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.
Highlights
In this work, we present a rapid and efficient method of measuring a high-dimensional biphoton joint probability distribution via massively parallel coincidence counting
Entangled photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a β-barium borate (BBO) crystal, cut for type-I phase matching
Measurement of the biphoton joint probability distribution Γij is possible with an EMCCD camera due to its high quantum efficiency and low noise floor
Summary
Entangled states of light are essential for quantum technologies and fundamental tests of physics. Measurement of the biphoton joint probability distribution Γij is possible with an EMCCD camera due to its high quantum efficiency and low noise floor. The paradox is often circumvented by considering the low-photon-count limit, in which the joint probability distribution Γij becomes proportional to the measured coincidence count rate 〈Cij〉 This assumption is not necessary here; Eq (4) remains valid up to detector saturation. While some variation can survive averaging by projection onto 2D planes, such as phase-matching and spatial walk-off effects (as observed in type II SPDC28), in contrast our method is capable of measuring arbitrary 4D joint probability distributions. We image a resolution chart using spatially entangled biphoton illumination—where one photon is localized near its partner (i ≈ j)—by projecting the output facet of the nonlinear crystal onto the object, which is imaged onto the camera (see Fig. 3a, Methods). The visibility for entangled photon pairs and incoherent light should be the same; the discrepancy here may be due to the way we approximate Γii with Γi,i+1 using adjacent pixels (see Methods)
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