Device-independent quantum secure direct communication (DI-QSDC) transmits a secret message directly over a quantum channel with security certified only by the observed violation of a Bell inequality, without trusting the internal workings of the devices. The original DI-QSDC protocol of Zhou, Sheng and Long (2020) and all subsequent variants establish security and secret-message capacity only against collective attacks, where the eavesdropper attacks each signal independently and may then measure all her ancillas jointly. The open problem is a full device-independent security proof of QSDC against the most general coherent attacks, in which the eavesdropper couples a single global ancilla to all transmitted systems — with secrecy of the directly transmitted message and, as recognized open sub-directions of the 2024 survey rather than strict completion conditions, a finite-size analysis covering the Bell-test statistics and the idealized device assumptions (perfect quantum memories and single-photon detectors). The technique that achieved this for device-independent quantum key distribution, the entropy accumulation theorem, has not been extended to the direct-communication setting, and a 2024 survey confirms that security proofs of QSDC against coherent attacks remain work in progress.

Background

Quantum secure direct communication (QSDC) is a branch of quantum cryptography in which Alice sends a secret message to Bob directly through the quantum channel, without first establishing a shared secret key; eavesdropping on the quantum carriers disturbs them and can be detected, so the message need never be encrypted classically. This differs from quantum key distribution (QKD), where a raw key is transmitted and then distilled by classical error correction and privacy amplification. In QSDC the transmitted data must not leak to the eavesdropper Eve at all, which makes the security notion more delicate: there is no post-transmission hashing step that could remove Eve's partial information. A 'device-independent' (DI) protocol removes trust in the physical apparatus: security is inferred only from the classical input–output correlations observed by Alice and Bob, specifically from the violation of the CHSH (Clauser–Horne–Shimony–Holt) Bell inequality — an inequality on measurement correlations that any local hidden-variable theory satisfies and that quantum entangled states can violate. The degree of CHSH violation upper-bounds the information any quantum adversary can hold about the outcomes, a technique introduced by Acín et al. (Phys. Rev. Lett. 2007) and Pironio et al. (New J. Phys. 2009) for DI-QKD. In the DI-QSDC protocol family of Zhou, Sheng and Long (Sci. Bull. 2020) and its successors, Alice and Bob first distribute entangled photon pairs (EPR pairs, i.e. maximally entangled two-particle states), test a random subset by CHSH measurement to bound Eve's information, then Alice encodes her message directly on her photons (for example by local Pauli operations) and sends them to Bob, who reads the message from Bell-state measurement outcomes (a joint measurement projecting onto maximally entangled states). Two heralded probabilistic modules — noiseless linear amplification (NLA, an operation that probabilistically reverses part of the channel loss) and entanglement purification protocols (EPP, which distill fewer higher-fidelity entangled pairs from several noisy ones) — counter channel loss and decoherence. The existing analyses consider the collective attack, in which Eve attaches an independent ancilla to each signal and stores all ancillas for a later joint measurement. The strongest attack class is the coherent attack, in which Eve prepares one global ancilla interacting with all transmitted systems in an arbitrary way and performs an arbitrary joint measurement; a scheme is not considered information-theoretically secure in the usual sense until it is proven secure against coherent attacks. For DI-QKD this gap was closed by the entropy accumulation theorem of Arnon-Friedman et al. (Nat. Commun. 2018), which reduces the analysis of general attacks to single-round entropic bounds and simultaneously yields finite-key guarantees. No analogous reduction exists for DI-QSDC, where the security target is the secrecy of a directly encoded message read out by Bell-state measurements in a two-way transmission, rather than a distilled key.

Problem Statement

Provide a device-independent security proof of quantum secure direct communication against the most general coherent attacks. For a DI-QSDC protocol of the Zhou–Sheng–Long family (or a concrete variant that preserves device-independent direct communication), in which security is certified solely by observed CHSH violation and the message is encoded directly on quantum systems and read out by Bell-state measurements, establish: (i) a formal security criterion stating that Eve, restricted only by quantum physics and allowed a single global ancilla coupled arbitrarily to all transmitted systems across both transmission rounds with an arbitrary joint (coherent) measurement, obtains negligible information about the directly transmitted message — negligible in the number of signal rounds nn at fixed failure probability; composability in the DI-QKD sense (the protocol remaining secure when arbitrarily composed with other uses of the same or other cryptosystems) is a desirable property of such a criterion, not a separate acceptance requirement; and (ii) a positive secret-message capacity (or leakage) bound in terms of the observed CHSH value and channel parameters that reduces, in the collective-attack special case, to the collective-attack communication-efficiency bound established for the source protocol (arXiv:1907.01235, Eq. (17): Ec1≥1−h(Q2)−I2(S2)E_{c1} \geq 1 - h(Q_2) - I_2(S_2), with the CHSH interception bound I2(S2)≤h((1+(S2/2)2−1)/2)I_2(S_2) \leq h((1+\sqrt{(S_2/2)^2-1})/2) of Eq. (14) and hh the binary entropy of Eq. (15)), or to the corresponding collective-attack bound of the chosen variant. A complete treatment may additionally address the finite-size statistics of the Bell test (guarantees holding at a fixed, finite number of signal rounds rather than only asymptotically) and either remove or explicitly justify the idealized assumptions of perfect quantum memories and perfect single-photon detectors used in the existing collective-attack analyses; both points are open sub-directions recognized in the 2024 survey (Pan et al., Sec. V-B) rather than strict completion conditions. This is the core open problem left by the source paper's collective-attack-only proof; the paper's companion acknowledged directions (non-destructive protection of encoded pairs against second-transmission decoherence, and optimization of the heralded NLA/EPP throughput trade-off) are related but separate open questions outside this problem's completion boundary.

References

  1. Lan Zhou, Yu-Bo Sheng, Gui-Lu Long, 'Device-independent quantum secure direct communication against collective attacks', Science Bulletin 65(1), 12-20 (2020). DOI: 10.1016/j.scib.2019.10.025, https://doi.org/10.1016/j.scib.2019.10.025
  2. Lan Zhou, Yu-Bo Sheng, 'One-step device-independent quantum secure direct communication', Science China Physics, Mechanics & Astronomy 65(5), 250311 (2022). DOI: 10.1007/s11433-021-1863-9, https://doi.org/10.1007/s11433-021-1863-9
  3. Lan Zhou, Bao-Wen Xu, Wei Zhong, Yu-Bo Sheng, 'Device-Independent Quantum Secure Direct Communication with Single-Photon Sources', Physical Review Applied 19, 014036 (2023). DOI: 10.1103/PhysRevApplied.19.014036, arXiv:2303.15858, https://arxiv.org/abs/2303.15858
  4. Hui Zeng, Ming-Ming Du, Wei Zhong, Lan Zhou, Yu-Bo Sheng, 'High-capacity device-independent quantum secure direct communication based on hyper-encoding', Fundamental Research 4(4), 851-857 (2024). DOI: 10.1016/j.fmre.2023.11.006, https://doi.org/10.1016/j.fmre.2023.11.006
  5. Pritam Roy, Subhankar Bera, Shashank Gupta, A. S. Majumdar, 'Device-independent quantum secure direct communication under non-Markovian quantum channels', Quantum Information Processing 23(5), 170 (2024). DOI: 10.1007/s11128-024-04397-8, arXiv:2312.03040, https://arxiv.org/abs/2312.03040
  6. Nayana Das, Goutam Paul, 'Device-Independent Quantum Secure Direct Communication with User Authentication' (2023). arXiv:2304.03201, https://arxiv.org/abs/2304.03201
  7. Dong Pan, Gui-Lu Long, Liuguo Yin, Yu-Bo Sheng, Dong Ruan, Soon Xin Ng, Jianhua Lu, Lajos Hanzo, 'The Evolution of Quantum Secure Direct Communication: On the Road to the Qinternet', IEEE Communications Surveys & Tutorials 26(3), 1898-1949 (2024). DOI: 10.1109/COMST.2024.3367535, arXiv:2311.13974, https://arxiv.org/abs/2311.13974
  8. Seyed Arash Ghoreishi, Giovanni Scala, Renato Renner, Letícia Lira Tacca, Jan Bouda, Stephen Patrick Walborn, Marcin Pawłowski, 'The future of secure communications: Device independence in quantum key distribution', Physics Reports 1149, 1-97 (2025). DOI: 10.1016/j.physrep.2025.09.006, arXiv:2504.06350, https://arxiv.org/abs/2504.06350
  9. Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, Valerio Scarani, 'Device-Independent Security of Quantum Cryptography against Collective Attacks', Physical Review Letters 98, 230501 (2007). DOI: 10.1103/PhysRevLett.98.230501, https://doi.org/10.1103/PhysRevLett.98.230501
  10. Stefano Pironio, Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Valerio Scarani, 'Device-independent quantum key distribution secure against collective attacks', New Journal of Physics 11, 045021 (2009). DOI: 10.1088/1367-2630/11/4/045021, https://doi.org/10.1088/1367-2630/11/4/045021
  11. Rotem Arnon-Friedman, Frédéric Dupuis, Omar Fawzi, Renato Renner, Thomas Vidick, 'Practical device-independent quantum cryptography via entropy accumulation', Nature Communications 9, 459 (2018). DOI: 10.1038/s41467-017-02307-4, https://doi.org/10.1038/s41467-017-02307-4
  12. Jianyong Hu, Mingyong Jing, Peng Zhang, Qiangqiang Zhang, Huifang Hou, Liantuan Xiao, Suotang Jia, 'Security proof of the two-way quantum secure direct communication with channel loss and noise' (2017). arXiv:1706.03234, https://arxiv.org/abs/1706.03234