Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection

TL;DR

The paper tackles secure, fault-tolerant long-distance quantum communication by eliminating the need for pre-shared entanglement through a scheme that encodes quantum data with quantum error-correcting codes and deliberately injects uncorrectable errors. By combining data with dummy states in mutually unbiased bases, randomly permuting components, and performing syndrome-based verification, the approach detects eavesdropping while enabling reliable transmission over noisy channels. A rigorous security analysis shows resilience against intercept-and-resend attacks and bounds accessible information, with leakage diminishing as data length grows, though the absolute leakage scales with total message size. Resource and fidelity analyses indicate that, in low-noise regimes, the proposed method reduces qubit overhead and can surpass traditional long-distance entanglement distribution schemes in fidelity, suggesting practical scalability for quantum networks and future quantum internet applications.

Abstract

Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification, leading to significant resource overhead and operational complexity. In this study, we propose a novel fault-tolerant and secure quantum communication scheme based on uncorrectable error injection. Our method exploits a quantum state encoding scheme based on quantum error correction codes, which strategically introduces uncorrectable errors to enhance security. It eliminates the need for entanglement distribution while reducing resource requirements. The injected errors protect against eavesdropping by preventing unauthorized parties from retrieving meaningful information. Security analysis shows that as the data length and encoded message size increase, information leakage becomes negligible relative to the size of the total message. Comparative performance analysis with existing approaches indicates that our method reduces transmission overhead while maintaining comparable fidelity in low-error regimes. These findings suggest that the proposed method offers a scalable and practical alternative for secure long-distance quantum communication, distributed quantum computing, and future quantum internet applications.

Figures (7)

• Figure 1: Schematic of the long-distance entanglement distribution Blue spheres represent the entangled pairs and gray spheres represent the ancilla qubits used for purification. By repeatedly performing entanglement purification to enhance fidelity and entanglement swapping, entangled pairs can be shared over long distances.
• Figure 2: Schematic of the proposed scheme's encoding, and encryption.(a) The sender prepares an arbitrary quantum data $|\psi'\rangle = \sum_{i=0}^{2^{k'}-1} c_i |m_i\rangle$, which is to be transmitted. We assume that the quantum channel is noisy and insecure, while the classical channel is error-free and authenticated. This state is embedded into a larger quantum register by appending mutually unbiased dummy states $|D\rangle= \bigotimes_{i=1}^{k-k'} X^{\mathbf{\kappa^{1}_{i}}}Z^{\mathbf{\kappa^{2}_{i}}}H^{\mathbf{\kappa^{3}_{i}}} |0\rangle^{\otimes k-k'}$ and zero ancillary qubits, yielding $|\psi\rangle = |\psi'\rangle|D\rangle|0\rangle^{\otimes n-k}$. (b) The $k'$ quantum data qubits and $k-k'$ dummy states are randomly shuffled into $k$ slots. This permutation is implemented by the operator $P_{\mathbf{\kappa^4}}$, which is determined by a random $k$-bit key $\mathbf{\kappa^4}$ with a Hamming weight of $k'$. This state is expressed as $|\psi\rangle = U_c |\psi'\rangle |0\rangle^{\otimes n-k'}$, where $U_c = (P_{\kappa^4} \otimes I^{\otimes n-k})(I^{\otimes k'} \otimes U_{MUB} \otimes I^{\otimes n-k})$ denotes the composite operation including permutation and mutually unbiased basis transformation. This state is subsequently encoded using a $[[n,k,d]]$ QECC, yielding the logical state $|\psi\rangle_L = U_E |\psi\rangle$. (c) An uncorrectable error $E_{un}$ is intentionally injected into the logical state to generate the encrypted state $|\psi\rangle_E = E_{un}|\psi\rangle_L$. The sender transmits both the syndrome $s$ corresponding to $E_{un}$ and the encrypted state $|\psi\rangle_E$ to the receiver, who performs syndrome-based decoding and verification to recover the original message.
• Figure 3: Schematic of the proposed scheme's decryption process: (a-i) The receiver performs syndrome-based error correction on the received encrypted state using the attached syndrome. (b-i) The receiver transmits $\textit{ACK}_1$ to notify successful receipt of the state. (b-ii) Upon receiving the acknowledgment, the sender transmits the injected uncorrectable error $E_{un}$ to the receiver. (b-iii) The receiver applies $E_{un}$ and verifies whether an all-zero syndrome is extracted; the protocol is aborted if the syndrome is not a zero vector. (c-i) If verification succeeds, the receiver sends $\textit{ACK}_2$ to the sender. (c-ii) The sender then transmits $P_{\kappa^4}$ and $U_{MUB}$. (c-iii) The receiver uses them to validate the dummy states $|D\rangle$ and check for possible eavesdropping attempts.
• Figure 4: Distance extension of the proposed scheme Relay nodes can perform error correction based on $s$, ensuring that relay nodes cannot obtain any information about the quantum states.
• Figure 5: Fidelity comparison between $F_{\mathrm{our}}$ and $F_{\mathrm{LDED}}$ with varying purification resource levels ($N_A = 2$, $3$, and $4$). The network consists of five nodes (i.e., $N=2$), and the Bell state measurement parameter is $n_{\mathrm{bsm}} = 2$. Solid lines indicate $F_{\mathrm{our}}$, and dashed lines indicate $F_{\mathrm{LDED}}$. The results show that in the low-error regime, the proposed scheme achieves higher fidelity.