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arXiv · 2210.10717

High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements

Alexandria J. Moore·Andrew M. Weiner
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Abstract

Entanglement -- the coherent correlations between parties in a joint quantum system -- is well-understood and quantifiable in the two-dimensional, two-party case. Higher (>2)-dimensional entangled systems hold promise in extending the capabilities of various quantum information applications. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We review entanglement certification approaches and the large number of -- often difficult -- measurements required to apply them. We present a novel certification method whose measurement requirements scale linearly with subsystem dimension (scaling with the square-root of the system dimension) and which requires only a single complex measurement. The certification method places a lower-bound on the relative entropy of entanglement of any maximally correlated state thereby certifying system entanglement. A lower bound is also shown for any maximally correlated state in the presence of noise -- the expected experimental case. We discuss experimental realization of all required measurements.

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Alexandria J. Moore, Andrew M. Weiner. 2022-10-19. High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements. https://arxiv.org/abs/2210.10717

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