Quantum entanglement beyond Gaussian criteria

Abstract

Most of the attention given to continuous variable systems for quantum information processing has traditionally been focused on Gaussian states. However, non-Gaussianity is an essential requirement for universal quantum computation and entanglement distillation, and can improve the efficiency of other quantum information tasks. Here we report the experimental observation of genuine non-Gaussian entanglement using spatially entangled photon pairs. The quantum correlations are invisible to all second-order tests, which identify only Gaussian entanglement, and are revealed only under application of a higher-order entanglement criterion. Thus, the photons exhibit a variety of entanglement that cannot be reproduced by Gaussian states.continuous variables | quantum information | non-Gaussian states | transverse spatial modes S ince the realization that quantum systems could prove useful for the efficient processing of information, there have appeared many proposals designed to exploit their power. From database searching and factoring algorithms to secure communication, these protocols achieve an impressive range of tasks. Typically, these quantum protocols have been first designed for discrete variable systems, described by finite dimensional Hilbert spaces, and hence are mathematically simpler than continuous variable (CV) systems with infinite dimensional spaces (1). CV systems provide a very interesting ground for quantum information processing, precisely due to their large and rich Hilbert space structure, which, however, makes characterization and detection of CV entanglement a difficult task.One way to tackle the difficulty in dealing with infinite dimensions is to confine the allowed states to a sector of Hilbert space defined by a finite number of parameters. Among the infinite ways one could do this, the most common is to restrict oneself to Gaussian states. For zero mean values, these states can be completely characterized by their covariance matrix containing moments up to second order (e.g. x 2 , xp , etc.) (1). This simplification has allowed for many results from the realm of finite-dimensional discrete-variable entanglement to find their CV analog (2, 3).It has recently become apparent, however, that the use of non-Gaussian states and operations is not only advantageous but at times necessary to successfully perform quantum information tasks. Non-Gaussian operations are required for entanglement distillation or swapping (4-8), and their use along with non-Gaussian states has been shown to improve quantum teleportation (9, 10) and cloning (11). It is also particularly remarkable that non-Gaussianity (either states or operations) is necessary for universal quantum computation with CVs (12), and proof of quantum nonlocality through violation of Bell's inequality (13). These advantages have motivated the experimental de-Gaussification of Gaussian states (14-17) and the idea that non-Gaussianity is a resource that can be quantified (18).The most popular criteria for identifying CV entanglement deal with mom...

Interferometric scheme for direct measurement of moments of transverse spatial variables of photons

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