The concept of weak measurements and the super-efficiency of quantum tomography

Yu. I. Bogdanov; N. A. Bogdanova; B. I. Bantysh; Yu. A. Kuznetsov

doi:10.1117/12.2522078

15 March 2019 The concept of weak measurements and the super-efficiency of quantum tomography

Yu. I. Bogdanov, N. A. Bogdanova, B. I. Bantysh, Yu. A. Kuznetsov

Proceedings Volume 11022, International Conference on Micro- and Nano-Electronics 2018; 110222O (2019) https://doi.org/10.1117/12.2522078
Event: The International Conference on Micro- and Nano-Electronics 2018, 2018, Zvenigorod, Russian Federation

Abstract

The quantum measurement procedure based on the Lorentz transformation formalism and weak perturbation of the system is considered. In the simple case of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation along with ordinary 3-dimension rotations on the Bloch sphere. These pseudo-rotations are similar to the Lorentz transformation in special relativity theory. The extension of the Lorentz transformation for many-qubit systems is also considered. The quantum measurement protocols based on the Lorentz transformation are proposed. It has been shown that these protocols cease to form the decomposition of unity and could be superefficient providing the fidelity higher than any POVM-measurement protocol. However, one can perform the complement of the Lorentz protocol to POVMprotocol by an additional measurement operator. If the initial mixed state is close to the pure one this operator corresponds to weak perturbation of the state while the original Lorentz protocol sets the strong perturbations. As the result, the feedback provides an effective control of a quantum system introducing weak perturbations to the quantum state.

Citation Download Citation

Yu. I. Bogdanov, N. A. Bogdanova, B. I. Bantysh, and Yu. A. Kuznetsov "The concept of weak measurements and the super-efficiency of quantum tomography", Proc. SPIE 11022, International Conference on Micro- and Nano-Electronics 2018, 110222O (15 March 2019); https://doi.org/10.1117/12.2522078

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