Hybrid encoding of quantum information is a promising approach towards the realization of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable resource for quantum information protocols. In this work we present a hybrid entanglement witness that can be implemented on available experiments and is robust to noise currently observed in quantum optical setups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterized with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables.
Hybrid encoding of quantum information is a promising approach towards the realization of optical quantum protocols. It combines advantages of continuous variables encoding, such as high efficiencies, with those of discrete variables, such as high fidelities. In particular, entangled hybrid states were shown to be a valuable resource for quantum information protocols. In this work we present a hybrid entanglement witness that can be implemented on available experiments and is robust to noise currently observed in quantum optical setups. The proposed witness is based on measurements of genuinely hybrid observables. The noise model we consider is general. It is formally characterized with Kraus operators since the considered hybrid system can be expressed in a finite dimension basis. A practical advantage of the witness is that it can be tested by measuring just a few experimentally available observables.
Single-photon entangled states constitute the simplest form of entanglement, yet they provide a valuable resource in quantum information sciences. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped and purified with linear optics. The main drawback of such resource is the difficulty in measuring it. Here, we present and experimentally test the first operational witness suited for single-photon entanglement which relies only on local homodyning and does not require post-selection. Our results highlight the potential of hybrid methods, where discrete entanglement is characterized through continuous-variable measurements, in verifying the proper functioning of future quantum networks.
Entanglement, a critical resource for quantum information processing, needs to be witnessed in many practical scenarios. Theoretically, witnessing entanglement is by measuring a special Hermitian observable, called an entanglement witness (EW), which has non-negative expected outcomes for all separable states but can have negative expectations for certain entangled states. In practice, an EW implementation may suffer from two problems. The first one is reliability. Due to unreliable realization devices, a separable state could be falsely identified as an entangled one. The second problem relates to robustness. A witness may not be optimal for a target state and fail to identify its entanglement. To overcome the reliability problem, we employ a recently proposed measurement-device-independent entanglement witness scheme, in which the correctness of the conclusion is independent of the implemented measurement devices. In order to overcome the robustness problem, we optimize the EW to draw a better conclusion given certain experimental data. With the proposed EW scheme, where only data postprocessing needs to be modified compared to the original measurement-device-independent scheme, one can efficiently take advantage of the measurement results to maximally draw reliable conclusions.
Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
Entanglement and contextuality are among the most intriguing and fundamental features of quantum mechanics. Entanglement concerns quantum states:it is a phenomenon that happens when a system can not be described by the knowledge of its subparts. Contextuality concerns quantum observables: it is the capacity they have to give rise to different experimental results depending on the observables with which they are measured. Both have received tremendous attention during the last decades, following the second quantum revolution, that saw the attitude towards quantum features switch from "why is that so?" to "how can we use this?".This thesis conceives protocols to detect and characterise entanglement and contextuality in specific setups, seeking to fill the gaps between the theoretical studies and the experimental implementations. Entanglement is studied in the case of optical hybrid variables, a recent approach that tries to join the advantages of the discrete and continuous variables encoding of information for quantum communication and computation protocols. In a first chapter, we study how the formalism of matrices of moments can be adapted to the hybrid case and apply it to several hybrid entangled states. We then explore various possible improvements and refinements using the theory of positive maps, in order to gain sensitivity with regard to our detection thresholds. In a second chapter, we focus on a specific setup, define an entanglement witness and explain how it can be implemented on available experiments. It is robust to noise currently observed in quantum optical setups and is based on measurements of genuinely hybrid observables. Contextuality is studied in a last part. A review is made of the theory, from its emergence through philosophical questions to the first mathematical proofs that quantum mechanics is contextual. The main structural theories that yield a global approach to this concept are presented. They are summoned to understand and discuss the loopholes that can affect experiments of contextuality. A protocol is given for a much-studied experiment, that of the Peres-Mermin square.
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.