Quantum Key Distribution Contingency in the Absence of the Classical Channel
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis manuscript investigates a novel problem in Quantum Key Distribution (QKD): when the classical channel in the BB84 protocol fails or becomes unavailable due to attacks, can the system still provide limited key distribution functionality? The author proposes a scheme utilizing Trine POVM measurements to generate partially overlapping keys (approximately 72.77% overlap rate) and designs two quantum circuit implementation schemes based on Naimark extension. Experimental verification was conducted on the IBM quantum computing platform. The research topic is innovative and the findings are interesting. However, several critical issues need to be addressed before the manuscript can be considered for publication. I recommend Major Revision given my comments below can be taken into account:
- Security analysis is severely insufficient. The proposed scheme cannot perform core QKD security procedures such as basis reconciliation, error rate detection, and privacy amplification. The assumption that "the quantum channel is trusted" is difficult to establish in practical applications. Without these security guarantees, the generated keys may be vulnerable to eavesdropping attacks. The author should add a dedicated security analysis section to clearly define the applicable boundaries and security assumptions of the proposed scheme. Specifically: (1) How does the scheme detect the presence of an eavesdropper without classical channel communication? (2) What are the specific security guarantees provided by the 72.77% key overlap rate? Can this overlap rate be exploited by an adversary? (3) Under what attack models (individual attacks, collective attacks, or coherent attacks) can this scheme be considered secure?
- Analysis of practical application scenarios is not sufficiently deep. The author argues that when the classical channel fails, the quantum channel can serve as a backup. However, in practical QKD systems, the classical channel is typically more stable and reliable than the quantum channel, making the scenario where the classical channel fails first relatively rare. The author should analyze specific application scenarios in detail, such as: (1) In quantum satellite communications, classical communication may be interrupted due to weather conditions or satellite orbit changes, while quantum signals can still be received. Can the proposed scheme be applied in such scenarios? (2) In quantum networks, if certain nodes are attacked and classical communication is blocked, can this scheme provide emergency key distribution services? (3) What is the probability of the classical channel failing while the quantum channel remains functional in real-world deployments?
- Key generation efficiency analysis is missing. The author proposes using repetition coding and majority voting to handle key inconsistencies, but this approach significantly reduces the effective key generation rate. For example, with 3-bit repetition coding and approximately 27% error rate, the effective key generation rate is only about 3% of the original. The author should: (1) Provide quantitative efficiency analysis, including key generation rate, resource consumption, and time overhead. (2) Compare with other error correction schemes (such as LDPC codes, Cascade protocol) to demonstrate the advantages of the chosen scheme. (3) Consider whether more efficient error-correcting codes can be employed to improve key generation efficiency.
- Comparison with related work is insufficient. The manuscript lacks adequate comparison with related work in the field. The author should discuss the relationship between the proposed scheme and the following research directions: (1) Fault-tolerant QKD protocols: How does this scheme compare with existing fault-tolerant designs? (2) Measurement-Device-Independent QKD (MDI-QKD): Can similar ideas be applied to MDI-QKD systems? (3) Quantum state discrimination theory: How does the Trine POVM scheme relate to optimal quantum state discrimination? (4) Quantum error correction and fault-tolerant quantum computing: Are there connections with quantum error correction codes?
- Writing and formatting issues need to be addressed. Several writing and formatting issues should be corrected: (1) The keyword "quantum resilience" appears twice in the abstract, which should be corrected. (2) Some statements are not sufficiently clear. For example, the discussion of "negative search space" in Section 3 is not clearly related to the main topic. The author should reorganize or streamline this section. (3) Experimental details are insufficient. Although the author mentions that code is available on GitHub, the main text should provide more details about experimental setup, including specific quantum device models used, number of experimental runs, error bars, etc. (4) Some figures (such as Figure 3) are not strongly related to the main topic. The author should reconsider the necessity of each figure. (5) Some references are incomplete. The author should unify the format according to journal requirements.
Author Response
Dear Reviewer,
Thank you for your comments and recommendations for extending my work. I am attaching a revised pdf, where the added text is colored in blue (pages 14 and 21). Your points were implemented in detail as shown below.
Comment 1: Security analysis is severely insufficient. The proposed scheme cannot perform core QKD security procedures such as basis reconciliation, error rate detection, and privacy amplification. The assumption that "the quantum channel is trusted" is difficult to establish in practical applications. Without these security guarantees, the generated keys may be vulnerable to eavesdropping attacks. The author should add a dedicated security analysis section to clearly define the applicable boundaries and security assumptions of the proposed scheme. Specifically: (1) How does the scheme detect the presence of an eavesdropper without classical channel communication? (2) What are the specific security guarantees provided by the 72.77% key overlap rate? Can this overlap rate be exploited by an adversary? (3) Under what attack models (individual attacks, collective attacks, or coherent attacks) can this scheme be considered secure?
Response: Indeed, the security of the quantum channel is necessary for the protocol to work. Note that, this is a contingency plan and in no way an optimal setting. The purpose of the algorithm is to offer some functionality, or in other words, it is the difference between zero keys or some keys. The analysis of the error rate and key generation rate has also been added, this is the extensive answer to comment 3. Thank you for this comment.
Comment 2: Analysis of practical application scenarios is not sufficiently deep. The author argues that when the classical channel fails, the quantum channel can serve as a backup. However, in practical QKD systems, the classical channel is typically more stable and reliable than the quantum channel, making the scenario where the classical channel fails first relatively rare. The author should analyze specific application scenarios in detail, such as: (1) In quantum satellite communications, classical communication may be interrupted due to weather conditions or satellite orbit changes, while quantum signals can still be received. Can the proposed scheme be applied in such scenarios? (2) In quantum networks, if certain nodes are attacked and classical communication is blocked, can this scheme provide emergency key distribution services? (3) What is the probability of the classical channel failing while the quantum channel remains functional in real-world deployments?
Response: In the section “5. Methods”, I have added paragraphs that describe practical situations where the classical channel is unavailable. The most promising setting is, as you state, the satellite to ground connection. I have marked the extra text colored in blue in the pdf attached.
Comment 3: Key generation efficiency analysis is missing. The author proposes using repetition coding and majority voting to handle key inconsistencies, but this approach significantly reduces the effective key generation rate. For example, with 3-bit repetition coding and approximately 27% error rate, the effective key generation rate is only about 3% of the original. The author should: (1) Provide quantitative efficiency analysis, including key generation rate, resource consumption, and time overhead. (2) Compare with other error correction schemes (such as LDPC codes, Cascade protocol) to demonstrate the advantages of the chosen scheme. (3) Consider whether more efficient error-correcting codes can be employed to improve key generation efficiency.
Response: the you for the comment. Key efficiency is indeed a straightforward necessity of the analysis. I have added an analysis of key production efficiency and rate of failing to actually retrieve the correct plaintext. The formulas have been explain and given for general values and then applied for the values chosen in the experiments. The efficiency was calculated in general again, but I have also added an example with realistic values for satellite QKD implementations. I acknowledge that repetition coding is inefficient, yet when the classical channel is not functioning, any rate is an advantage over complete blackout. Other options for encodings remain for future research and this idea is mentioned at the end of the subsection “Analysis and Comparisons”.
Comment 4: Comparison with related work is insufficient. The manuscript lacks adequate comparison with related work in the field. The author should discuss the relationship between the proposed scheme and the following research directions: (1) Fault-tolerant QKD protocols: How does this scheme compare with existing fault-tolerant designs? (2) Measurement-Device-Independent QKD (MDI-QKD): Can similar ideas be applied to MDI-QKD systems? (3) Quantum state discrimination theory: How does the Trine POVM scheme relate to optimal quantum state discrimination? (4) Quantum error correction and fault-tolerant quantum computing: Are there connections with quantum error correction codes?
Response: The ideas of comparing to fault-tolerant QKDs and MDI-QKDs are good options for the applications of the contingency protocol. This has been added to the paper as the subsection “6.5. Comparison to Related Work”. Extensive discrimination theory is not within the scope of this paper and has not been additionally treated. Also, no additional reference to error correction codes were not studies, as the author considers this outside of the scope of the paper.
Comment 5: Writing and formatting issues need to be addressed. Several writing and formatting issues should be corrected: (1) The keyword "quantum resilience" appears twice in the abstract, which should be corrected. (2) Some statements are not sufficiently clear. For example, the discussion of "negative search space" in Section 3 is not clearly related to the main topic. The author should reorganize or streamline this section. (3) Experimental details are insufficient. Although the author mentions that code is available on GitHub, the main text should provide more details about experimental setup, including specific quantum device models used, number of experimental runs, error bars, etc. (4) Some figures (such as Figure 3) are not strongly related to the main topic. The author should reconsider the necessity of each figure. (5) Some references are incomplete. The author should unify the format according to journal requirements.
Response: Typos and other errors have been corrected consistently. (1) The keywords have been updated. (2 and 4) The description of the “negative-space” with its representation have been positively appreciated as a conceptual parallel, by another reviewer and could not be removed. (5) References have been improved. (3) – The codes are run simply in the Qiskit simulator, as stated in the paper.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsPlease find attached
Comments for author File: Comments.pdf
Author Response
Dear Reviewer,
Thank you for your comments and your attention to the structure of the paper. Your recommendations have been carefully analyzed and a detailed answer is given below. I am attaching a revised pdf, where the added text is colored in brown.
Presentation aspects
Comment 1: I suggest setting the Abstract in a more technical manner. Currently, it is depicted in a colloquial way to catch the problem to be addressed (just a little, in any case the current description is also valuable, but lacks technical details commonly stating a clear statement).
Response: Parts of the abstract were rewritten to give more technical detail about the scheme described in the paper. Here is part of the text that was added/changed: “The scheme described in this paper, uses the quantum channel only to distribute imperfect keys. The distributed key has a theoretical overlap of approximately $75\%$. The experimental POVM circuit is implemented with two different Naimark dilation approximations: one using $R_z$ gates and the other using $R_y$ gates. The practical implementations results are close to the theoretical analysis. As the keys have a partial overlap, the encryption/ decryption algorithm also needs to adjust to this reality. The encryption/decryption algorithm used in the experiments is a repetition algorithm, which is simple, but shows the resilience of the scheme. Ultimately, the classical channel is not used during the contingency QKD at all, while the quantum channel needs to be trusted during the protocol.”
Comment 2: The Introduction exhibits the same lack of formal or technical description. Although the qualitative description is reported, it is not sufficiently clear how the promised task will be addressed. In addition to this naive description, the lack of references (more than those mainly centered on BB84) does not let guess the technical content. Please improve.
Response: I have added to the introduction three paragraphs, which now appear before the last paragraph of the introduction. These paragraphs describe the main approaches of the paper and also have an enumerated list of achievements of the paper. The added paragraph show colored in brown in the attachment.
Comment 3: Although interesting, the descriptions provided in section 3 to explain the “negative space” becomes excessive, deviating the central topic, which has no be settled technically since the Introduction. The manuscript should maintain a balance between clarity and concreteness but avoiding certain didactic explanations to set easy contents. Please rewrite this section in a more concrete way.
Response: There was another reviewer that positively appreciated this explanation as a metaphorical touch to the concepts of the paper. Thus, I have left this section within the paper to satisfy the other reviewer.
Content improvements
Comment 4: I believe that the content referring to the qubits description and projective measurements are unnecessary in the manuscript. It is expected that readers domain these descriptions. POVMs are different because the Trine encoding is crucial in the procedure. I suggest removing that content (before page 5) or otherwise moving to an appendix.
Response: This is a good point, thank you. I have removed four paragraphs and adapted the text below to cover the missing points.
Comment 5: Also, the Examples reported on page 6 are unnecessary or also be moved into the corresponding already existent appendix. The remaining content is clear, valuable and well developed.
Response: Done.
Comment 6: Despite section 4 describing technical aspects of BB84 implementation, the real proposal begins until section 5, after the mid content development. It should show how the previous content is quite extensive with a lack of technical proposals from the first sections.
Response: Thank you for the comments on the structural organization of the paper. I moved the last paragraph of section 4 to section 5, so section five, only, contains the description of the contingency architecture and I have mentions clearly in the introduction that it is section 5 and on that contains the contribution of the paper. Some of the work on the previous points you made actually also contributes to answering Comment 6.
Comment 7: Section 5 and 6 develops clearly the proposal and its value. Conclusions are adequate for the development. Thus, this work should be improved in its first parts to become valuable and concretely written in a scientific matter.
Response: Thank you for the appreciation.
Minor format aspects
Comment 8: Please write the Figure 3 caption including there the description of the panels: Search space with equivalent foreground and background. (a) …., and (b) …. Of course, marking each subpanel with (a) and (b). The same applies to the further figures exhibiting panels.
Response: I have explained more thoroughly both Figure 3 and Figure 4..
Comment 9: Description of q0 and q1 should not include the gate symbols in line. It should be reviewed in the overall document (as instance, Table 5).
Response: This representation method was recommended to the author for easy (iconized) recognition of the concept, for readers used to memes. I therefore decided to keep the inline icons.
Comment 10: Although I previously recommended moving some materials to appendices, note that the overall materials included there should be dramatically reduced to become meaningful. Didactic content is not expected here, only technical details to accelerate the reading. Detailed calculations are not recommended.
Response: I am not sure what to say about this comment. The appendices can be readily ignored by a versatile reader. As they are written here, they are fully self contained with the calculations and avoid any doubt on the correctness of the values mentioned in the paper. I can contact the Symmetry editor and ask about the policy on Appendices.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authors- Please review the manuscript for missing or misused symbols. In Chapter 1, "65-75of" is likely a typo and should be corrected to "65-75% of". Please check for similar errors elsewhere.
- Please delete the "******" at the end of Chapter 1, as it has no actual meaning and appears to be a remnant of typesetting or writing.
- Please correct several spelling errors throughout the manuscript. For example, "betwen" should be "between", "stll" should be "still", and "Firgure" should be "Figure".
- Please replace the nonstandard term "positive operation vector measurement" with the correct expression "Positive OperatorValued Measure (POVM)" to ensure academic rigor and compliance with standard terminology.
- Please clarify in the experimental section whether all forms of classical coordination were truly disabled. The authors should specify that no classical information exchange took place in the simulation.
Author Response
Dear Reviewer,
Thank you for your comments and appreciation of my work. Your points were implemented in detail as shown below.
Comment 1: Please review the manuscript for missing or misused symbols. In Chapter 1, "65-75of" is likely a typo and should be corrected to "65-75% of". Please check for similar errors elsewhere.
Response: Typos were corrected: the one you mentioned and additionally the paper was analyzed by a spell checker.
Comment 2: Please delete the "******" at the end of Chapter 1, as it has no actual meaning and appears to be a remnant of typesetting or writing.
Response: Done.
Comment 3: Please correct several spelling errors throughout the manuscript. For example, "betwen" should be "between", "stll" should be "still", and "Firgure" should be "Figure".
Response: Typos were corrected: the ones you mentioned and additionally the paper was analyzed by a spell checker.
Comment 4: Please replace the nonstandard term "positive operation vector measurement" with the correct expression "Positive OperatorValued Measure (POVM)" to ensure academic rigor and compliance with standard terminology.
Response: Done.
Comment 5: Please clarify in the experimental section whether all forms of classical coordination were truly disabled. The authors should specify that no classical information exchange took place in the simulation.
Response: The following text was added at the end of the description of the algorithm:
“ … the theoretical Trine measurement can be approximately implemented within quantum circuits using Naimark's dilation and thus can be implemented with existing superconducting quantum technology. Notably, no classical communication between Alice and Bob exists. In the establishment of the contingency keys, classical coordination is not needed and is thus completely absent in the implementation of the algorithm.”
Reviewer 4 Report
Comments and Suggestions for Authorsplease see the attachment
Comments for author File: Comments.pdf
Author Response
Dear Reviewer,
Thank you for your comments and your attention to details of the content of the paper. Your recommendations have been carefully analyzed and a detailed answer is given below. I am attaching a revised pdf, where the added text is colored in green.
Presentation aspects
Comment 1: In this work, the quantum channel is assumed trusted by necessity during the contingency period. Technically, without the classical authenticated channel for parameter estimation, how can Alice and Bob detect the man-in-the-middle attack？
Response: Within the framework described in the paper, this problem cannot be solved.
Thus, the advantage of the scheme is to get some functionality from a badly damaged architecture. The scheme described in this paper does not intend to replace correctly functioning QKD deployment. I have added a description text to the paper to make this limitation clear: in the introduction and in the conclusion.
Comment 2: In Algorithm 2, Bob must know $l_b=l_{\text{key}}/l_p$ to correctly partition the received ciphertext and perform majority voting. However, this kind of information needs to be transmitted over the classical channel. The author should illustrate in details.
Response: Thank you, this is a good point. The parameter $l_b$, the size of the block needs to be agreed upon before the contingency conditions occur. As this can be part of the setup of the original QKD, prepared for the contingency, this is easy to be cone. I have added a more detailed description on this in the initial description of the algorithm in the section “Methods”, page 14.
Comment 3: The proposed trine positive operator-valued measurement should be compared with other methods.
Response: The Trine measurement was chosen for its similarity to the Fibonacci phyllotaxis. Alternatives, such as the Square POVM needs a larger Naimark expansion and therefore increases the space. While such comparisons could be done, they do not follow the primary direction of the paper. I have added a comment on this, towards the end of section 6. Thank you for the idea.
Comment 4: Some inconsistencies exist in the normalization factors during the state vector expansion.
Response: I have checked the formulas in the paper, I cannot find any further non-unitary states.
Comment 5: The author should illustrate how the proposed $R_y$ gate satisfy the IBM hardware.
Response: Thank you for the comment. I have added a paragraph in the description of the $R_y$ circuit the the controlled-$R_y$ is not a native gate in any of the IBM processors. I also , mentioned that the transpilation is different depending on the specific processor and I gave a reference to the description of the Eagle, Heron, and Falcon IBM quantum processors.
Comment 6: The author should discuss the sensitivity of the Trine measurement outcomes to potential initialization errors or decoherence of this ancilla qubit.
Response: We thank the reviewer for this important question. We have added a new subsection (Section 6.6, "Sensitivity Analysis") that analyzes the impact of ancilla qubit initialization errors on our Trine measurement circuits. For the addition of decoherence, the paper needs the addition of the description of impure states $\rho$. It is the intention of the author to make this paper understandable and explain every formula. I therefore, leave this part for future research and thank the reviewer for this idea.
Comment 7: Please carefully check the presentation and modify the typos.
Response: The entire text has been checked for typos and text errors.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsFor this manuscript to be considered for publication, the security issue must be fundamentally addressed. At a minimum, this requires a clearly defined security model (for example, restricting the adversary's capabilities to only blocking the classical channel but not perfectly manipulating the quantum channel, or assuming a model based on trusted nodes) and providing an information-theoretic security analysis or composable security analysis under that model. Merely stating that 'the quantum channel is trusted' is far from sufficient.
Author Response
Thank you for this repeated critique. I agree that the original manuscript did not sufficiently address the security model, and I did take this comment seriously.
The contingency scheme presented is intentionally not a full cryptographic key distribution protocol. It is an operational fallback mechanism that provides partial key material when the classical channel is unavailable. In this setting, the quantum channel is trusted by operational necessity — analogous to the assumption of a trusted node in relay-based QKD networks.
That said, the new subsection “5.3. Security Model for the Contingency Protocol”, contains now a formal adversary model: Eve is restricted to blocking the classical channel. On the quantum channel, Eve is limited to individual (non-coherent) and passive attacks.
Also, clear statements have been added, that this scheme does not offer unconditional security in the full BB84 sense, and that it should be understood as a resilience mechanism under a restricted threat model, not as a replacement for a fully secure QKD protocol.
Necessary changes have been added at the end of the abstract.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI have reviewed the new version of this work. Although the author has implemented some changes to his work (barely the initial), one of my comments (not catched) was that the rearrangement of this work should be into the scientific direction. Still this article looks crowded, not being directed to the main discussion, including some "didactic" contents not necessarily appropiate for a scientific paper. Concretely, some parts which exhibit an excessive didactic orientation:
a) Pages 4, 5 and 6 include detailed calculations and specifications more able for a didactic material, becoming in an unnecessary extension.
b) Initial example in section 6, it exceeds in details, not needed for readers having dominion in quantum information and in the topic
c) Examples about Trine apprach is valuable as Appendix, but still excessively developed, not necessarily required in a scientific presentation. For instance, the inclusion of Dirac notation together with matrix notation is more a didactic necessity than a concrete presentation. This kind of extensive content should be synthetized (despite it is an appendix).
d) The same is true for Appendices D and E, worst, mixing matrix and Diract notation, showing almost step-by-step calculations.
In terms of format, Tables and Figures do not follow the journal style (already previously indicated in my first review), moreover, they exhibit a lack of care to become immediately clear and readable.
a) Size of legends in figures (I should not remark which, but... 1, 2, 6 and 7); other as 3 and 4 does not follow the correct style, previously remarked in the round 1. Fig. 7 is incomplete (it was incorrectly cutted).
b) Labels for figure panels should not include text, it should be provided in the caption.
This work could become attractive, so author should understand that recommendations provided by reviewers, so it is not necessarily a fight against reviewers, instead a self-fight against self-resistance to improve his own work in a scientific and clear style. Unfortunately if the author does not show an open vision for the improving his own work, the article does not reach an improved attractiveness. I kindly invite to the author to improve the presentation of this works in order to become slender. Thus, changes should not be minimal and aesthetic, instead deeper, by performing a more self-critical review of simplification. The objective should not be publish the work, instead produce a piece of valuable contribution.
Author Response
Dear Reviewer,
Thank you for the renewed comments. The more comprehensive removal of some parts and alignment to MDPI standards is shown below.
About the content.
Comment 1: Pages 4, 5 and 6 include detailed calculations and specifications more able for a didactic material, becoming in an unnecessary extension.
Response: This content has been reduced to approximately one third of the original length.
Comment 2: Initial example in section 6, it exceeds in details, not needed for readers having dominion in quantum information and in the topic
Response: The example of the Python code simulation has been removed.
Comment 3: Examples about Trine approach is valuable as Appendix, but still excessively developed, not necessarily required in a scientific presentation. For instance, the inclusion of Dirac notation together with matrix notation is more a didactic necessity than a concrete presentation. This kind of extensive content should be synthetized (despite it is an appendix).
Response: The presentation of the examples has been shortened. The second appendix was removed and remains available on github.
Comment 4: The same is true for Appendices D and E, worst, mixing matrix and Diract notation, showing almost step-by-step calculations.
Response: Appendices D and E were removed. A reference was given to github that retains the original calculations for anyone interested in the didactic version.
About the formatting.
Comment 5: Size of legends in figures (I should not remark which, but... 1, 2, 6 and 7); other as 3 and 4 does not follow the correct style, previously remarked in the round 1. Fig. 7 is incomplete (it was incorrectly cutted).
Response: The figures were regenerated to follow MDPI styling: font sizes and color palette. Also the legends were reformatted according to MDPI requirements.
Figure 7 was regenerated.
Comment 6: Labels for figure panels should not include text, it should be provided in the caption.
Response: Labels for figure panels were removed.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsNo further comments
Author Response
There were no further comments.
Round 3
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author has notably improved the current version. It now is more readable and slender. Some minor details of Tables and Figures should be still addressed in a style review to fulfill the style guidelines.
Author Response
The tables especially have been improved in styling, and in-cell images have been aligned.
Thank you for the comments.
