As applications of quantum information and processing grow in scale in sophistication, the ability to quantify the resources present in very high-dimensional quantum systems is an important experimental problem needing solution. In particular, quantum entanglement is a resource fundamental to most applications in quantum information, but becomes intractable to measure in high dimensional systems, both because of the difficulty in obtaining a complete description of the entangled state, and the subsequent calculation of entanglement measures. In this paper, we discuss how one can measure record levels of entanglement simply using the same correlations employed to demonstrate the EPR paradox. To accomplish this, we developed a new entropic uncertainty relation where the Einstein-Podolsky-Rosen (EPR) correlations between positions and momenta of photon pairs bound quantum entropy, which in turn bounds entanglement. To sample the EPR correlations efficiently, one can sample at variable resolution, and combine this with relations in information theory so that only regions of high probability are sampled at high resolution, while entanglement is never over-estimated. This approach makes quantifying extremely high-dimensional entanglement scalable, with efficiency that actually improves with higher entanglement.
James Schneeloch, Christopher C. Tison, Michael L. Fanto, Paul M. Alsing, and Gregory A. Howland, "Quantifying record entanglement in extremely large Hilbert spaces with adaptively sampled EPR correlations," Proc. SPIE 10803, Quantum Information Science and Technology IV, 108030O (Presented at SPIE Security + Defence: September 11, 2018; Published: 8 October 2018); https://doi.org/10.1117/12.2503449.
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