Quantifying entanglement in a 68-billion-dimensional quantum state space

Abstract

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. Exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which demands an intractable number of measurements even for modestly-sized systems. Here we demonstrate a 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 by two spatially-entangled photons. With a Hilbert space exceeding 68 billion dimensions, we need 20-million-times fewer measurements than the uncompressed approach and 10 18 -times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera

“…Furthermore, we have certified high-dimensional entanglement up to 48 dimensions in just 140 s, a significant development in quantum information processing with high-dimensional quantum states. While certifying high-dimensional entanglement is now routinely performed using single-outcome projective measurement techniques 34,45,49,50 , these approaches are tedious and prohibitively time-consuming. Our SPAD camera-based technique outperforms these approaches in term of speed and scalability, with a demonstrated speed-up by more than a factor 500× and the potential access to up to 4 × 10 6 two-photon modes ((32 × 64) 2 ) in parallel, indicating a key role to be played in future quantum information processing systems based on highdimensional entanglement.…”

Programmable Coherent Linear Quantum Operations with High-Dimensional Optical Spatial Modes

“…High-dimensional QFT and compiled modular exponential [42] are applied on twin beams from SPDC, respectively. The optical nonlinear process could provide a large enough state space for further demonstration [25]. Furthermore, our scheme is also available for indistinguishable multi-photon manipulation including boson sampling [18].…”

“…Particularly, spatial mode entanglement induced by spontaneous parametric down conversion (SPDC) in nonlinear crystals [2,3,[20][21][22][23][24] has been well investigated. Two photon spatial entanglement with high Schmidt number is potentially available with meticulously designed pump parameters [16,17,25]. However, the exploitation of such quantum resources has been hindered by the lack of universal operation protocols.…”

Uncertainty Relations for Coarse–Grained Measurements: An Overview

“…Since 2007, EPR-steering has been understood to make up part of a hierarchy of quantum correlations, situated between entanglement [ 81 , 82 ] and Bell non-locality [ 83 ]. In addition to methods utilizing variance-based URs [ 84 ], entropic URs, such as those in Section 2.2 , can be used to identify EPR-steering [ 85 , 86 ] and to quantify high-dimensional entanglement [ 87 , 88 ]. Some of these URs can be used to test security in continuous variable quantum cryptography [ 89 , 90 ], and it has been shown that violation of entropic EPR-steering criteria are directly related to the secret key rate in one-sided device independent cryptography [ 91 ].…”