In a quantum teleportation protocol, each successful transmission requires 2 classical bits to transmit 1 qubit. The system transmits 45 qubits per second, but 5% of qubits fail and must be retransmitted. How many total classical bits are used in 2 minutes?

["Title: How Quantum Teleportation Uses Classical Bits: Calculating Total Classical Bits Transmitted", "Quantum teleportation is a foundational process in quantum communication, enabling the transfer of quantum states between distant locations using entanglement and classical communication. One key aspect of this protocol is the dependency on classical bits to ensure accurate transmission. Understanding how many classical bits are involved helps clarify the efficiency and resource demands of real-world quantum networks.", "### The Basis: Classical Bits Per Qubit", "In a standard quantum teleportation protocol, transmitting one qubit reliably requires 2 classical bits. These bits encode measurement results from the entangled pair, allowing the receiver to reconstruct the original qubit faithfully. Without these classical signals, the quantum state cannot be recovered correctly.", "### System Performance: Qubit Transmission Rate", "The system transmits 45 qubits per second. However, due to quantum decoherence and imperfections in qubit generation and detection, 5% of transmitted qubits fail and must be resent. This means only 95% of attempted transmissions succeed on the first try.", "### Calculating Total Qubits Sent in 2 Minutes", "- 2 minutes = 120 seconds\n- Qubits transmitted per second: 45\n- Total attempted qubits = 45 qubits/sec × 120 sec = 5,400 qubits", "Because 5% of qubits must be retransmitted, the system must send extra qubits to compensate for failures.", "Let’s compute how many total qubits are sent (including retransmissions):", "Let ( x ) be the total number of qubits sent. Since only 95% of these succeed, we have:", "[\n0.95x = 5,400\n]", "Solving for ( x ):", "[\nx = \frac{5,400}{0.95} = 5,684.21 \approx 5,684 \ ext{ total qubits sent (rounded up)}\n]", "Rounding up ensures all failed qubits are retransmitted.", "### Calculating Total Classical Bits Used", "Each qubit requires 2 classical bits. Therefore, total classical bits transmitted =\n[\n\ ext{Total qubits sent} \ imes 2 = 5,684 \ imes 2 = 11,368 \ ext{ classical bits}\n]", "This value accounts for all transmissions—both initial attempts and required retransmissions.", "### Summary", "- Transmit rate: 45 qubits/sec\n- Raw qubits over 2 minutes: 5,400 (first attempt only)\n- With 5% failure: total classical bits = 11,368 bits", "This figure highlights the overhead introduced by quantum noise and the crucial role of error correction and classical communication in enabling reliable quantum teleportation.", "### Key Takeaways", "- 2 classical bits are used per qubit in teleportation\n- Retransmissions due to failure increase total classical communication\n- Efficient management of qubit transmission and classical feedback is essential for scalable quantum networks", "Understanding these quantities not only deepens insight into quantum communication mechanics but also aids in designing efficient and robust quantum systems.", "---", "Keywords: quantum teleportation, classical bits, qubit transmission, error correction, quantum communication, retransmission rate, 45 qubits/sec, 5% failure, 2-minute transmission, quantum networking."]