Fundamental Limits of Repeaterless Quantum Communications

Fundamental Limits of Repeaterless Quantum Communications

24 Jan 2017 | Stefano Pirandola, Riccardo Laurenza, Carlo Ottaviani, Leonardo Banchi
The paper "Fundamental Limits of Repeaterless Quantum Communications" by Pirandola et al. investigates the optimal rates achievable in point-to-point quantum communications without the use of quantum repeaters. The authors determine the two-way quantum capacity ($Q_2$), two-way entanglement distribution capacity ($D_2$), and secret key capacity ($K$) for various fundamental quantum channels, including bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels. They achieve this by combining the relative entropy of entanglement (REE) with a technique called "teleportation stretching," which simplifies quantum protocols based on adaptive local operations and classical communication (LOCCs). The key findings include: 1. **Upper Bounds on Two-Way Capacities**: The authors establish upper bounds on the two-way capacities using the REE, showing that these capacities are bounded by the REE of the Choi matrix of the channel. 2. **Teleportation Stretching**: This technique reduces the adaptive protocols to a block form, allowing the REE bound to be simplified to a single-letter quantity. This simplification is crucial for deriving precise formulas for the two-way quantum and secret key capacities. 3. **Fundamental Rate-Loss Trade-offs**: The study provides a detailed analysis of the fundamental rate-loss trade-offs in quantum key distribution (QKD), particularly for lossy channels. The results show that the secret key capacity scales as $K \simeq 1.44\eta$ secret bits per channel use at high loss $\eta$, characterizing the maximum achievable rate in QKD. 4. **Generalizations and Applications**: The authors extend their results to various scenarios, including fading channels, multiband channels, and Gaussian noise channels. They also provide explicit formulas for the two-way capacities of specific channels, such as the lossy channel, quantum-limited amplifier, and additive-noise Gaussian channel. 5. **Classification of Channels**: The paper classifies channels into distillable and non-distillable categories, with distillable channels having capacities equal to their entanglement flux. The study also discusses the achievable rates for qubit channels and Pauli channels. Overall, the work sets the ultimate limits of point-to-point quantum communications and provides precise benchmarks for quantum repeaters, highlighting the importance of understanding the fundamental rate-loss scaling in quantum optical communications.The paper "Fundamental Limits of Repeaterless Quantum Communications" by Pirandola et al. investigates the optimal rates achievable in point-to-point quantum communications without the use of quantum repeaters. The authors determine the two-way quantum capacity ($Q_2$), two-way entanglement distribution capacity ($D_2$), and secret key capacity ($K$) for various fundamental quantum channels, including bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels. They achieve this by combining the relative entropy of entanglement (REE) with a technique called "teleportation stretching," which simplifies quantum protocols based on adaptive local operations and classical communication (LOCCs). The key findings include: 1. **Upper Bounds on Two-Way Capacities**: The authors establish upper bounds on the two-way capacities using the REE, showing that these capacities are bounded by the REE of the Choi matrix of the channel. 2. **Teleportation Stretching**: This technique reduces the adaptive protocols to a block form, allowing the REE bound to be simplified to a single-letter quantity. This simplification is crucial for deriving precise formulas for the two-way quantum and secret key capacities. 3. **Fundamental Rate-Loss Trade-offs**: The study provides a detailed analysis of the fundamental rate-loss trade-offs in quantum key distribution (QKD), particularly for lossy channels. The results show that the secret key capacity scales as $K \simeq 1.44\eta$ secret bits per channel use at high loss $\eta$, characterizing the maximum achievable rate in QKD. 4. **Generalizations and Applications**: The authors extend their results to various scenarios, including fading channels, multiband channels, and Gaussian noise channels. They also provide explicit formulas for the two-way capacities of specific channels, such as the lossy channel, quantum-limited amplifier, and additive-noise Gaussian channel. 5. **Classification of Channels**: The paper classifies channels into distillable and non-distillable categories, with distillable channels having capacities equal to their entanglement flux. The study also discusses the achievable rates for qubit channels and Pauli channels. Overall, the work sets the ultimate limits of point-to-point quantum communications and provides precise benchmarks for quantum repeaters, highlighting the importance of understanding the fundamental rate-loss scaling in quantum optical communications.
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Understanding Fundamental limits of repeaterless quantum communications