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Photon added cat state: phase space structure and statistics.

Arman, Gargi Tyagi, Prasanta K Panigrahi

    Optics Letters
    |March 2, 2021
    PubMed
    Summary

    Photon addition to quantum states like cat and Yurke-Stoler states alters their phase space structure. This modification can serve as an error syndrome detector and potentially reduce quantum noise.

    Area of Science:

    • Quantum optics
    • Quantum information theory
    • Phase space quantum mechanics

    Background:

    • The study focuses on quantum states, specifically cat states and Yurke-Stoler states, which are fundamental in quantum mechanics.
    • Understanding the phase space structure and statistical properties of these states is crucial for quantum information processing.
    • Photon addition is a key quantum operation that can modify the properties of quantum states.

    Purpose of the Study:

    • To investigate the effects of photon addition on the phase space structure and statistics of quantum states.
    • To explore the potential applications of these modifications, such as error syndrome detection and quantum noise reduction.

    Main Methods:

    • Analysis of the general form of photon-added cat states.

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  • Examination of phase space interference patterns of the Wigner function.
  • Study of sub-Planck structures and their transformations.
  • Investigation of statistical properties (Poissonian vs. sub-Poissonian) of modified states.

    • Main Results:

    • Photon addition induces a π phase shift at the origin in the Wigner function's phase space interference, acting as a potential error syndrome detector.
    • The maxima and minima of sub-Planck tiles in the kitten state's phase space are interchanged, leading to orthogonality after photon addition.
    • Photon addition transforms the Yurke-Stoler state from Poissonian to sub-Poissonian statistics.

    Conclusions:

    • Photon addition significantly alters the phase space characteristics of quantum states.
    • The observed phase shift offers a potential method for quantum error detection.
    • The transition to sub-Poissonian statistics suggests applications in quantum noise reduction.