Entanglement Detection of Multiphoton States

Multiparticle entangled states cannot be characterized easily by conventional quantum state tomography due to the requirement of a large number of measurements for reconstructing the corresponding density matrix [1]. Therefore, it is essential to identify certain observables called entanglement witnesses whose expectation values provide a test for entanglement of such many-body states and is measured like a Bell inequality. For photonic states, another challenge is to inculcate the practical limitations of photodetection mechanisms that hinder number-resolved measurements of a single pulse [2]. Here we present a theoretical scheme for experimental verification of entanglement in infinite-dimensional multiphotonic states without performing a full state tomography. Our proposed experiment involves a reduced Hilbert space where the photonic state is either detected or not detected by the photodetectors, thereby reducing the dimensionality of our problem. Further, we elucidate the observables for testing entanglement and their associated entropic uncertainties to quantify the resolution of the measurements.

 

[1] M. Paris and J. Rehacek, Quantum state estimation, Vol. 649 (Springer Science & Business Media, 2004)

[2] R. H. Hadfield, Nat. Photonics 3, 696 (2009)