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Frontiers in Optics

Generating a 4-photon tetrahedron state: towards simultaneous super-sensitivity to non-commuting rotations

Hugo Ferretti, Y. Batuhan Yilmaz, Kent Bonsma-Fisher, Aaron Z. Goldberg, Noah Lupu-Gladstein, Arthur O. T. Pang, Aephraim M. Steinberg

Published Jan 1, 2023• 1 citation
Publisher

Abstract

A primary goal of quantum metrology is to understand the optimal way to measure multiple incompatible observables. Here, we report on the experimental demonstration and characterisation of a four-photon state, the “tetrahedron state”, which is the optimal state for simultaneous estimation of all parameters describing a rotation.
DOI
10.1364/fio.2023.jtu4a.54

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It is often thought that the super-sensitivity of a quantum state to an observable comes at the cost of a decreased sensitivity to other non-commuting observables. For example, a squeezed state squeezed in position quadrature is super-sensitive to position displacements, but very insensitive to momentum displacements. This misconception was cleared with the introduction of the compass state [ Nature 412 , 712 ( 2001 ) 10.1038/35089017 ], a quantum state equally super-sensitive to displacements in position and momentum. When looking at quantum states used to measure spin rotations, N 00 N states are known to be more advantageous than classical methods as long as they are aligned to the rotation axis. When considering the estimation of a rotation with unknown direction and amplitude, a certain class of states stands out with interesting properties. These states are equally sensitive to rotations around any axis, are second-order unpolarized, and can possess the rotational properties of Platonic solids in particular dimensions. Importantly, these states are optimal for simultaneously estimating the three parameters describing a rotation. In the asymptotic limit, estimating all d parameters describing a transformation simultaneously rather than sequentially can lead to a reduction of the appropriately weighted sum of the measured parameters’ variances by a factor of d . We report the experimental creation and characterization of the lowest-dimensional such state, which we call the “tetrahedron state” due to its tetrahedral symmetry. This tetrahedron state is created in the symmetric subspace of four optical photons’ polarization in a single spatial and temporal mode, which behaves as a spin-2 particle. While imperfections due to the hardware limited the performance of our method, ongoing technological advances will enable this method to generate states which out-perform any other existing strategy in per-photon comparisons.
Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings of Quantumness are especially germane for this task when the rotation axis is unknown, as they have a sensitivity independent of that axis and they achieve a Heisenberg-limit scaling. Here, we report the experimental realization of these states by generating up to 21-dimensional orbital angular momentum states of single photons, and confirm their high metrological abilities.
Quantum metrology allows for a tremendous boost in the accuracy of measurement of diverse physical parameters. The estimation of a rotation constitutes a remarkable example of this quantum-enhanced precision. The recently introduced Kings of Quantumness are especially germane for this task when the rotation axis is unknown, as they have a sensitivity independent of that axis and they achieve a Heisenberg-limit scaling. Here, we report the experimental realization of these states by generating up to 21-dimensional orbital angular momentum states of single photons, and confirm their high metrological abilities. (C) 2017 Optical Society of America.