave cavity (Sayrin et al. Nat. (Lond.) 477:73, 2011), as well as in the context of energy measurements of trapped ions. However, to the best of our knowledge, unsharp biased measurements have not yet been probed experimentally. For this purpose, we propose in this work, an empirically realizable scheme using non-ideal Stern–Gerlach setup. The relevant formulation involves identifying one-to-one correspondences between biasedness, unsharpness of measurements and the key parameters characterizing non-ideal Stern–Gerlach setup. This study has the potential to be useful for the implementations of various quantum information tasks as well as for experiments related to quantum foundational studies based on POVMs.

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  • 25 June 2018

    The value of the non-ideal parameter α has been incorrectly stated to be between 0 and 1 after derivation of the time evolution of the corrupt Gaussian distribution in Section 6.2.


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Correspondence to Soumik Ghosh.

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Adhikary, A., Ghosh, S. Scheme for implementing dichotomic quantum measurements through non-ideal Stern–Gerlach setup. Quantum Stud.: Math. Found. 6, 107–120 (2019).

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  • Stern–Gerlach experiment
  • Dichotomic quantum measurements
  • POVM
  • Coarse-grained measurements
  • Quantum foundations