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CRC Press eBooks

Generation of the Four-Photon W State and Other Multiphoton-Entangled States Using Parametric Down-Conversion

Takayoshi Kobayashi

Published Oct 15, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9781003618997-29

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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.
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.
We propose a method of generating the three-photon W state. The method uses parametric down-conversion process and hybrid entanglement swapping from multiphoton spin-entangled states to multiphoton orbital angular momentum (OAM) entangled states, with the aid of a pair of polarization photons. They generate W state entangled in different degrees of freedom of polarization and OAM with a high-dimensional Hilbert space. By simply changing the methods of generating a polarization-OAM-linear momentum entangled W state. Our method produces two mutually symmetric W states with strong entanglement and high dimension, which is expected to realize the secure communication of extending quantum bits.
High-quality entangled photon pairs generated via spontaneous parametric down-conversion have made great contributions to the modern quantum information science and the fundamental tests of quantum mechanics. However, the quality of the entangled states decreases sharply when moving from biphoton to multiphoton experiments, mainly due to the lack of interactions between photons. Here, for the first time, we generate a four-photon Greenberger-Horne-Zeilinger state with a fidelity of 98%, which is even comparable to the best fidelity of biphoton entangled states. Thus, it enables us to demonstrate an ultrahigh-fidelity entanglement swapping-the key ingredient in various quantum information tasks. Our results push the fidelity of multiphoton entanglement generation to a new level and would be useful in some demanding tasks, e.g., we successfully demonstrate the genuine multipartite nonlocality of the observed state in the nonsignaling scenario by violating a novel Hardy-like inequality, which requires very high state-fidelity.
Advancing quantum information processing is predicated on the preparation of ever-larger multiqubit states. Photonic realizations of such states may be achieved by increasing the number of photons populating the state or the number of qubits encoded per photon. Typical approaches to the latter strategy utilize distinct degrees of freedom of the photon field. We present here an approach that encodes two qubits per photon in the spatial parity of its transverse spatial profile. Simple linear optical devices transform each parity qubit separately or the two qubits jointly. Furthermore, we demonstrate that entangled photon pairs produced by spontaneous parametric down-conversion may be used to prepare arbitrary four-qubit states through sculpting the spatial profile of the classical optical pump. Two examples are highlighted---the preparation of two-photon four-qubit Greenberger-Horne-Zeilinger and WWW states, whose encoding in a photon pair has thus far eluded other approaches.
Quantum Dicke state belongs to the class of maximally entangled state. Due to its complicated entangled structure and robustness against decoherence, it is the important resource for the investigation of entanglement properties and the creation of quantum network. How to generate Dicke state and apply Dicke state in quantum communication protocol becomes a hot topic in the area of quantum information science. In this paper, we focus on the problem how to create arbitrary multi-photon Dicke state efficiently. The experimental generations and applications of four-photon and six-photon Dicke state had been reported in recent years. However, the generation is not scalable, that is it is difficult to generate Dicke state with more photons only using spontaneous parametric down-conversion and linear optical technology. If assisted with the weak cross-Kerr nonlinearity, it is possible to generate multi-photon Dicke state with some probability. However, it is still impossible to generate Dicke state with arbitrary coefficients, and the success probability decreases exponentially with the increasing of photon number. Here, we use three element gates called c-path gate, merging gate, entangler, which are introduced in former works, to design the generation of Dicke state. Firstly, the deterministic scheme of four-photon Dicke state generation is provided. After that, we modify the former W state generation scheme to be available for arbitrary coefficients W state generation. For the generation of arbitrary Dicke state, we decompose it to be a series of W state generations, with the help of c-path gates and merging gates. This scheme is deterministic and available for arbitrary coefficients. Especially, for some classes of Dicke states generation, the required resources are only polynomial growth with the increasing of photon number. All these features will make the investigation of multi-photon Dickes to be more convenient than the former schemes. In addition, our scheme is theoretically feasible with the current experimental technology.