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arXiv · 0901.2232

Two-photon speckle as a probe of multi-dimensional entanglement

C. W. J. Beenakker·J. W. F. Venderbos·M. P. van Exter
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Abstract

We calculate the statistical distribution P_2(I_2) of the speckle pattern produced by a photon pair current I_2 transmitted through a random medium, and compare with the single-photon speckle distribution P_1(I_1). We show that the purity Tr rho^2 of a two-photon density matrix rho can be directly extracted from the first two moments of P_1 and P_2. A one-to-one relationship is derived between P_1 and P_2 if the photon pair is in an M-dimensional entangled pure state. For M>>1 the single-photon speckle disappears, while the two-photon speckle acquires an exponential distribution. The exponential distribution transforms into a Gaussian if the quantum entanglement is degraded to a classical correlation of M>>1 two-photon states. Two-photon speckle can therefore discriminate between multi-dimensional quantum and classical correlations.

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C. W. J. Beenakker, J. W. F. Venderbos, M. P. van Exter. 2009-01-15. Two-photon speckle as a probe of multi-dimensional entanglement. https://doi.org/10.1103/physrevlett.102.193601

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