Quantum correlations are at the core of quantum information processing and are necessary to achieve a quantum computational advantage. In the context of continuous-variable quantum systems, another necessary resource for quantum advantages is non-Gaussianity. In this work, we propose a witness based on previously known relations between metrological power and quantum correlations, to detect a strong form of entanglement that only non-Gaussian states possess and that cannot be undone by passive optical operations, i.e., entanglement in all mode bases. The strength of our witness is two-fold: it only requires measurements in one basis to check entanglement in any arbitrary mode basis; it can be made applicable experimentally using homodyne measurements and without requiring a full tomography of the state.
Quantum correlations are at the core of quantum information processing and are necessary to achieve a quantum computational advantage. In the context of continuous-variable quantum systems, another necessary resource for quantum advantages is non-Gaussianity. In this work, we propose a witness based on previously known relations between metrological power and quantum correlations, to detect a strong form of entanglement that only non-Gaussian states possess and that cannot be undone by passive optical operations, i.e., entanglement in all mode bases. The strength of our witness is two-fold: it only requires measurements in one basis to check entanglement in any arbitrary mode basis; it can be made applicable experimentally using homodyne measurements and without requiring a full tomography of the state.
Detection of entanglement in quantum states is one of the most important problems in quantum information processing. However, it is one of the most challenging tasks to find a universal scheme which is also desired to be optimal to detect entanglement for all states of a specific class--as always preferred by experimentalists. Although, the topic is well studied at least in case of lower dimensional compound systems, e.g., two-qubit systems, but in the case of continuous variable systems, this remains as an open problem. Even in the case of two-mode Gaussian states, the problem is not fully solved. In our work, we have tried to address this issue. At first, a limited number of Hermitian operators is given to test the necessary and sufficient criterion on the covariance matrix of separable two-mode Gaussian states. Thereafter, we present an interferometric scheme to test the same separability criterion in which the measurements are being done via Stokes-like operators. In such case, we consider only single-copy measurements on a two-mode Gaussian state at a time and the scheme amounts to the full state tomography. We further analyze the robustness of the proposed detection method against experimentally relevant imperfections and demonstrate that the separability test remains reliable under moderate levels of detection inefficiency. Although this latter approach is a linear optics-based one, nevertheless it is not an economic scheme. Resource-wise a more economical scheme than the full state tomography is obtained if we consider measurements on two copies of the state at a time. However, optimality of the scheme is not yet known.
Certifying reliable sources for quantum information processing is still one of the major challenges towards practical applications. Continuous variable quantum information provides a very promising platform where important resources such as scalable entanglement come "for free" [1] . In that context, a crucial quantum feature to look for and investigate is the so-called non-Gaussianity, which, beyond its conceptual relevance, is a necessary resource for any quantum computational advantage as well as for effective error correction, entanglement distillation and more. Non-Gaussian states have been produced and probed using full tomography techniques [2] . However, performing a full tomography of multimode continuous variable systems is a hard problem. Indeed, systems aimed at overcoming classical approach are by definition too complex to be fully characterized, thus alternative approaches are required.
Abstract Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.
Entanglement and non-Gaussianity are physical resources that are essential for a large number of quantum-optics protocols. Non-Gaussian entanglement is indispensable for quantum-computing advantage and outperforms its Gaussian counterparts in a number of quantum-information protocols. The characterization of non-Gaussian entanglement is a critical matter as it is in general highly demanding in terms of resources. We propose a simple protocol based on the Fisher information for witnessing entanglement in an important class of non-Gaussian entangled states: photon-subtracted states. We demonstrate that our protocol is relevant for the detection of non-Gaussian entanglement generated by multiple photon-subtraction and that it is experimentally feasible through homodyne detection.
Efficiently certifying non-Gaussian entanglement in continuous-variable quantum systems is a central challenge for advancing quantum information processing, photonic quantum computing, and metrology. Here, we put forward continuous-variable counterparts to the recently introduced entanglement criteria based on moments of the partially transposed state, together with simple readout schemes that require only a few replicas of the state, passive linear optics, and particle-number measurements. We develop a multicopy method that enables the detection of strongly non-Gaussian entanglement for various relevant state families overlooked by standard approaches, which include the entire class of NOON states. Further, it is robust against realistic experimental constraints (losses, noise, and finite statistics), which we demonstrate by extensive numerical simulations.
The characterisation of quantum correlations, also known as entanglement, is central to quantum information theory. Operationally, entanglement gives rise to the notion of quantum non-locality, which challenges the ‘reality’ of quantum mechanics (adopting the terminology of Einstein, Podolski and Rosen) and arguably represents its most distinctive feature, in the sense that it calls for a departure from certain foundational tenets of classical physics. It should thus not come as a surprise that entanglement turns out to be a key resource for the implementation of a number of quantum communication protocols and also necessary to achieve computational speed-ups with quantum hardware, in the sense that accessing regions of the Hilbert space with entangled states allows one to shorten the computational depth of certain algorithms. Not surprisingly, generating and maintaining entanglement is generally difficult in practice, as it requires strong interactions between selected components of a system that must at the same time be isolated from the environment. Thanks to the techniques developed in quantum optical set-ups to achieve squeezed light, entanglement is, however, comparatively accessible with optical quantum continuous variables. As we shall see, in fact, continuous variable entanglement is closely related to the notion of squeezing. It is therefore of the utmost importance to be able to qualify and quantify the entanglement of quantum continuous variables, which is the subject matter of the present chapter. The first part of the chapter is devoted to techniques and criteria based on second moments to detect the entanglement of Gaussian states and also to the description of possible ways to quantify such quantum correlations, bearing in mind that the determination of entanglement monotones of clear operational significance is still an open problem, even in the restricted arena of Gaussian states. Although the criteria based on second moments are sufficient, but not necessary, for the detection of non-Gaussian entanglement too, we will push our analysis further by introducing more general criteria based on higher order statistical moments, which will be put to use to detect, on paper, the quantum correlations of an entangled cat-like state. We will also address the issues of entanglement distillation and quantum non-locality tests, in whose contexts we shall encounter other non-Gaussian operations and states, such as photon-subtracted states.