Heralded quantum steering over a high-loss channel

Abstract

Entanglement is the key resource for many long-range quantum information tasks, including secure communication and fundamental tests of quantum physics. These tasks require robust verification of shared entanglement, but performing it over long distances is presently technologically intractable because the loss through an optical fiber or free-space channel opens up a detection loophole. We design and experimentally demonstrate a scheme that verifies entanglement in the presence of at least 14.8 ± 0.1 dB of added loss, equivalent to approximately 80 km of telecommunication fiber. Our protocol relies on entanglement swapping to herald the presence of a photon after the lossy channel, enabling event-ready implementation of quantum steering. This result overcomes the key barrier in device-independent communication under realistic high-loss scenarios and in the realization of a quantum repeater.

Fig. 1. Conceptual representation of the quantum steering protocols.

The blue background denotes untrusted channel components that belong to Alice, and the green background denotes the trusted side, Bob. (A) Conventional steering: ① Alice prepares a pair of photons and sends one of them to Bob. ② Bob announces his measurement setting, k, from a predetermined set of n observables. ③ Bob records his measurement outcome ${\widehat{\mathrm{\sigma }}}_{\mathit{k}}^{\mathit{B}}$, and Alice declares her result A_k. Steps 1 to 3 are iterated to obtain the steering parameter S_n. (B) Heralded quantum steering protocol. Bob uses a classical signal from a successful Bell state measurement (BSM) measurement ②a to herald the presence of Alice’s photon after the lossy channel, ignoring all the trials when the BSM was not successful. From step ②b, the protocol proceeds as in (B).

Fig. 2. Experimental setup.

Two group-velocity-matched sources (25), PS₁ and PS₂, are pumped by a mode-locked femtosecond Ti:sapphire laser to generate two polarization-entangled photon pairs at 1570 nm in the |Ψ⁻〉 state. Blue and green backgrounds outline the untrusted and trusted sides, respectively (all untrusted elements are grouped with Alice, even if they are not in her “lab” in practice). A-PA and B-PA are the polarization analyzer (tomography) stages of Alice and Bob, and BSM is the Bell state measurement gate, composed of a nonpolarizing 50:50 beam splitter. A variable neutral density (ND) filter is used in the output of PS₂ leading to the BSM to introduce the channel loss, L. Eight-nanometer band-pass (BP) filters were placed in the path of the photon going to B-PA and after beam splitter (BS), increasing the singlet state fidelity and interference visibility while maintaining Alice’s high heralding efficiency. For the conventional steering measurement, the output of PS₂ containing the ND filter was directly connected to the A-PA stage through the fiber, bypassing the BSM gate and PS₁. SNSPD, superconducting nanowire single-photon detector; PP-KTP, periodically poled potassium titanyl phosphate.

Fig. 3. Experimental results.

(A) Real and (B) imaginary parts of the reconstructed density matrix ρ of the entanglement-swapped two-photon state with no additional loss applied to the quantum channel. (C) Quantum steering measurement results for different amounts of channel loss. Black and gray lines are, respectively, the C₆(ε) and C_∞(ε) steering bounds from the study of Bennet et al. (21), and the red background highlights the region where detection loophole–free steering with the n = 6 measurement fails. The black circle, green triangles, yellow diamonds, and red squares mark the steering results achieved in the presence of 0, 7.7 ± 0.1, 11.3 ± 0.1, and 14.8 ± 0.1 dB of added channel loss, respectively. Filled markers correspond to steering parameters measured with the conventional steering protocol. Empty markers correspond to the heralded quantum steering results, each calculated from at least 500 fourfold coincidence counts (Table 1).