Composable, unconditional security without a Quantum secret key: public broadcast channels and their conceptualizations, adaptive bit transmission rates, fidelity pruning under wiretaps
Pete Rigas
quant-phcs.ITmath.PRSubmitted Dec 19, 2025• Announced Dec 23, 2025• 0 citations
We examine public broadcast, forward conceptual, and backward conceptual, Quantum channels in the context of communication protocols that are independent of secret keys. Given research directions of interest previously identified in arXiv: 1804.01797, besides converse upper bounds on the bit transmission rate obtained by the author in recent work (arXiv: 2507.03035), additional possibilities remain, including: (1) determining whether aspects of QKD dependent protocols can be incorporated into steps of QKD independent protocols; (2) whether there would be any amplification to the Quantum-classical performance gap that Alice and Bob can exploit towards prospective Quantum advantage; (3) formulating the conditions under which secrecy and authentication can be simultaneously achieved. To characterize the conditions for which secrecy can be achieved with high probability, we argue that there not only exists suitable protocols which enable Alice and Bob to map into the authenticated space of bit codewords with high probability, but also that forward conceptual channels, through cascading, can significantly increase Eve's probability of false acceptance. Albeit the fact that secrecy, along with conceputalizations of the public broadcast channel, were initially discussed by Maurer for QKD dependent protocols, determining whether aspects of such protocols can be adapted for unconditional security without the use of a secret key is of great interest to explore. We demonstrate that Eve's error probability, through the cascading procedure, can be analyzed with the Holevo information under an optimal decoder. Furthermore, through post-processing of the outputs of a Completely Positive Trace Preserving (CPTP) map, we also demonstrate how to decrease Holevo sum quantities with data-processing and entropy-continuity bounds.
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Template (46 pages). Discussions of this work are available at: https://youtu.be/BHrHLnZl_Aw?si=lFjWjfAq_cWmqC_t, https://youtu.be/GC-Mx1ZldbA?si=xu_mWEqyKd4vfV_e, https://youtu.be/1vh5dnyNzgA?si=7jKCrZc02Spg72Kt. Related topics are at: https://youtube.com/playlist?list=PL3rTBtU0TK_BTmZkWaRifBGw66cOBtbtD&si=poL1JTmAiwfsyy9Y
We examine public broadcast, forward conceptual, and backward conceptual, Quantum channels in the context of communication protocols that are independent of secret keys. Given research directions of interest previously identified in arXiv: 1804.01797, besides converse upper bounds on the bit transmission rate obtained by the author in recent work (arXiv: 2507.03035), additional possibilities remain, including: (1) determining whether aspects of QKD dependent protocols can be incorporated into steps of QKD independent protocols; (2) whether there would be any amplification to the Quantum-classical performance gap that Alice and Bob can exploit towards prospective Quantum advantage; (3) formulating the conditions under which secrecy and authentication can be simultaneously achieved. To characterize the conditions for which secrecy can be achieved with high probability, we argue that there not only exists suitable protocols which enable Alice and Bob to map into the authenticated space of bit codewords with high probability, but also that forward conceptual channels, through cascading, can significantly increase Eve's probability of false acceptance. Albeit the fact that secrecy, along with conceputalizations of the public broadcast channel, were initially discussed by Maurer for QKD dependent protocols, determining whether aspects of such protocols can be adapted for unconditional security without the use of a secret key is of great interest to explore. We demonstrate that Eve's error probability, through the cascading procedure, can be analyzed with the Holevo information under an optimal decoder. Furthermore, through post-processing of the outputs of a Completely Positive Trace Preserving (CPTP) map, we also demonstrate how to decrease Holevo sum quantities with data-processing and entropy-continuity bounds.
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for the bit transmission rate without the presence of significant noise over the channel shared by Alice and Bob for the purposes of encoding, decoding, transmission and authentication, the author suggests that upper bounding the bit transmission rate could be of use towards classifying paradoxical aspects of communication protocols, as well as constructing error correcting codes which are resilient to noise. The upper bound that is obtained in this work for the bit transmission rate, as a converse result, is dependent upon the natural logarithm of the size of each player's alphabet, as well as smaller alphabets, which can be leveraged for simultaneously realizing Quantum advantage for maximizing error correction and minimizing false acceptance. Crucially, the upper bound to the bit transmission rate is dependent upon a pruning procedure, which seeks to determine whether letters from player's alphabets can be removed so that prospective Quantum advantage, in order for Alice and Bob to implement error correction protocols with high probability, despite the fact that there is more noise over the channel between Alice and Bob in comparison to that between Bob and Eve.
Quantum cryptography converts structural restrictions on quantum information into operational secrecy. This article develops the chain connecting nonorthogonal-state discrimination, trace distance and fidelity, the Helstrom bound, no-cloning, no-broadcasting, information-disturbance relations, conditional entropy, and privacy amplification. A linearity argument proves that no universal device can copy arbitrary pure states, while the mixed-state no-broadcasting theorem identifies pairwise commutativity as the exact boundary of exact broadcastability. These results explain why an eavesdropper cannot retain a perfect replica of every signal and wait for later basis disclosure. They are not, however, complete security proofs. Modern quantum key distribution must cover coherent attacks, quantum memory, public reconciliation leakage, imperfect sources and detectors, finite samples, authentication, and composition with later applications. The review connects state discrimination to adversarial guessing probability through conditional min-entropy and explains how entropic uncertainty and entanglement-based reductions transform observed statistics into a lower bound on extractable key. Approximate cloning, unambiguous discrimination, channel loss, side channels, and device-independent certification are examined as qualifications to elementary intuition. The central result is a hierarchy: nonorthogonality restricts distinguishability; data processing forbids perfect information amplification; parameter estimation bounds an adversary’s conditional states; and quantum-proof hashing yields a key close in trace distance to an ideal independent key. Cryptographic security therefore depends on quantum limitations embedded within a fully specified protocol and adversarial model.
Objective of this paper is the study of Quantum Key Distribution (QKD) protocols based on classical error-correcting codes. The Quantum Key Distribution (QKD) systems and related protocols, in particular conditions, can use the classic channel coding techniques, instead of quantum error-correcting codes, both for correcting errors that occurred during the exchange of a cryptographic key between two authorized users, and to allow privacy amplification, in order to make completely vain a possible intruder attempt. The secret key is transmitted over a quantum, and thus safe, channel, characterized by very low transmission rates and high error rates. This channel is safe for the properties of a quantum system, where each measurement on the system perturbs the system itself, allowing the authorized users to “feel” if there is any intruder listening. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate (QBER) takes values between 0.05 and 0.11), both because of the inherent characteristics of the system, and of the presence of a possible attacker. Thus, in order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, conversely characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit.
The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and give rise to an intriguing tradeoff between exploiting the state to boost secret-message rates versus extracting cryptographic key to improve secrecy capabilities. This issue has yet to be understood how to optimally reconcile the two. We newly devised the “iterative” forward-backward coding scheme, combining wiretap channel coding and secret-key-agreement-based one-time pad cipher. We then established reasonable lower bounds of the secrecy capacity for wiretap channels with causal channel state information available only at the encoder (Theorem 1), which can be easily extended to general cases with various kinds of correlated channel state information at the encoder (Alice), decoder (Bob), and wiretapper (Eve). In particular, for degraded wiretap channels, we give the secret-message (secret-key) capacity bounds (Theorems 2, 4, and 5).
Characterizing secret communication over noisy quantum channels is an interesting problem from both a practical and theoretical perspective. Suppose Alice and Bob wish to communicate secret information so that an eavesdropper Eve will not suspect any type of encoded communication between the two. Classical or quantum cryptography will not suffice since it is always clear secret communication is taking place. Therefore Alice and Bob must execute what is known as a quantum steganographic protocol. Assuming Eve only has partial knowledge of the channel connecting Alice and Bob, we show that for the bit-flip and depolarizing channels Alice can use Eve's lack of knowledge of the channel parameter to encode quantum information steganographically. We give an explicit encoding procedure and calculate the rate at which Alice and Bob can communicate secretly. We also show that our encoding is optimal for nondegenerate quantum codes. We calculate the rate at which a secret key must be consumed. Finally, we discuss the possibility of steganographic communication over more general quantum channels and conjecture a general formula for the steganographic rate.
We obtain estimates for Eve's forgery probability, namely the probability that she is able to forge a message which Alice or Bob mistakenly accept over a noisy Quantum channel for generating a shared Quantum secret key. This probability is related to Eve's success probability obtained in a previous work due to Renner and Wolf, which was obtained from assumptions on the min-entropy for characterizing asymmetric security. To demonstrate that protocols over noisy Quantum channels are dependent upon a single, unified security threshold in comparison to multiple security parameters in the Renner-Wolf interactive authentication protocol framework we upper bound Eve's forgery probability with a Holevo-type quantity that can be made negligibly small. By leveraging estimates for Eve's false acceptance probability that have previously been obtained by the author, we obtain the desired security threshold by bounding the false acceptance probability with a suitably chosen two-universal function which serves as a counterpart to two-universal hashing functions that have previously been examined for cryptographic protocols in Quantum key distribution. As a result the protocol is not only ε-secure, for some ε>0, but also composable against forgery and key leakage.