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Bulletin of the American Physical Society

360-degree quantum tomography of a qudit

Charles H. Baldwin, Amir Kalev, Hector Sosa Martinez, Nathan Lysne, Poul Jessen, Ivan Deutsch

Published Jun 12, 2015• 0 citations
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Abstract Photons carrying orbital angular momentum (OAM) are excellent qudits and are widely used in several applications, such as long distance quantum communication, d -dimensional teleportation and high-resolution imaging and metrology. All these protocols rely on quantum tomography to characterise the OAM state, which currently requires complex measurements involving spatial light modulators and mode filters. To simplify the measurement and characterisation of OAM states, here we apply a recent tomography protocol [Asadian et al , Phys. Rev. A 94 010301 (2016)]. Our scheme for OAM tomography in d dimensions requires only a set of measurements on a path qubit, i.e., a two-dimensional system. This replaces the current complexity of OAM measurements by the ability to perform generalized Pauli operators X d , Z d on OAM states. Our scheme can be adapted in principle to other degrees of freedom, thus opening the way for more complex qudit tomography.
Abstract We propose compact three-dimensional photonic circuit designs that guarantee a remarkable reduction in the complexity of circuits to perform quantum state tomography of N -dimensional path qudits. We obtain solutions such that the number of beam splitters obeys a polynomial function of degree three with the quantum system dimension, whereas, in current proposals, this quantity grows with a polynomial function of degree four. In addition, the optical depth reduces from quadratic to linear over the dimension of the Hilbert space.