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Critical Point in the Problem of Maximizing the Transition Probability Using Measurements in an n-Level Quantum System

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Abstract

We consider the problem of maximizing the transition probability in an n-level quantum system from a given initial state to a given final state using nonselective quantum measurements. We find a sequence of measurements that is a critical point of the transition probability and, moreover, a local maximum in each variable on the set of one-dimensional projectors. We consider the class of one-dimensional projectors because these projectors describe the measurements of populations of pure states of the system.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    N. B. Il’in

  2. MISIS National University of Science and Technology, Moscow, Russia

    A. N. Pechen

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  1. N. B. Il’in
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Correspondence to N. B. Il’in.

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Il’in, N.B., Pechen, A.N. Critical Point in the Problem of Maximizing the Transition Probability Using Measurements in an n-Level Quantum System. Theor Math Phys 194, 384–389 (2018). https://doi.org/10.1134/S0040577918030066

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  • DOI: https://doi.org/10.1134/S0040577918030066

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