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Journal of the Optical Society of America B

Sharing quantum nonlocality and teleportation over long distances using optical hybrid states

Subhankar Bera, Soumyakanti Bose, Hyunseok Jeong, A. S. Majumdar

Published Sep 26, 2025• 2 citations
Publisher

Abstract

We analyze the sharing Bell-type nonlocal correlation between two distant parties with optical hybrid states comprising a single photon polarization state and a multiphoton coherent state. By deploying entanglement swapping over the coherent state parts at the middle station, we show that the optical hybrid states can efficiently generate a polarization-entangled state that violates the Clauser–Horne–Shimony–Holt Bell-inequality well over a metropolitan distance. We further assess the quality of the shared entangled state in the information processing task of quantum teleportation of an unknown polarization qubit. Our results with realistic devices, embedding detection inefficiency and transmission losses, indicate the viability of faithful quantum teleportation over large distances, consistent with the quality of the shared correlation.

DOI
10.1364/josab.573536

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We analyze the sharing Bell-type nonlocal correlation between two distant parties with optical hybrid states comprising a single photon polarization state and a multiphoton coherent state. By deploying entanglement swapping over the coherent state parts at the middle station, we show that the optical hybrid states can efficiently generate a polarization-entangled state that violates the Clauser–Horne–Shimony–Holt Bell-inequality well over a metropolitan distance. We further assess the quality of the shared entangled state in the information processing task of quantum teleportation of an unknown polarization qubit. Our results with realistic devices, embedding detection inefficiency and transmission losses, indicate the viability of faithful quantum teleportation over large distances, consistent with the quality of the shared correlation.
We analyze sharing Bell-type nonlocal correlation between two distant parties with optical hybrid states comprising a single photon polarization state and a multiphoton coherent state. By deploying entanglement swapping over the coherent state parts at the middle station, we show that the optical hybrid states can efficiently generate a polarization-entangled state that violates Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality well over a metropolitan distance. We further assess the quality of the shared entangled state in the information processing task of quantum teleportation of an unknown polarization qubit. Our results with realistic devices, embedding detection inefficiency and transmission losses, indicate the viability of faithful quantum teleportation over large distances, consistent with the quality of the shared correlation.
Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.
It was shown that using multiphoton qubits, a nearly deterministic Bell-state measurement can be performed with linear optics and on-off photodetectors [Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are generally more fragile than single-photon qubits under a lossy environment. In this paper, we propose and analyze a scheme to teleport multiphoton-qubit information using hybrid entanglement with a loss-tolerant carrier qubit. We consider three candidates for the carrier qubit: a coherent-state qubit, a single-photon polarization qubit, and a vacuum-and-single-photon qubit. We find that teleportation with the vacuum-and-single-photon qubit tolerates about 10 times greater photon losses than with the multiphoton qubit of the photon number $N\ensuremath{\ge}4$ in the high fidelity regime ($F\ensuremath{\ge}90%$). The coherent-state qubit encoding may be even better than the vacuum-and-single-photon qubit as the carrier when its amplitude is as small as $\ensuremath{\alpha}<0.78$. We further point out that the fidelity of the teleported state by our scheme is determined by loss in the carrier qubit while the success probability depends on loss only in the multiphoton qubit to be teleported. Our study implies that the hybrid architecture may complement the weaknesses of each qubit encoding.
Quantum steering, which lies between Bell nonlocality and entanglement, is a characteristic quantum correlation. Its application in quantum information tasks is worth pursuing. In this paper, we investigate the application of quantum steering as resource of quantum teleportation. It is found that two-qubit states violating the three-setting linear steering inequality are always useful for teleportation. Some steerable states which obey the Bell--Clauser-Horne-Shimony-Holt (CHSH) inequality could be used for teleportation. Two-qubit states that are optimal for quantum teleportation for a fixed amount of steering are present. The optimal states achieve the maximal average fidelity and also exhibit zero fidelity deviation.
Long-distance quantum state transfer (QST), which can be achieved with the help of quantum teleportation, is a core element of important quantum protocols. A typical situation for QST based on teleportation is one in which two remote communication partners (Alice and Bob) are far from the entanglement source (Charlie). Because of the atmospheric turbulence, it is challenging to implement the Bell-state measurement after photons propagate in atmospheric channels. In previous long-distance free-space experiments, Alice and Charlie always perform local Bell-state measurement before the entanglement distribution process is completed. Here, by developing a highly stable interferometer to project the photon into a hybrid path-polarization dimension and utilizing the satellite-borne entangled photon source, we demonstrate proof-of-principle QST at the distance of over 1200 km assisted by prior quantum entanglement shared between two distant ground stations with the satellite Micius. The average fidelity of transferred six distinct quantum states is 0.82±0.01, exceeding the classical limit of 2/3 on a single copy of a qubit.
We present a hybrid quantum repeater protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable ddd-level systems, each of, in principle, arbitrary dimension ddd, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially efficient continuous-variable homodyne detections (``hybrid'' here refers to the simultaneous exploitation of discrete- and continuous-variable degrees of freedom for the local processing and storage of entangled states as well as their nonlocal distribution, respectively) and unambiguous state discrimination. For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. For example, employing unambiguous state discrimination, with three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at an ideal maximal rate (assuming perfect gate operations) on the order of 100 Hz.