Entanglement Preservation and Clauser-Horne Nonlocality in Electromagnetically Induced Transparency Quantum Memories

TL;DR

The paper addresses whether electromagnetically induced transparency (EIT) quantum memories can preserve entanglement and nonlocality in the presence of ground-state decoherence. It develops a unified open-system model that merges the dark-state polariton (DSP) description with reduced density-operator theory to derive the retrieved state under realistic decoherence. A key result is the identification of a storage-efficiency threshold of about $0.897$, above which retrieved states violate the Clauser-Horne inequality, demonstrating preservation of nonlocal correlations. The framework extends to $N$ memory nodes, predicting near-unity fidelity in the ideal limit and providing a rigorous foundation for scalable entanglement distribution in quantum networks.

Abstract

Entanglement preservation in noisy quantum memories represents a long-standing conceptual challenge in quantum information science. While experiments have shown that electromagnetically induced transparency (EIT) memories can store entangled photons, a rigorous theoretical demonstration of whether such memories fundamentally preserve nonlocality has remained elusive. Here we develop a unified open-system model that combines the dark-state polariton formalism with reduced density operator theory to describe the retrieved photon state under realistic ground state decoherence. The analysis reveals that decoherence inevitably transforms an initially pure Bell state into a mixed state and predicts a critical storage efficiency threshold of 89.7%. Above this threshold, the retrieved photon violates the Clauser-Horne inequality, confirming the preservation of nonlocal quantum correlations, whereas below it, nonlocality is lost. This work provides the first systematic theoretical proof that EIT quantum memories can in principle preserve entanglement and nonlocality, thereby resolving a fundamental question in the physics of quantum information storage.

Figures (4)

• Figure 1: EIT quantum memory in an atomic ensemble. (a) Energy-level diagram illustrating the $\Lambda$-type EIT scheme and the corresponding transitions for the two participating fields. (b) Schematic representation showing the propagation directions of the two participating fields, where all light fields propagate in the same direction.
• Figure 2: The Rabi frequency of the coupling field $\Omega_c(t)$ and the mixing angle $\theta(t)$ as functions of time during the storage and retrieval processes in EIT quantum memory. For $t \leq t_1$ or $t \geq t_2$, the coupling Rabi frequency remains constant, and the mixing angle approaches zero, i.e., $\Omega_c(t) = \Omega_c(0)$ and $\theta(t) \approx 0$. During the storage interval ($t_1 \leq t \leq t_2$), except for the brief switching periods of the coupling field, $\Omega_c(t) = 0$ and $\theta(t) = \frac{\pi}{2}$. In this regime, the probe field is completely mapped into the spin-wave coherence of the atomic medium.
• Figure 3: Fidelity of EIT quantum memory as functions of ground-state decoherence rate $\gamma_{21}$ and storage time $\Delta t_s$. (a) Fidelity versus $\gamma_{21}$ for various $\Delta t_s$. (b) Fidelity versus $\Delta t_s$ for various $\gamma_{21}$. Note that $\Gamma_{780} = 2\pi \times 6.063$ MHz for $^{87}\text{Rb}$ atoms.
• Figure 4: Entanglement preservation and nonlocality in EIT quantum memories demonstrated via Clauser-Horne (CH) tests. (a) Schematic of an EIT memory scheme for a pair of single-rail-encoded qubits $\mathrm{Q_A}$ and $\mathrm{Q_B}$. The two spatially separated qubits are stored simultaneously in respective EIT quantum memories, $\mathrm{QM_A}$ and $\mathrm{QM_B}$, with the phases of the retrieved fields corrected by phase shifters (PSs). In the CH Bell test, the retrieved qubits $\mathrm{Q_A'}$ and $\mathrm{Q_B'}$ are sent to Alice and Bob, respectively, after being combined with local oscillators $|\gamma_a\rangle$ and $|\gamma_b\rangle$ via beam splitters (BSs). (b) Fidelity between the input state $|\phi_p(0)\rangle$ and the retrieved state $\rho_p(t)$ as a function of the storage efficiencies $\eta_A$ and $\eta_B$ in the EIT memory scheme. (c) Minimum value of the CH combination for the retrieved state $\rho_p(t)$ as a function of the storage efficiencies $\eta_A$ and $\eta_B$. The dark plane indicates the CH inequality boundary ($CH = -1$) for local theories, with nonlocality confirmed in the region where $CH_{\text{min}} < -1$.