Optimal Frames for Polarisation State Reconstruction

Abstract

Complete determination of the polarisation state of light requires at least four distinct projective measurements of the associated Stokes vector. Stability of state reconstruction, however, hinges on the condition number $\kappa$ of the corresponding instrument matrix. Optimisation of redundant measurement frames with an arbitrary number of analysis states, $m$, is considered in this Letter in the sense of minimisation of $\kappa$. The minimum achievable $\kappa$ is analytically found and shown to be independent of $m$, except for $m=5$ where this minimum is unachievable. Distribution of the optimal analysis states over the Poincaré sphere is found to be described by spherical 2-designs, including the Platonic solids as special cases. Higher order polarisation properties also play a key role in nonlinear, stochastic and quantum processes. Optimal measurement schemes for nonlinear measurands of degree $t$ are hence also considered and found to correspond to spherical $2t$-designs, thereby constituting a generalisation of the concept of mutually unbiased bases.

References in corpus (3)

• Polarimetric characterization of light and media
• Evanescent-wave and open-air chiral sensing via signal-reversing cavity-enhanced polarimetry
• Choice of Measurement Sets in Qubit Tomography

Cited by in corpus (13)

• Quantum metasurface for multi-photon interference and state reconstruction
• Integrated Plasmonic Metasurfaces for Spectropolarimetry
• Scalable on-chip quantum state tomography
• Two-photon tomography using on-chip quantum walks
• Single Pixel Polarimetric Imaging through Scattering Media
• Polarisation optics for biomedical and clinical applications: a review
• Three-Photon Stokes Mueller Polarimetry
• In-line detection and reconstruction of multi-photon quantum states
• Single-shot characterization of vector beams by generalized measurements
• Robust Classical and Quantum Polarimetry with a Single Nanostructured Metagrating
• Universal Optimal Estimation of the Polarization of Light with Arbitrary Photon Statistics
• Adaptive tomography of qubits: Purity versus statistical fluctuations
• Metasurface-enabled small-satellite polarisation imaging