Journal
NEW JOURNAL OF PHYSICS
Volume 21, Issue 12, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/ab58a0
Keywords
quantum metrology; quantum information; quantum imaging
Categories
Funding
- UK EPSRC [EP/K04057X/2]
- UK National Quantum Technologies Programme [EP/M01326X/1, EP/M013243/1]
- University of Warwick Global Partnership Fund
- EPSRC [EP/K04057X/2, EP/M01326X/1] Funding Source: UKRI
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Localisation microscopy of multiple weak, incoherent point sources with possibly different intensities in one spatial dimension is equivalent to estimating the amplitudes of a classical mixture of coherent states of a simple harmonic oscillator. This enables us to bound the multi-parameter covariance matrix for an unbiased estimator for the locations in terms of the quantum Fisher information matrix, which we obtained analytically. In the regime of arbitrarily small separations we find it to be no more than rank two-implying that no more than two independent parameters can be estimated irrespective of the number of point sources. We use the eigenvalues of the classical and quantum Fisher information matrices to compare the performance of spatial-mode demultiplexing and direct imaging in localisation microscopy with respect to the quantum limits.
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