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arXiv:2302.00697 · Physical Review A

Generating Greenberger-Horne-Zeilinger states using multiport splitters

Daniel Bhatti, Stefanie Barz

Published Mar 30, 2023• 10 citations
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Abstract

Symmetric multiport splitters are versatile tools in optical quantum information processing. They can be used for studying multiparticle scattering, for studying distinguishability and mixedness, and also for the generation of multipartite entangled quantum states. Here, we show that $N$-photon $N$-mode Greenberger-Horne-Zeilinger (GHZ) states can be generated using symmetric multiport beam splitters. Varying the input states' internal degrees of freedom and postselecting onto certain photon-number distributions allows the probabilistic generation of GHZ states with arbitrary photon numbers. We present two schemes, one for odd and one for even numbers of photons, to generate GHZ states using symmetric multiport splitters and compare them to a strategy utilizing a $2N$-port network as well as the standard postselection method.

DOI
10.1103/physreva.107.033714

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Abstract One of the most important resources for quantum optical experiments and applications are on-demand highly entangled multiphoton quantum states. A promising way of generating them is heralding entanglement generation at a high rate from letting independent photons interfere. However, such schemes often work for a specific internal degree of freedom of the interfering photons only. Going to higher numbers of entangled photons, the success probabilities decrease while the number of necessary resources, e.g. auxiliary photons and optical elements, increases. To make probabilistic schemes feasible also for larger quantum states, it is therefore important to find resource-efficient generation schemes with high success probabilities. In this work, we introduce easily implementable schemes to herald qubit Greenberger–Horne–Zeilinger (GHZ) states, higher-dimensional Bell states and higher-dimensional three-party GHZ states. Our schemes solely rely on multiphoton interference, i.e. they can be adjusted to work for arbitrary degrees of freedom. Furthermore, they demonstrate high success probabilities and need comparably few auxiliary photons.
Abstract Multipartite entanglement plays a central role in optical quantum technologies. One way to entangle two photons is to prepare them in orthogonal internal states, for example, in two polarisations, and then send them through a balanced beam splitter. Post-selecting on the cases where there is one photon in each output port results in a maximally entangled state. This idea can be extended to schemes for the post-selected generation of larger entangled states. Typically, switching between different types of entangled states requires different arrangements of beam splitters and so a new experimental setup. Here, we demonstrate a simple and versatile scheme to generate different types of genuine tripartite entangled states with only one experimental setup. We send three photons through a three-port splitter and vary their internal states before post-selecting on certain output distributions. This results in the generation of tripartite W, G and GHZ states. We obtain fidelities of up to ( 87.3 ± 1.1 ) % with regard to the respective ideal states, confirming a successful generation of genuine tripartite entanglement.
Abstract Multipartite entanglement is a critical resource in quantum information processing that exhibits much richer phenomenon and stronger correlations than in bipartite systems. This advantage is also reflected in its multi-user applications. Although many demonstrations have used photonic polarization qubits, polarization-mode dispersion confines the transmission of photonic polarization qubits through an optical fiber. Consequently, time–bin qubits have a particularly important role to play in quantum communication systems. Here, we generate a three-photon time–bin Greenberger–Horne–Zeilinger (GHZ) state using a 2 × 2 optical switch as a time-dependent beam splitter to entangle time–bin Bell states from a spontaneous parametric down-conversion source and a weak coherent pulse. To characterize the three-photon time–bin GHZ state, we performed measurement estimation, showed a violation of the Mermin inequality, and used quantum state tomography to fully reconstruct a density matrix, which shows a state fidelity exceeding 70%. We expect that our three-photon time–bin GHZ state can be used for long-distance multi-user quantum communication.
High-dimensional multipartite entanglement plays a crucial role in quantum information science. However, existing schemes for generating such entanglement become complex and costly as the dimension of quantum units increases. In this Letter, we overcome the limitation by proposing a significantly enhanced linear optical heralded scheme that generates the d-level N-partite Greenberger-Horne-Zeilinger (GHZ) state with single-photon sources and linear operations. Our scheme requires dN photons, which is the minimal required photon number, with substantially improved success probability from previous schemes. It employs linear optical logic gates compatible with any qudit encoding system and can generate generalized GHZ states with installments of beam splitters. With efficient generations of high-dimensional resource states, our work opens avenues for further exploration in high-dimensional quantum information processing.
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