We describe a method to detect twin-beam multiphoton entanglement based on a beam splitter and weak nonlinearities. For the twin-beam four-photon entanglement, we explore a symmetry detector. It works not only for collecting two-pair entangled states directly from the spontaneous parametric down-conversion process, but also for generating them by cascading these symmetry detectors. Surprisingly, by calculating the iterative coefficient and the success probability we show that with a few iterations the desired two-pair can be obtained from a class of four-photon entangled states. We then generalize the symmetry detector to n-pair emissions and show that it is capable of determining the number of the pairs emitted indistinguishably from the spontaneous parametric down-conversion source, which may contribute to explore multipair entanglement with a large number of photons.
We describe a method to detect twin-beam multiphoton entanglement based on a beam splitter and weak nonlinearities. For the twin-beam four-photon entanglement, we explore a symmetry detector. It works not only for collecting two-pair entangled states directly from the spontaneous parametric down-conversion process, but also for generating them by cascading these symmetry detectors. Surprisingly, by calculating the iterative coefficient and the success probability we show that with a few iterations the desired two-pair can be obtained from a class of four-photon entangled states. We then generalize the symmetry detector to n-pair emissions and show that it is capable of determining the number of the pairs emitted indistinguishably from the spontaneous parametric down-conversion source, which may contribute to explore multipair entanglement with a large number of photons.
Abstract A higher-order parametric down-conversion (PDC) photon state is amazingly different from the states involving independent photon pairs. We focus on the third-order PDC photons. Firstly, we present a symmetry detector which is capable of analyzing twin-beam six-photon symmetric states in the regime of weak nonlinearities. By cascading symmetry detectors, then, it is shown that one can generate third-order PDC photons from a class of twin-beam six-photon symmetric states. Finally, as an example, we describe an application of third-order PDC photons for exploring six-mode-photon entangled states with linear optics.
Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.
Abstract We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility χ ( 2 ) . Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method at 0.0783 for a specific concrete example. Our method is more effective because the conversion efficiency (entangled biphotons per incident pump photons) in the spontaneous parametric downconversion is of the order of 4 × 10 − 6 . The only drawback is that it requires very fine tuning of the frequency of signal photons fed into the photonic crystal; for example, an adjustment is given by Δ ν = 3.11 × 10 8 Hz for the signal light of ν = 3.23 × 10 14 Hz. We investigate the application of entangled photons produced by our method to the BB84 quantum key distribution protocol, and we explore how to detect an eavesdropper. We suggest that our method is promising for decoy-state quantum key distribution using weak coherent light.
Nowadays,the generation of multiphoton entangled states is almost realized by combining the coupled entangled photons emitted from spontaneous parametric down-conversion (SPDC) with the first-order term.In this case,one may focus mainly on the first-order term,and then avoid multipair emission events by restricting experimental parameters.On the other hand,for the higher-order terms in SPDC source,these emitted entangled photons have interesting features.For example,they are entangled maximally not only in photon number for the spatial modes,but also in polarization degree of freedom.In general,two photons,which are entangled in two or more degrees of freedom,are called hyperentangled pair of photons or hyperentangled state.We present a scheme to generate the four-photon hyperentangled state based on four indistinguishable photons emitted from SPDC source with the second-order term.Consider two SPDC sources with equal probability of emission of photons in respective spatial modes.With the passive linear optical devices,i.e., beam splitters,half wave plates,polarizing beam splitters,etc.,under the condition of registering a specified four-photon coincidence,we can obtain the four-photon hyperentangled state in which the photons are entangled in both polarization and spatial-mode degrees of freedom.Here,of course,for an arbitrary fourfold coincidence detection,one obtains a canonical four-photon Greenberger-Horne-Zeilinger (GHZ) state.Then we show the results of fourfold coincidence detections and the corresponding probabilities for the four-photon GHZ states,where the generation of the four-photon hyperentangled state is included as long as we are not to distinguish the two detectors located at the same locations. As a result,our scheme has two notable features.When we only consider the second-order emission,since it is not needed for us to distinguish between the two SPDC sources,the present scheme is simple and feasible.Also,based on the postselection with fourfold coincidence detection,our scheme is suitable for the normal first-order emission where we restrict the four photons emitted from the same source.In this sense,our scheme is efficient.In a word,we describe a method to generate the four-photon hyperentangled state with the second-order emission in SPDC source,which may contribute to the exploration of multipair entanglement with higher-order emissions from the SPDC source.
A bipartite multiphoton entangled state is created through stimulated parametric down-conversion of strong laser pulses in a nonlinear crystal. It is shown how detectors that do not resolve the photon number can be used to analyze such multiphoton states. Entanglement of up to 12 photons is detected using both the positivity of the partially-transposed density matrix and a newly derived criteria. Furthermore, evidence is provided for entanglement of up to 100 photons. The multiparticle quantum state is such that even in the case of an overall photon collection and detection efficiency as low as a few percent, entanglement remains and can be detected.
We propose two interesting methods of generating the four-photon W state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon W state, the three-photon Greenberger–Horne–Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general n -photon W state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.