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arXiv · 1407.7426

Reconstructing high-dimensional two-photon entangled states via compressive sensing

Francesco Tonolini·Susan Chan·Megan Agnew·Alan Lindsay·Jonathan Leach
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Abstract

Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of singular value thresholding, we reconstruct the density matrix of a high-dimensional two-photon entangled system. The dimension of each photon is equal to $d= 17$, corresponding to a system of 83521 unknown real parameters. Accurate reconstruction is achieved with approximately 2500 measurements, only 3\% of the total number of unknown parameters in the state. The algorithm we develop is fast, computationally inexpensive, and applicable to a wide range of quantum states, thus demonstrating compressive sensing as an effective technique for measuring the state of large-scale quantum systems.

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Francesco Tonolini, Susan Chan, Megan Agnew, Alan Lindsay, Jonathan Leach. 2014-07-29. Reconstructing high-dimensional two-photon entangled states via compressive sensing. https://arxiv.org/abs/1407.7426

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