Following up on previous work, using compressive sensing to probe a large quantum system !
Quantifying entanglement in a 68-billion dimensional quantum system by James Schneeloch, Christopher C. Tison, Michael L. Fanto, Paul M. Alsing, Gregory A. Howland
Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Achieving a quantum advantage requires scaling quantum systems to sizes that can support a large amount of entanglement. Because real-world systems are varied and imperfect, the quantum resources they provide must be characterized before use. However, exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which requires an intractable number of measurements even for modestly sized systems. Here we demonstrate a new method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of 7.11±.04 ebits shared between spatially-entangled photon pairs. With a Hilbert space exceeding 68 billion dimensions, this is 10-million-fold fewer measurements than traditional approaches. The procedure does not computationally recover an underlying state and allows straightforward error analysis. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.
Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations by James Schneeloch, Gregory A. Howland
Quantifying entanglement in a quantum system generally requires a complete quantum tomography followed by the NP-hard computation of an entanglement monotone --- requirements that rapidly become intractable at higher dimensions. Observing entanglement in large quantum systems has consequently been relegated to witnesses that only verify its existence. In this article, we show that the violation of recent entropic witnesses of the Einstein-Podolsky-Rosen paradox also provides tight lower bounds to multiple entanglement measures, such as the entanglement of formation and the distillable entanglement, among others. Our approach only requires the measurement of correlations between two pairs of complementary observables---not a tomography---so it scales efficiently at high dimension. Despite this, our technique captures almost all the entanglement in common high-dimensional quantum systems, such as spatially or temporally entangled photons from parametric down-conversion.
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