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Long-distance entanglement and quantum communication in coupled cavity arrays

S. M. Giampaolo, Fabrizio Illuminati

Published Jun 15, 2009• 0 citations
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Abstract

We introduce quantum spin models that allow for long-distance end-to-end entanglement and long-distance, high-fidelity teleportation, even at moderately high temperatures. We show how these models, that realize an optimal compromise between scalability and resilience to decoherence, can be implemented in simply engineered arrays of coupled optical cavities. We demonstrate how the latter can be used to realize a quasi-deterministic scheme of long-distance quantum communication with high success rate, without direct projection on Bell states and Bell measurements.

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We introduce quantum spin models that allow for long-distance end-to-end entanglement and long-distance, high-fidelity teleportation, even at moderately high temperatures. We show how these models, that realize an optimal compromise between scalability and resilience to decoherence, can be implemented in simply engineered arrays of coupled optical cavities. We demonstrate how the latter can be used to realize a quasi-deterministic scheme of long-distance quantum communication with high success rate, without direct projection on Bell states and Bell measurements.
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
We propose a feasible scheme for teleporting an arbitrary polarization state or entanglement of photons by requiring only single-photon (SP) sources, simple linear optical elements and SP quantum non-demolition measurements. An unknown SP polarization state can be faithfully teleported either to a duplicate polarization state or to an entangled state. Our proposal can be used to implement long-distance quantum communication in a simple way. The scheme is within the reach of current technology and significantly simplifies the realistc implementation of long-distance high-fidelity quantum communication with photon qubits.
Isotropic XXXXXX models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We introduce two types of models: (i) open, dimerized XXXXXX chains, and (ii) open XXXXXX chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model (i) supports true long-distance entanglement at zero temperature, while model (ii) supports ``quasi-long-distance'' entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model (i) and algebraic in model (ii), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.
Quantum networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information processing. Deterministic entanglement distribution over long distances is a prerequisite for scalable quantum networks, enabling the utilization of device-independent quantum key distribution (DI-QKD) and quantum teleportation to achieve secure and efficient information transfer. However, the exponential photon loss in optical fibres prohibits efficient and deterministic entanglement distribution. Quantum repeaters, incorporating entanglement swapping and entanglement purification with quantum memories, offer the most promising means to overcome this limitation in fibre-based quantum networks. Despite numerous pioneering efforts toward realizing quantum repeaters, a critical bottleneck remains, as remote memory-memory entanglement suffers from decoherence more rapidly than it can be established and purified over long distances. We overcome this by developing long-lived trapped-ion memories, an efficient telecom interface, and a high-visibility single-photon entanglement protocol. This allows us to establish and maintain memory-memory entanglement over a 10 km fibre within the average entanglement establishment time for the same distance. As a direct application, we demonstrate metropolitan-scale DI-QKD, distilling 1,917 secret keys out of 4.05*10^5 Bell pairs over 10 km. We further report a positive key rate over 101 km in the asymptotic limit, extending the achievable distance by more than two orders of magnitude. Our work provides a critical building block for quantum repeaters and marks an important step toward scalable quantum networks.