We discuss some of the main features of a recently-generated form of hybrid entanglement between discrete- and continuous-variable states of light. Ideally, such a kind of entanglement should involve single-photon and coherent states as key representatives of the respective categories of states. Here we investigate the characteristics and limits of a scheme that, relying on a superposition of photon-creation operators onto two distinct modes, realizes the above ideal form of hybrid entanglement in an approximate way.
We discuss some of the main features of a recently-generated form of hybrid entanglement between discrete- and continuous-variable states of light. Ideally, such a kind of entanglement should involve single-photon and coherent states as key representatives of the respective categories of states. Here we investigate the characteristics and limits of a scheme that, relying on a superposition of photon-creation operators onto two distinct modes, realizes the above ideal form of hybrid entanglement in an approximate way.
In optical quantum information, one can distinguish two approaches: the discrete-variable (DV), involving single photons, for example c0|0〉 + c1|1〉, and the continuous-variable alternative (CV) encoding information into the quadrature components of the light field. In this CV approach, qubits can be implemented as superposition of coherent states of opposite phases, |cat ±〉 = |α〉 ± |−α〉, also called optical Schrodinger cat states. Combining these two approaches has recently led to a so-called optical hybrid quantum information aiming at merging the properties of both [1]. As both encodings have their own advantages and drawbacks, transferring information between them is a requirement which can be fulfill by teleportation using hybrid entanglement between particle-like qubits and wave-like qubits, i.e. entanglement of the form |0〉|α〉 + |1〉|−α〉.
By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. In contrast to previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete polarization and continuous quadrature optical qubits heralded by two-photon Bell-state measurement. As a novel nonclassical light resource, we further use it to discuss two examples of ways—entanglement swapping and quantum teleportation—in which quantum information processing and communications could make use of this hybrid technique.
We propose a feasible scheme based on the nonlinear Mach–Zehnder interferometer to realize the optical entanglement of a single-photon-added coherent state and show that, besides the Sanders entangled coherent state, the entangled single-photon-added coherent state also leads to new forms of hybrid entanglement of the quantum Fock state and the classical coherent state. We probe the essential difference between two types of hybrid entangled states. This hybrid entangled state provides a novel link between the discrete-variable and the continuous-variable entanglement in a natural way. Finally, we give a qualitative analysis of the losses in our scheme.
Abstract The generation and manipulation of hybrid entanglement of light involving discrete- and continuous-variable states have recently appeared as essential resources towards the realization of heterogeneous quantum networks. Here we investigate a scheme for the remote generation of hybrid entanglement between particle-like and wave-like optical qubits based on a non-local heralding photon detection. We also extend this scheme with additional local or non-local detections. An additional local heralding allows the resulting state to exhibit a higher fidelity with the targeted entangled qubits while a two-photon non-local heralding detection gives access to a higher dimensionality in the discrete-variable subspace, resulting thereby in the generation of hybrid entangled qutrits. The implementation of the presented schemes, in combination with ongoing works on high-fidelity quantum state engineering, will provide novel non-classical light sources for the development of optical hybrid architectures.
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.
Quantum information theory is a very young area of research offering a lot of challenging open questions to be tackled by ambitious upcoming physicists. One such problem is addressed in this thesis. Recently, several protocols have emerged which exploit both continuous variables and discrete variables. On the one hand, outperforming many of the established pure continuous variable or discrete variable schemes, these hybrid approaches offer new opportunities. However, on the other hand, they also lead to new, intricate, as yet uninvestigated, phenomena. An important ingredient of several of these hybrid protocols is a new kind of entanglement: The hybrid entanglement between continuous variable and discrete variable quantum systems, which is studied in detail in this work. An exhaustive analysis of this kind of entanglement is performed, where the focus is on bipartite entanglement. Nevertheless, also issues regarding multipartite hybrid entanglement are briefly discussed. The quintessence of this thesis is a new classification scheme which distinguishes between effective discrete variable hybrid entanglement and so-called true hybrid entanglement. However, along the way, also other questions are addressed, which have emerged during the studies. For example, entanglement witnessing is discussed not only for hybrid entangled states, but also for fully continuous variable two-mode Schroedinger cat states. Furthermore, subtleties regarding entanglement witnessing in a certain kind of mixed states are examined. Not only theoretical classification and analysis of hybrid entangled states are discussed, but also their generation is presented and a few applications are demonstrated.