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Ukrainian Information Security Research Journal

Analysis error correcting capability of error-correcting Fire code to implement ping-pong protocol with pairs of entangled qubits in a noisy quantum channel

Сергей Вадимович Николаенко, Евгений Викторович Василиу

Published Sep 15, 2012• 0 citations

Abstract

The paper develops the simulation model of a ping-pong protocol with pairs of entangled qubits in a noisy quantum channel in order to assess the error-correcting capability of error-correcting Fire code and to determine limits of applicability of code for quantum cryptography protocol. The detailed analysis of errors that will arise in the implementation of ping-pong protocol with pairs of entangled qubits in a noisy quantum channel is carried out. It is shown that the Fire code (60.44) fully corrects all errors, if the probability of qubit depolarizing channel is less than about 7% that corresponds to the modern experimental situation in the transmission of single photons over a distance about 100 km. With a higher noise level in the channel partial error correction with code Fire will increase the speed of information transmission in quantum ping-pong protocol.

DOI: 10.18372/2410-7840.14.3356

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Quantum cryptography protocols using entangled qubit pairs can increase the rate and security of information exchange through a quantum channel. Usually those protocols are non-deterministic, i.e. a classical bit is encoded in a quantum state, but the actual bit value cannot be determined. Therefore they request the transmission of additional information through a public channel. By contrast, the ping-pong coding scheme based on entangled photons allows for deterministic and direct key distribution. No qubit has to be discarded and information can be decoded without the need for a subsequent transmission of additional information. Communication through a public channel nevertheless is necessary to ensure asymptotical security against arbitrary eavesdropping attacks.

The "Ping-Pong" (PP) protocol is a two-way quantum key protocol based on entanglement. In this protocol, Bob prepares one maximally entangled pair of qubits, and sends one qubit to Alice. Then, Alice performs some necessary operations on this qubit and sends it back to Bob. Although this protocol was proposed in 2002, its security in the noisy and lossy channel has not been proven. In this report, we add a simple and experimentally feasible modification to the original PP protocol, and prove the security of this modified PP protocol against collective attacks when the noisy and lossy channel is taken into account. Simulation results show that our protocol is practical.

Quantum secure direct communication protocols offer confidential transmission of classic information over quantum channel without prior key agreement. The ping-pong based protocols provide asymptotic security and detailed analysis of security level provided by each variant of the protocol is required. The paper presents a general method of calculation of the eavesdropped information as a function of the attack detection probability. The method is applied to the ping-pong protocol based on completely entangled pairs of qudits. The upper and lower bounds on the amount of the leaked information and eavesdropping detection probability are provided.

Ping-Pong quantum communication protocol may be employed to transmit deterministically information, so it has instrigued mang researchers. However, there are drawbacks on the security due to the symmetry of the employed two-way quantum channel. In this paper we propose a new attack strategy to eavesdrop the initially transmitted information based on the techniques of quantum error correction code (QECC). In addition, an attack strategy of Ping-Pong scheme based either entanglement state or nonorthogonal state is proofed and demonstrated, respectively. Furthermore, information obtained by Eve and the possible probability detected by the legitimate communicators are analyzed by employing information theorems. Detail proofs and analysis illustrate all previous Ping-Pong quantum communication schemes are insecure, i.e., the eavesdropper may obtain all available information without being detected.

Quantum dense coding enables the transmission of two classical bits of information through the exchange of a single qubit, provided that an entangled state is shared between the communicating parties. While this protocol achieves a fundamental increase in channel capacity, its practical realization is strongly influenced by the presence of noise in realistic quantum channels. This work presents a simulation-based study of dense coding performance under two representative noise models: the depolarizing channel and the amplitude damping channel. Using Qiskit Aer, the bit error rate (BER), frame error rate (FER), and effective channel capacity are evaluated across a range of noise parameters. In addition, a classical threefold repetition strategy is examined as a lightweight error-mitigation technique. Results indicate that depolarizing noise produces more rapid degradation in both BER and channel capacity compared to amplitude damping, while repetition coding provides partial improvement in reliability at the expense of resource overhead. These findings highlight the trade-offs between efficiency and robustness in noisy implementations of dense coding and motivate further exploration of more advanced quantum error correction methods.