Two-photon speckle as a probe of multi-dimensional entanglement.
We calculate the statistical distribution P2(I2) of the speckle pattern produced by a photon pair current I2 transmitted through a random medium, and compare it with the single-photon speckle distribution P1(I1). We show that the purity of a two-photon density matrix can be directly extracted from the first two moments of P1 and P2. A one-to-one relationship is derived between P1 and P2 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.
Beenakker
C W J
CW
Instituut-Lorentz, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands.
Venderbos
J W F
JW
van Exter
M P
MP