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arXiv:1710.01781 · Scientific Reports

Massively Parallel Coincidence Counting of High-Dimensional Entangled States

Matthew C. Reichert, Hugo Defienne, Jason W. Fleischer

Published May 15, 2018• 51 citations
arXivHTMLPDF

Abstract

Abstract Entangled states of light are essential for quantum technologies and fundamental tests of physics. Current systems rely on entanglement in 2D degrees of freedom, e.g., polarization states. Increasing the dimensionality provides exponential speed-up of quantum computation, enhances the channel capacity and security of quantum communication protocols, and enables quantum imaging; unfortunately, characterizing high-dimensional entanglement of even bipartite quantum states remains prohibitively time-consuming. Here, we develop and experimentally demonstrate a new theory of camera detection that leverages the massive parallelization inherent in an array of pixels. We show that a megapixel array, for example, can measure a joint Hilbert space of 1012 dimensions, with a speed-up of nearly four orders-of-magnitude over traditional methods. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, generalizes readily to arbitrary numbers of entangled photons, and opens previously inaccessible regimes of high-dimensional quantum optics.

DOI
10.1038/s41598-018-26144-7

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Abstract Entangled states of light are essential for quantum technologies and fundamental tests of physics. Current systems rely on entanglement in 2D degrees of freedom, e.g., polarization states. Increasing the dimensionality provides exponential speed-up of quantum computation, enhances the channel capacity and security of quantum communication protocols, and enables quantum imaging; unfortunately, characterizing high-dimensional entanglement of even bipartite quantum states remains prohibitively time-consuming. Here, we develop and experimentally demonstrate a new theory of camera detection that leverages the massive parallelization inherent in an array of pixels. We show that a megapixel array, for example, can measure a joint Hilbert space of 1012 dimensions, with a speed-up of nearly four orders-of-magnitude over traditional methods. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, generalizes readily to arbitrary numbers of entangled photons, and opens previously inaccessible regimes of high-dimensional quantum optics.
Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.
Entanglement is a central resource in quantum technologies. In this respect, high-dimensional entangled states are very promising for developing robust quantum communication schemes and enhanced imaging protocols. Being able to quantify high-dimensional entanglement quickly and accurately is therefore essential. However, to date, all experimental methods use assumptions about the detected state or imperfect measurement techniques, such as single-outcomes and accidental subtractions. Entanglement certification processes are therefore not only slow, but they also contain loopholes, which is not acceptable in adversarial scenarios such as quantum key distribution (QKD). In our work, we demonstrate the certification of high-dimensional entanglement using an event-based single-photon sensitive camera by performing measurements in two mutually unbiased bases. Our work provides an experimental method allowing for the efficient characterization of high-dimensional quantum states, paving the way for the development of high-dimensional QKD protocols and practical photon-pairs-based quantum imaging approaches.
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.
High-dimensional entangled states, such as spatially-entangled photon pairs produced by Spontaneous Parametric Down-Conversion (SPDC), are a key resource for quantum technologies. In recent years, camera-based coincidence counting approaches have considerably improved the ability to characterize them in terms of speed and dimensionality. However, these methods have limitations, including in most of them the necessity to subtract accidental coincidences. Here, we study the role of these accidentals in entanglement certification for a single-photon avalanche diode (SPAD) array and an intensified time-stamping (Tpx3Cam) camera. Using both Einstein-Podolsky-Rosen (EPR) and entropy-based criteria, we show that the level of accidental coincidences - determined by the temporal characteristics of the camera - and whether they are subtracted critically impact entanglement certification. In particular, we demonstrate that current single-photon camera technologies enable entanglement certification without accidental subtraction only if a Gaussian approximation is applied to the measured two-photon state. Our work is important for developing quantum-optics application in adversarial scenarios, such as high-dimensional quantum key distribution (HD-QKD), and also for loophole-free experimental testing of quantum foundations.
High-dimensional entangled states, such as spatially entangled photon pairs produced by spontaneous parametric down-conversion (SPDC), are a key resource for quantum technologies. In recent years, camera-based coincidence counting approaches have considerably improved the ability to characterize them in terms of speed and dimensionality. However, these methods have limitations, including in most of them the necessity to subtract accidental coincidences. Here, we study the role of these accidentals in entanglement certification for a single-photon avalanche diode (SPAD) array and an intensified time-stamping (Tpx3Cam) camera. Using both Einstein-Podolsky-Rosen (EPR) and entropy-based criteria, we show that the level of accidental coincidences-determined by the temporal characteristics of the camera-and whether they are subtracted critically impact entanglement certification. In particular, we demonstrate that current single-photon camera technologies enable entanglement certification without accidental subtraction only if a Gaussian approximation is applied to the measured two-photon state. Our work is important for developing quantum-optics applications in adversarial scenarios, such as high-dimensional quantum key distribution (HD-QKD) and also for loophole-free experimental testing of quantum foundations.
We utilize a single-photon sensitive electron multiplying CCD camera as a massively parallel coincidence counting apparatus to study spatial entanglement of photon pairs. This allows rapid measurement of transverse spatial entanglement in a fraction of the time required with traditional point-scanning techniques. We apply this technique to quantum experiments on entangled photon pairs: characterization of the evolution of entanglement upon propagation, and measurement of one- and two-photon portions of the state transmitted through non-unitary (lossy) objects, and quantum phase imaging.