Cartesian and polar Schmidt bases for down-converted photons : how high dimensional entanglement protects the shared information from non-ideal measurements

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Miatto, Filippo and Brougham, Thomas and Yao, Alison (2012) Cartesian and polar Schmidt bases for down-converted photons : how high dimensional entanglement protects the shared information from non-ideal measurements. European Physical Journal D: Atomic, Molecular, Optical and Plasma Physics, 66 (7). pp. 183-190. ISSN 1434-6060 (https://doi.org/10.1140/epjd/e2012-30063-y)

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Abstract

We derive an analytical form of the Schmidt modes of spontaneous parametric down-conversion (SPDC) biphotons in both Cartesian and polar coordinates. We show that these correspond to Hermite- Gauss (HG) or Laguerre-Gauss (LG) modes only for a specific value of their width, and we show how such value depends on the experimental parameters. The Schmidt modes that we explicitly derive allow one to set up an optimised projection basis that maximises the mutual information gained from a joint measurement. The possibility of doing so with LG modes makes it possible to take advantage of the properties of orbital angular momentum eigenmodes. We derive a general entropic entanglement measure using the R ́enyi entropy as a function of the Schmidt number, K, and then retrieve the von Neumann entropy, S. Using the relation between S and K we show that, for highly entangled states, a non-ideal measurement basis does not degrade the number of shared bits by a large extent. More specifically, given a non-ideal measurement which corresponds to the loss of a fraction of the total number of modes, we can quantify the experimental parameters needed to generate an entangled SPDC state with a sufficiently high dimensionality to retain any given fraction of shared bits.

ORCID iDs

Miatto, Filippo, Brougham, Thomas and Yao, Alison ORCID logoORCID: https://orcid.org/0000-0002-6260-5852;
  • Item type:Article
    ID code:41914
    Dates:
    Date
    Event
    12 July 2012
    Published
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:05 Nov 2012 12:00
    Last modified:16 Nov 2024 23:05
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/41914
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