A quantum network uses 4 entangled node pairs, each capable of transmitting 128 qubits per second. Due to decoherence, 12.5% of qubits fail during transmission. How many operational qubits are successfully transmitted by all pairs in 5 minutes?

["Title: How a Quantum Network Achieves Reliable Communication with Entangled Nodes – A 5-Minute Performance Analysis", "Meta Description: Explore a quantum network using 4 entangled node pairs, capable of transmitting 128 qubits per second each. With 12.5% decoherence-related qubit loss, this guide calculates total successful qubit transmission over 5 minutes.", "---", "### Leveraging Quantum Entanglement: A Network Built on 4 Entangled Node Pairs", "Quantum networking is emerging as a cornerstone of future secure communications and distributed quantum computing. At the heart of this system lies a carefully engineered quantum network composed of four entangled node pairs—each acting as a quantum link capable of transmitting 128 qubits per second. These entangled pairs enable high-speed, secure data transfer by exploiting quantum superposition and entanglement. However, the fragile nature of quantum states introduces challenges such as decoherence, where environmental interactions degrade qubit integrity and lead to data loss. Understanding how such networks maintain performance despite these limitations is crucial. This article examines the operational transmission metrics of a 4-node quantum network, factoring in a 12.5% qubit loss due to decoherence, and calculates the total number of successfully transmitted qubits over a 5-minute period.", "---", "### Understanding the Quantum Transmission Setup", "Each of the 4 entangled node pairs in the network supports a bi-directional quantum channel, meaning each link enables simultaneous quantum information exchange. The specification states that each qubit pair transmits 128 qubits per second under ideal conditions. With four such pairs operating in parallel, the theoretical maximum transmission rate is established by multiplying:", "[\n\ ext{Maximum throughput} = 4 \ imes 128 = 512 \ ext{ qubits per second}\n]", "This represents the quantum channel’s raw capacity before accounting for physical losses.", "---", "### Accounting for Decoherence: The 12.5% Failure Rate", "In quantum communication, decoherence remains a primary obstacle. Over time, quantum states interact uncontrollably with their environment, causing measured qubit states to collapse prematurely—resulting in data corruption. The problem is quantified here by a 12.5% qubit failure rate across all transmissions. This value reflects approximate system-level optical loss, thermal noise, and control errors common in real-world quantum hardware.", "Thus, only 87.5% of transmitted qubits successfully maintain coherence and are recognized as valid at the receiver end in each node pair.", "---", "### Calculating Total Operational Qubits Over 5 Minutes", "The transmission window spans 5 minutes, which equals:", "[\n5 \ imes 60 = 300 \ ext{ seconds}\n]", "With steady throughput of 512 qubits per second across all 4 pairs, the total raw (unadjusted) qubit delivery is:", "[\n512 \ ext{ qubits/sec} \ imes 300 \ ext{ sec} = 153,600 \ ext{ raw qubits}\n]", "To determine the number of operational—i.e., decoherence-resistant—qubits:", "[\n\ ext{Operational qubits} = 153,600 \ imes 0.875 = 134,400\n]", "---", "### Conclusion", "Despite environmental challenges like decoherence reducing qubit fidelity, this quantum network achieves sustained performance by leveraging four synchronized entangled pairs. With transmission rates of 128 qubits per second each and a 12.5% loss rate, 134,400 operational qubits are successfully transmitted over 5 minutes. This demonstrates not only the scalability of quantum repeater architectures but also the critical role of error mitigation in tomorrow’s quantum internet.", "---", "Keywords: quantum network, entangled nodes, qubit transmission, decoherence, quantum communication, 5-minute performance, quantum repeater, 128 qubits per second, 87.5% loss rate, secure quantum data transfer."]