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arXiv:1003.2125 · Optics Express

Experimental quantum tomography of photonic qudits via mutually unbiased basis

G. Lima, Leonardo Neves, Robert Guzman, Esteban S. Gómez, W. A. T. Nogueira, A. Delgado, Asticio A. Vargas, C. Saavedra

Published Feb 8, 2011• 107 citations
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Abstract

We present the experimental quantum tomography of 7- and 8-dimensional quantum systems based on projective measurements in the mutually unbiased basis (MUB-QT). One of the advantages of MUB-QT is that it requires projections from a minimal number of bases to be performed. In our scheme, the higher dimensional quantum systems are encoded using the propagation modes of single photons, and we take advantage of the capabilities of amplitude- and phase-modulation of programmable spatial light modulators to implement the MUB-QT.

DOI
10.1364/oe.19.003542

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We present the experimental quantum tomography of 7- and 8-dimensional quantum systems based on projective measurements in the mutually unbiased basis (MUB-QT). One of the advantages of MUB-QT is that it requires projections from a minimal number of bases to be performed. In our scheme, the higher dimensional quantum systems are encoded using the propagation modes of single photons, and we take advantage of the capabilities of amplitude- and phase-modulation of programmable spatial light modulators to implement the MUB-QT.
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We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB projectors) as input states for a DDD-dimensional quantum system, with DDD being a power of a prime number. This approach connects the results of quantum-state tomography using mutually unbiased bases with the coefficients of a quantum process, expanded in terms of MUB projectors. We also study the performance of the reconstruction scheme against random errors when measuring probabilities at the MUB projectors.
We present a feasible proposal for quantum tomography of qubit and qutrit states via mutually unbiased measurements in dispersively coupled driven cavity QED systems. We first show that measurements in the mutually unbiased bases (MUBs) are practically implemented by projecting the detected states onto the computational basis after performing appropriate unitary transformations. The measurement outcomes can then be determined by detecting the steady-state transmission spectra (SSTS) of the driven cavity. It is found that all the measurement outcomes for each MUB (i.e., all the diagonal elements of the density matrix of each detected state) can be read out directly from only one kind of SSTS. In this way, we numerically demonstrate that the exemplified qubit and qutrit states can be reconstructed with the fidelities 0.952 and 0.961, respectively. Our proposal could be straightforwardly extended to other high-dimensional quantum systems provided that their MUBs exist.