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 1018-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.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 1018-times fewer measurements than tomography. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

Jun 25, 201944 citations

Quantifying entanglement in a 68-billion dimensional quantum system

James Schneeloch, Christopher C. Tison, Michael L. Fanto +2 more

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 $7.11 \pm .04$ 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.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 $7.11 \pm .04$ 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.

Apr 12, 20180 citations

Efficiently certifying large amounts of entanglement in high-dimensional quantum systems

Gregory A. Howland

Real-world platforms for enabling quantum information technologies are varied and imperfect; therefore, the quantum resources they provide must be characterized before they can be used. For some tasks, such as secure communication, resources like entanglement must be guaranteed, or certified. In large quantum systems, traditional approaches demand an intractable number of measurements. We demonstrate a practical method for quantifying high-dimensional entanglement from extremely limited data that does not require numerical optimization techniques. Using only 6,456 measurements, we certify over 7 ebits of entanglement-of-formation shared by entangled photon pairs in a joint-measurement space exceeding 68 billion dimensions.Real-world platforms for enabling quantum information technologies are varied and imperfect; therefore, the quantum resources they provide must be characterized before they can be used. For some tasks, such as secure communication, resources like entanglement must be guaranteed, or certified. In large quantum systems, traditional approaches demand an intractable number of measurements. We demonstrate a practical method for quantifying high-dimensional entanglement from extremely limited data that does not require numerical optimization techniques. Using only 6,456 measurements, we certify over 7 ebits of entanglement-of-formation shared by entangled photon pairs in a joint-measurement space exceeding 68 billion dimensions.

Photonics for Quantum (PfQ)Aug 27, 20210 citations

Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations

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.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.

arXiv:1709.03626Physical Review AApr 24, 201850 citations

Quantifying record entanglement in extremely large Hilbert spaces with adaptively sampled EPR correlations

James Schneeloch, Christopher C. Tison, Michael L. Fanto +2 more

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.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.

SPIE Quantum Information Science and TechnologyOct 8, 20180 citations

A witness to quantify high-dimensional entanglement

Bienvenu I. Ndagano, Andrew Forbes

Exploiting photonic high-dimensional entanglement allows one to expand the bandwidth of quantum communication and information processing protocols through increased photon information capacity. However, the characterization of entanglement in higher dimensions is experimentally challenging because the number of measurements required scales unfavourably with dimension. While bounds can be used to certify high-dimensional entanglement, they do not quantify the degree to which quantum states are entangled. Here, we propose a quantitative measure that is both an entanglement measure and a dimension witness, which we coin the P-concurrence. We derive this measure by requiring entanglement to extend to qubit subspaces that constitute the high-dimensional state. The computation of the P-concurrence is not contingent on reconstructing the full density matrix, and requires less measurements compared to standard quantum state tomography by orders of magnitude. This allows for faster and more efficient characterization of high-dimensional quantum states.Exploiting photonic high-dimensional entanglement allows one to expand the bandwidth of quantum communication and information processing protocols through increased photon information capacity. However, the characterization of entanglement in higher dimensions is experimentally challenging because the number of measurements required scales unfavourably with dimension. While bounds can be used to certify high-dimensional entanglement, they do not quantify the degree to which quantum states are entangled. Here, we propose a quantitative measure that is both an entanglement measure and a dimension witness, which we coin the P-concurrence. We derive this measure by requiring entanglement to extend to qubit subspaces that constitute the high-dimensional state. The computation of the P-concurrence is not contingent on reconstructing the full density matrix, and requires less measurements compared to standard quantum state tomography by orders of magnitude. This allows for faster and more efficient characterization of high-dimensional quantum states.

arXiv:1710.07146Oct 19, 20170 citations

7.11 \pm .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.