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REVIEW 4 major objections 5 minor 23 references

Secure Quantum Relay Networks Using Distributed Entanglement without Classical Authentication

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read This paper claims that pre-distributed entanglement can replace classical authentication in quantum relay networks, so relay nodes can forward encoded messages without ever reading them and without any handshake or key exchange.

desk verdict Under-specified entanglement-based relay scheme whose central 'no classical authentication' claim fails on its own terms; desk-reject. read the letter →

arxiv 2507.05460 v1 pith:QDEBTLL2 submitted 2025-07-07 quant-ph physics.optics

classification quant-phphysics.optics MSC 81P9481P45
keywords quantumrelaynetworksentanglement-assisteddecodingauthentication-freeprotocolsdistributedtrustno-keycommunicationentanglement-exclusivedecryptionsecurity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to establish that classical authentication can be removed entirely from quantum relay networks by using pre-shared entanglement as both the encryption key and the identity check. Messages are encoded with one half of an entangled pair; only the receiver holding the other half can reconstruct them, while intermediate relays see only noise. If correct, this would let untrusted relay infrastructure forward confidential traffic with information-theoretic exclusivity and no classical trust primitive, cutting latency by eliminating handshakes. The paper reports simulations showing decoding fidelity above 97% under loss and noise, and argues the scheme resists eavesdropping, collusion, and replay.

What carries the argument

The central mechanism is entanglement-exclusive decoding: a message qubit is transformed by a controlled operation conditioned on Alice's half of a pre-shared EPR pair, so the reduced density matrix of the transmitted qubit alone is maximally mixed. Bob's joint measurement with his entangled partner reconstructs the logical message with high fidelity, while any receiver lacking that partner gets outcomes consistent with noise. The same idea extends to GHZ and W states for multicast, conditional, or hierarchical access, and single-use entanglement makes replay attacks fail because each decoding collapses the shared state.

What would settle it

Perform the protocol without any authenticated classical setup for the initial entanglement distribution: an active adversary impersonates the source during distribution and substitutes a forged entangled partner; if the receiver accepts the forged state and the attacker can then decode a later message with fidelity above random guessing, the exclusivity claim is refuted.

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Extended reading notes

Core claim

The central claim is that entanglement possession alone can enforce both confidentiality and origin integrity in a relay network. Alice prepares an EPR pair, keeps one qubit, and sends the other to Bob out-of-band; she then uses her local qubit as an ancilla to encode the message onto a transmitted qubit via a controlled unitary. Bob undoes the encoding with a joint measurement on his entangled partner; anyone else measuring the intercepted qubit sees a mixed state indistinguishable from noise. Because no classical key, basis information, or handshake is ever exchanged, the paper argues that the relay nodes' pass-through role makes them unable to forge, read, or replay messages, and that the exclusivity of the entangled resource is what authenticates the receiver.

Load-bearing premise

The load-bearing premise is that Alice and Bob can already share authenticated entangled pairs before any message is sent; the paper's own security discussion concedes that the entanglement graph is protected by source authentication, so if that distribution step requires classical authentication, the 'authentication-free' claim collapses.

Editorial extensions

If this is right

  • No intermediate relay node can recover a message even if it intercepts every qubit, because it lacks the entangled partner held by the intended receiver.
  • Colluding relays and classical eavesdroppers cannot forge origin or content, since authentication is carried by non-local quantum correlations rather than metadata.
  • Eliminating the classical handshake removes a class of authentication attacks and cuts end-to-end latency by the reported 36.5% compared with QKD-style reconciliation.
  • The protocol claims quantum-forward secrecy: reusing the same entangled pair yields garbage, so a compromised pair does not compromise past or future messages.
  • The simulated fidelity stays above roughly 95% up to 30% entanglement loss, and above 97.2% with 25% entanglement loss plus 15% photon loss.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The 'authentication-free' claim only holds if the initial entanglement distribution itself can be performed without authenticated classical communication; the paper's own security section invokes source authentication and delayed-choice distribution, which are classical or classically controlled, so the real contribution may be relocating trust to the distribution phase rather than removing it.
  • A testable extension: run the protocol without any authenticated classical setup for the initial entanglement distribution and check whether an active man-in-the-middle can substitute a forged entangled partner during that phase.
  • The scheme is structurally similar to quantum teleportation without classical communication, so it may be constrained by the no-communication theorem; clarifying the exact information-theoretic capacity of the encoded channel would place bounds on the claimed exclusivity.
  • A consequence the authors leave implicit is that malicious relays can still drop or delay packets even if they cannot read them, so the protocol offers confidentiality and integrity but not availability.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a scheme for quantum relay networks in which Alice encodes a message qubit using her half of a pre-shared EPR pair, sends the qubit through untrusted relay nodes, and Bob decodes it using his entangled half, with the claimed result that no relay or eavesdropper lacking the entangled partner can access the message and that no classical authentication is needed. The manuscript describes the architecture, a qualitative encoding/decoding protocol, a security analysis against eavesdropping and collusion, and simulation results claiming high fidelity under loss and latency reduction.

Significance. If the central claims were substantiated, the paper would present a significant conceptual shift: replacing classical authentication with entanglement possession for both confidentiality and origin integrity in relay networks. The claimed capability to achieve end-to-end authentication without any classical trust primitive would be of broad interest to the quantum communication community. However, the significance is presently not realized because the protocol is not formally specified, the security properties are asserted rather than derived, and the 'authentication-free' premise is internally contradicted by the reliance on authenticated entanglement distribution. The paper does not provide machine-checked proofs, reproducible simulation code, or parameter-free derivations; rather, its validation is largely qualitative and, in one simulation claim, circular.

major comments (4)
  1. [Section 3] The encoding and decoding operations are never explicitly specified. No unitary for Alice's encoding, no joint measurement for Bob, and no correction operation are defined. As a result, the claim that Bob can reconstruct the message 'with high fidelity' without any classical communication cannot be verified. More importantly, whatever the decoding operation is, it is a fixed quantum operation on the received qubit q_M and Bob's half B. If a malicious relay replaces q_M with its own state |φ>, Bob's output depends only on |φ> and B; for the natural decoder suggested by the text (e.g., a controlled-NOT from B to the received qubit followed by a B measurement and a correction), an injected state |φ> is reconstructed as exactly |φ>. Thus the Section 4 claim that 'colluding relays cannot ... simulate authenticity because authentication is encoded in non-local correlations' fails even under the ideal assumption that Alice and Bob share a securely pre-distributed EPR pair. The decoder cannot certify the provenance of q_M, so the protocol provides no message-origin authentication.
  2. [Section 4] The security claims are asserted, not derived. There is no adversary model (passive versus active, bounded versus unbounded quantum memory, collusion structure), no formal definition of 'origin integrity' or 'quantum-forward secrecy', and no information-theoretic security proof. The statement that an eavesdropper without entanglement 'cannot reconstruct the global state' and sees a mixed state is a direct consequence of the encoding construction (the reduced density matrix of the message qubit is maximally mixed), but this does not constitute a proof against coherent attacks, multi-qubit adversarial strategies, or active impersonation. The later statement that the entanglement graph is protected through 'source authentication' (Section 4) is especially problematic: source authentication is a classical or classically-controlled identity process, which contradicts the abstract's claim that the protocol 'completely avoids classical authentication.' This internal inconsistency undermines the central premise of the paper.
  3. [Section 5] The simulation results are unverifiable and partially circular. The paper provides no simulator code, no detailed parameters beyond 'stochastic depolarizing channel' and '10–30 dB per hop', no statistical error bars, and no specification of the simulated adversary's strategy. In particular, the claim that an eavesdropper 'failed to recover message states beyond random guessing (50%)' is not a meaningful security test: for a qubit message, a random guess achieves exactly 50% fidelity, so the reported outcome merely confirms that the message qubit's marginal state is maximally mixed—a property already built into the encoding by construction. This does not independently validate the 'exclusivity mechanism' against an adversary who may hold auxiliary quantum registers or interact coherently with the transmitted qubit.
  4. [Section 2] The protocol assumes that entangled qubit pairs are 'pre-shared ... over out-of-band quantum links' without specifying how the parties verify each other's identity during entanglement distribution. Since Section 4 explicitly invokes 'source authentication' and 'delayed-choice entanglement distribution' as protective measures, the scheme does not eliminate classical authentication; it merely relocates it to the entanglement-distribution phase. This is a load-bearing issue: the abstract and Section 1 claim that 'classical authentication can be replaced with non-classical correlation filters,' but the paper provides no mechanism for authenticating the initial entanglement distribution without a classical trust primitive.
minor comments (5)
  1. [Section 1] The sentence describing 'encoding control logic (e.g., message validity, expiry, origin ID) within the structure of the entanglement itself' is not supported by any concrete construction; GHZ and cluster states are mentioned, but no explicit encoding of such metadata is given.
  2. [Section 2] Figures 1–5 are referenced in the text but are not actually included; the manuscript contains only placeholder captions. This prevents the reader from checking the claimed schematic illustrations and comparison table.
  3. [Section 4] The final paragraph repeats the sentence 'Ultimately, the protocol's security emerges not from secrecy of parameters, but from exclusivity of quantum resources' verbatim twice.
  4. [References] References [14] and [15] are cited as evidence that 'access control is enforced solely through entanglement possession,' but neither paper demonstrates authentication-free origin integrity in a relay network; the citations do not support the claim made.
  5. [Section 5] The reported '36.5%' latency reduction is not reproducible: no baseline QKD protocol, no network conditions, and no simulation methodology are described for this metric.

Circularity Check

3 steps flagged · score 7.0 of 10

The paper's advertised 'authentication-free origin integrity' reduces to its own definitions: authorization is defined as entanglement correlation (Section 2), and the only security validation (Section 5) restates the encoding's mixed-marginal construction; Section 4 then concedes 'source authentication' protects the entanglement graph, so the authentication-free premise presupposes the…

  1. self definitional [Section 5, 'Simulation and Performance Evaluation' (Adversarial reconstruction bullet); cf. Section 3, 'Entanglement-Assisted Decoding Protocol']
    "Adversarial reconstruction: Simulated eavesdroppers holding complete classical knowledge of the system but lacking entanglement failed to recover message states beyond random guessing (50%), confirming the exclusivity mechanism."

    Section 3 constructs the protocol so that the transmitted qubit q_M is entangled with Bob's off-path half B (Alice encodes q_M using her EPR half A as ancilla), and the paper itself states that without the partner 'the state appears randomized due to the mixed reduced density matrix of the marginal system.' A reduced state of an entangled half is maximally mixed by definition, so an eavesdropper lacking B necessarily measures noise at chance level. The Section 5 simulation 'confirms' this mathematical identity of the encoding design and presents it as validation of the exclusivity mechanism. The tested prediction is equivalent to the construction by design; no alternative hypothesis is simulated, so the confirmation is circular.

  2. self definitional [Abstract; Section 4, 'Security Analysis against Intrusion and Collusion'; cf. Section 2 and Section 6]
    "The system routes messages across multiple relay nodes, yet ensures that no intermediate node can access the message unless it possesses the entangled state partner. ... the protocol guarantees quantum-forward secrecy and end-to-end origin integrity without trusted intermediaries. (Abstract) Even colluding relays cannot intercept content or simulate authenticity because authentication is encoded in non-local correlations, not metadata. (Section 4)"

    Authorization is defined by the paper as possession of quantum correlation: 'A node is authorized not because it is listed in a classical ledger or possesses a private key, but because its quantum state is correlated to the message's encryption substrate' (Section 2), and Section 6 declares 'authentication is intrinsic, based on entanglement possession.' The Abstract and Section 4 then conclude that access exclusivity ('no intermediate node can access the message unless it possesses the entangled state partner') yields 'end-to-end origin integrity' and that colluding relays cannot 'simulate authenticity.' Since 'authenticated' here means 'holds the correlated qubit,' the conclusion is the definition restated.

1 more flagged steps
  1. other [Section 4, 'Security Analysis against Intrusion and Collusion' (final defense paragraph)]
    "In fact, any attempt to substitute their own entangled state or induce entanglement swapping requires active participation in the entanglement graph, which is protected through quantum network control layers (e.g., source authentication, delayed-choice entanglement distribution) [14]."

    The protocol's substitute for classical authentication is pre-distributed entanglement (Section 2: 'pre-shared entangled qubit pairs over out-of-band quantum links'), and the Abstract claims the scheme 'completely avoids classical authentication.' But this passage concedes that the entanglement graph — the very substrate that confers exclusivity — is 'protected through quantum network control layers (e.g., source authentication).' Source authentication is an identity-verification step, so the premise (a securely established, authenticated entangled graph) already contains the classical trust primitive the paper claims to eliminate.

full rationale

This paper contains no self-citations: references [14] (Zwerger et al., 2018) and [15] (Ciobanu et al., 2025) are external works, so the self-citation and uniqueness-imported-from-authors patterns do not apply. The circularity found is definitional and validation-level. First, the only security validation of the scheme (Section 5) — the eavesdropper's chance-level reconstruction — is a direct mathematical consequence of the encoding design: Section 3 makes the message qubit entangled with Bob's off-path half, and the reduced state of an entangled half is maximally mixed by definition; the simulation 'confirms' the design assumption rather than testing an independent hypothesis. Second, the central advertised result (authentication and origin integrity via entanglement possession) is established by definition: Section 2 defines authorization as quantum correlation, Section 6 calls authentication 'intrinsic, based on entanglement possession,' and the Abstract/Section 4 infer origin integrity from access exclusivity. Because no protocol step verifies the provenance of the received qubit, 'origin integrity' is a renaming of exclusivity, not a derived property; the paper conflates confidentiality with authenticity. Third, Section 4 concedes that the entanglement graph is protected by 'source authentication,' meaning the 'without classical authentication' premise presupposes an authenticated distribution step — the conclusion is begged. Some components are non-circular: the fidelity-versus-loss and latency simulations are genuine model outputs, and the confidentiality property (noise without the partner) is mathematically real. But the core claim of the paper reduces by definition and its validation is tautological, so a moderately high circularity score is warranted; the absence of any self-citation chain and the presence of a concrete (if flawed) construction keep the score below 8-10.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The protocol relies on standard quantum information results (no-cloning, monogamy, partial-trace noise) but also on unproven domain assumptions: that entanglement can be pre-distributed without classical authentication, that relays are passive and cannot disrupt delivery, and that a fixed joint measurement recovers arbitrary messages. The paper introduces no new physical entities; its conceptual terms (entanglement-exclusive decryption, correlation-assisted decoding) are labels for the proposed mechanism rather than independent postulates.

free parameters (3)
  • Entanglement loss rate = 25-30% (scenario input)
    Chosen simulation condition for the fidelity claim; not fitted to data, but no error bars or code are provided.
  • Photon loss per hop = 10-30 dB
    Scenario input for the simulated relay channel.
  • Temporal coherence window = ~3 microseconds
    Simulator parameter for asynchronous reception; no derivation is given.
assumptions (4)
  • standard math No-cloning theorem and monogamy of entanglement hold and are sufficient to guarantee that an eavesdropper without the entangled partner sees only noise.
    Invoked in Sections 3 and 4 to argue exclusivity; these are standard results, but sufficiency for the claimed security properties is not proven.
  • ad hoc to paper Entanglement can be pre-distributed between Alice and Bob without classical authentication or identity verification.
    Assumed in the abstract and Section 3, but Section 4 relies on "source authentication" and "delayed-choice entanglement distribution", contradicting the assumption.
  • domain assumption Relay nodes are purely passive and cannot disrupt, modify, or substitute the message qubit without detection.
    Assumed in Sections 2 and 4, but no mechanism is described to detect or prevent a malicious relay from dropping or replacing the qubit, so integrity and availability are unsupported.
  • domain assumption The receiver can recover arbitrary message states with a fixed joint measurement on the received qubit and the entangled partner, without classical reconciliation.
    Section 3 describes "a joint measurement" without specifying it or proving it works for all inputs; the actual scheme may require measuring the partner and applying a conditional correction, i.e., using the entangled qubit as a one-time key.

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Cite this review

Pith. "Pith review of Secure Quantum Relay Networks Using Distributed Entanglement without Classical Authentication." pith.science (2026). https://pith.science/paper/QDEBTLL2

@misc{pith2026250705460,
  author       = {Pith},
  title        = {Pith review of: Secure Quantum Relay Networks Using Distributed Entanglement without Classical Authentication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QDEBTLL2}},
  note         = {Machine review of arXiv:2507.05460}
}
read the original abstract

Current quantum communication protocols rely heavily on classical authentication for message origin verification, leaving them vulnerable to evolving attacks that exploit classical trust assumptions. In this work, we propose a novel framework for secure quantum relay networks that completely avoids classical authentication. Instead, we leverage pre-distributed entanglement graphs and non-classical correlation-assisted decoding to enable exclusive message retrieval by designated nodes without broadcasting any key or handshake. The system routes messages across multiple relay nodes, yet ensures that no intermediate node can access the message unless it possesses the entangled state partner. We demonstrate that even in multi-path scenarios with asynchronous entanglement distribution, the protocol guarantees quantum-forward secrecy and end-to-end origin integrity without trusted intermediaries. Simulation results confirm both functionality and robustness under entanglement loss and imperfect detection. This architecture paves the way for scalable quantum communication systems where physical quantum states replace classical authentication mechanisms entirely.

Figures

Figures reproduced from arXiv: 2507.05460 by the authors.

Figure 3
Figure 3. Adversarial Failure under Missing Entanglement. Comparison of output states between authorized (with entanglement) and unauthorized (without entanglement) receivers. The unauthorized output is statistically indistinguishable from noise. Ultimately, the protocol’s security emerges not from secrecy of parameters, but from exclusivity of quantum resources. Ultimately, the protocol’s security emerges not from secrecy of… view at source ↗
Figure 4
Figure 4. Simulation Results: Decryption Fidelity vs. Entanglement Loss. Decryption fidelity as a function of entanglement degradation (0–40%). Message reconstruction remains above 95% up to 30% entanglement loss. Additionally, when Bob’s entangled qubit was deliberately delayed (to simulate asynchronous reception), the protocol still succeeded as long as temporal coherence was maintained within the de-coherence window (~3 μs… view at source ↗
Figure 5
Figure 5. Protocol Comparison Table. Comparison between classical authentication-based systems, QKD, MDI￾QKD, and the proposed protocol in terms of trust assumptions, classical overhead, and exclusivity. 7. Applications and Future Perspectives The proposed entanglement-assisted, authentication-free communication framework opens new frontiers in both secure infrastructure and fundamental quantum architecture—especially in doma… view at source ↗

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Reference graph

Works this paper leans on

23 extracted references · 22 canonical work pages

  1. [1]

    Bennett, G

    C.H. Bennett, G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theoretical computer science, 560 (2014) 7-11

  2. [2]

    Ekert, Quantum cryptography based on Bell’s theorem, Physical review letters, 67 (1991) 661

    A.K. Ekert, Quantum cryptography based on Bell’s theorem, Physical review letters, 67 (1991) 661

  3. [3]

    Weedbrook, S

    C. Weedbrook, S. Pirandola, R. García -Patrón, N.J. Cerf, T.C. Ralph, J.H. Shapiro, S. Lloyd, G aussian quantum information, Reviews of Modern Physics, 84 (2012) 621-669

  4. [4]

    Bernstein, T

    D.J. Bernstein, T. Lange, Post-quantum cryptography, Nature, 549 (2017) 188-194

  5. [5]

    Alagic, G

    G. Alagic, G. Alagic, J. Alperin -Sheriff, D. Apon, D. Cooper, Q. Dang, Y. -K. Liu, C. Miller, D. Moody, R. Peralta, Status report on the first round of the NIST post-quantum cryptography standardization process, DOI (2019)

  6. [6]

    Pirandola, C

    S. Pirandola, C. Ottaviani, G. Spedalieri, C. Weedbrook, S.L. Braunstein, S. Lloyd, T. Gehring, C.S. Jacobsen, U.L. Ander sen, High -rate measurement -device-independent quantum cryptography, Nature Photonics, 9 (2015) 397-402

  7. [7]

    Silverstone, D

    J.W. Silverstone, D. Bonneau, J.L. O’Brien, M.G. Thompson, Silicon quantum photonics, IEEE Journal of Selected Topics in Quantum Electronics, 22 (2016) 390-402

  8. [8]

    Broadbent, J

    A. Broadbent, J. Fitzsimons, E. Kashefi, Universal blind quantum computation, 2009 50th annual IEEE symposium on foundations of computer science, IEEE, 2009, pp. 517-526

Show all 23 references
  1. [9]

    Briegel, D.E

    H.J. Briegel, D.E. Browne, W. Dür, R. Raussendorf, M. Van den N est, Measurement-based quantum computation, Nature Physics, 5 (2009) 19-26

  2. [10]

    C. Liu, M. Wang, S.A. Stein, Y. Ding, A. Li, Quantum memory: A missing piece in quantum computing units, arXiv preprint arXiv:2309.14432, DOI (2023)

  3. [11]

    Lingaraju, H

    N.B. Lingaraju, H. -H. Lu, D.E. Leaird, S. Estrella, J.M. Lukens, A.M. Weiner, Bell state analyzer for spectrally distinct photons, Optica, 9 (2022) 280-283

  4. [12]

    Chrostowski, M

    L. Chrostowski, M. Hochberg, Silicon photonics design: from devices to systems, Cambridge University Press2015

  5. [13]

    Mor-Ruiz, W

    M.F. Mor-Ruiz, W. Dür, Influence of noise in entanglement-based quantum networks, IEEE Journal on Selected Areas in Communications, DOI (2024)

  6. [14]

    Zwerger, A

    M. Zwerger, A. Pirker, V. Dunjko, H.J. Briegel, W. Dür, Long -range big quantum -data transmission, Physical Review Letters, 120 (2018) 030503

  7. [15]

    Ciobanu, T

    B. Ciobanu, T. Calafeteanu, A. Popa, R. Tătăroiu, P. Popescu, Optimal entanglement distribution within a multi-ring topology, Scientific Reports, 15 (2025) 1-18

  8. [16]

    Rivest, A

    R.L. Rivest, A. Shamir, L. Adleman, A method f or obtaining digital signatures and public -key cryptosystems, Communications of the ACM, 21 (1978) 120-126

  9. [17]

    Koblitz, Elliptic curve cryptosystems, Mathematics of computation, 48 (1987) 203-209

    N. Koblitz, Elliptic curve cryptosystems, Mathematics of computation, 48 (1987) 203-209

  10. [18]

    Miller, Use of elliptic curves in cryptograp hy, Conference on the theory and application of cryptographic techniques, Springer, 1985, pp

    V.S. Miller, Use of elliptic curves in cryptograp hy, Conference on the theory and application of cryptographic techniques, Springer, 1985, pp. 417-426

  11. [19]

    Regev, On lattices, learning with errors, random linear codes, and cryptography, Journal of the ACM (JACM), 56 (2009) 1-40

    O. Regev, On lattices, learning with errors, random linear codes, and cryptography, Journal of the ACM (JACM), 56 (2009) 1-40

  12. [20]

    Micciancio, Lattice-based cryptography, Encyclopedia of Cryptography and Security, Springer2011, pp

    D. Micciancio, Lattice-based cryptography, Encyclopedia of Cryptography and Security, Springer2011, pp. 713-715

  13. [21]

    Mosca, Cybersecurity in an era with quantum computers: Will we be ready?, IEEE Security & Privacy, 16 (2018) 38-41

    M. Mosca, Cybersecurity in an era with quantum computers: Will we be ready?, IEEE Security & Privacy, 16 (2018) 38-41

  14. [22]

    Scarani, H

    V. Scarani, H. Bechmann -Pasquinucci, N.J. Cerf, M. Dušek, N. Lütkenhaus, M. Peev, The security of practical quantum key distribution, Reviews of modern physics, 81 (2009) 1301-1350

  15. [23]

    Clarke, R.J

    P.J. Clarke, R.J. Collins, V. Dunjko, E. Andersson, J. Jeffers, G.S. Buller, Experimental demonstration of quantum digital signatures using phase -encoded coherent states of light, Nature communications, 3 (2012) 1174

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