Abstract
Symmetric informationally complete positive operator-valued measures provide efficient quantum state tomography in any finite dimension. In this work, we implement state tomography using symmetric informationally complete positive operator-valued measures for both pure and mixed photonic qudit states in Hilbert spaces of orbital angular momentum, including spaces whose dimension is not power of a prime. Fidelities of reconstruction within the range of 0.81–0.96 are obtained for both pure and mixed states. These results are relevant to high-dimensional quantum information and computation experiments, especially to those where a complete set of mutually unbiased bases is unknown.
- Received 3 May 2015
DOI:https://doi.org/10.1103/PhysRevX.5.041006
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Published by the American Physical Society
Popular Summary
Determining an unknown quantum state, i.e., quantum state tomography, plays an essential role in fundamental studies of quantum mechanics, quantum computations, and quantum key distribution. Various methods have been proposed to optimize quantum state tomography by implementing a minimum number of projective measurements or maximizing the accuracy of the state estimation. Among these different approaches, mutually unbiased bases and symmetric informationally complete positive operator-valued measures are well-recognized techniques. However, determining the single “best” optimal technique is still an open question. Here, we experimentally show that symmetric informationally complete positive operator-valued measures provide the best state estimation for dimensions where a complete set of mutually unbiased bases is unknown, i.e., Hilbert spaces with dimensions that are not a power of a prime number.
We experimentally test the use of symmetric informationally complete positive operator-valued measures in up to ten dimensions, although our technique can be applied to any finite dimension. We generate photon pairs via spontaneous parametric down-conversion and put our technique to the test by reconstructing orbital angular-momentum eigenstates, superpositions, and mixed states of photon pairs. In addition, we explore a particular aspect of quantum key distribution known as the Singapore protocol with twisted photons.
We expect that our findings will inform studies of how photonic states can be used experimentally in quantum cryptography.