This work analyzes a temporal-mode extension of the two-way LM05 quantum communication primitive, in which a message block is encoded into a fixed-weight binary occupation vector (the support) alongside classical ordering information, and derives the exact maximum-a-posteriori recovery probability.
Abstract
We analyze a temporal-mode extension of the two-way LM05 quantum communication primitive, in which a message block is encoded into a fixed-weight binary occupation vector (the support) alongside classical ordering information. We demonstrate that applying an independent-slot recovery model to this correlated source is fundamentally inconsistent. For an ideal erasure channel, we derive the exact maximum-a-posteriori (MAP) recovery probability, showing that source-aware decoding outperforms independent guessing by orders of magnitude. We extend this analysis to a realistic threshold-detector model, quantifying the degradation caused by dark counts and inefficiency. Furthermore, we clarify the quantum-classical information split: in the ideal single-photon limit, preparation averaging renders Eve's state independent of the support, yielding zero Holevo information. We establish conditional security bounds using entropic uncertainty relations and identify photon-number-splitting as the primary practical vulnerability. These results provide a rigorous source-aware recovery benchmark and define the physical conditions under which the quantum layer offers a key-consumption advantage over classical constant-weight coding.
The recovery of quantum information after subsystem loss is a central challenge in quantum information processing. However, some states remain beyond the reach of any recovery strategies. Here we identify the algebraic origin of virtual irrecoverability, the \emph{ghost information}---correlations encoded in the global state that leave no trace on any accessible subsystem. We introduce a scalar measure quantifying its magnitude and prove a universal error floor below which no virtual recovery map can operate, irrespective of resource investment. In such cases only \emph{approximate} virtual recovery is available. We study the sampling cost when approaching the minimal attainable recovery error, and find it bounded when the underlying linear map exhibits a spectrum gap, and divergent in the gapless regime, respectively. Together with the universal error floor, this dichotomy partitions all multipartite quantum states into four classes. Moreover, we show that conditional mutual information, the standard entropic diagnostic, does not constrain virtual recoverability. As an implication, we show that the error floor imposes a detection threshold for loss-tolerant quantum metrology.
The choice of optical receiver determines which properties of the transmitted states remain visible in the observed data and therefore affects the performance of different quantum protocols. We compare continuous-variable, photon-counting and hybrid receivers within the same prepare-and-measure framework, using semi-device-independent randomness generation as the main case study. The measurement device is left uncharacterised, while the source is described by the Gram matrix of its pure signal states using an energy-derived overlap constraint, a magnitude-Gram benchmark or the full complex Gram matrix of a certified coherent phase-shift-keyed constellation. Within this framework, the observed receiver statistics are used to bound $H_{\min}(B|X,\Lambda)$ against classical side information correlated with the measurement device but independent of the input. For a fixed Gram matrix, this bound is obtained from an exact semidefinite program, with complex multi-input cases treated in block-real form and checked through the corresponding dual certificate. Photon counting alone is phase blind for fixed-modulus phase encoding and therefore certifies no worst-case randomness. Continuous-variable receivers give the highest certified entropy at moderate energy, while under the nominal source calibration a hybrid receiver performs better at low energy when the beacon-region label is retained in the output. The same receiver statistics also provide receiver-level comparisons for discrete-modulated continuous-variable quantum key distribution, quantum reading, covert communication and quantum-signature verification, without replacing the full security analysis required for each protocol.
Mediated multi-party quantum key distribution (M-MQKD) is studied for repeater-assisted quantum networks with an untrusted repeater layer and end users restricted to single-qubit local operations and one-way quantum reception. Building on the 1D+star mediated construction, the repeater path is treated as an untrusted measurement layer and the security analysis adopts a corrected-frame GHZ model. Under authenticated timing windows, trusted user-side measurements, a calibrated Check observable, and an explicit public-reconciliation transcript, we establish a corrected-frame finite-key theorem yielding a conference-key length bound from two experimentally accessible statistics: Share-mode disagreement and Check-mode parity-violation. The virtual phase-error variable for privacy amplification is related to the corrected-frame Check parity observable by a stabilizer-complementarity argument with quantum side information, while the entropy term in entropy accumulation is replaced by a predeclared affine lower bound on 1−h2(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1- h_{2} (x)$\end{document}. Error-correction leakage is accounted for through a designated-leader pairwise reconciliation transcript, including syndrome traffic, verification tags, and auxiliary public messages. The protocol is hardened by announcement-consistency traps, salted commit-then-open commitments over modes and parameter-estimation outcomes, randomized reveal order, and authenticated timing windows. These mechanisms detect or exclude dishonest classical disclosures before parameter estimation and treat trap failures as an abort/detection statistic rather than an unproved entropy penalty. The framework gives an auditable finite-key extraction rule as a function of observed error rates, finite-sampling radii, reconciliation leakage, EAT finite-size penalties, trap thresholds, and commitment length. Numerical evaluation maps rate-security trade-offs and gives parameter-selection guidance, supporting resilient infrastructure for secure multi-party quantum communication.
Hamza Sohail, B. Khan, A. Mir et al.· EPJ Quantum Technology· 0 citations
Continuous-variable quantum key distribution is a compelling framework for scalable quantum networks due to its seamless integration with existing optical communication infrastructure. However, a fundamental gap persists between theoretical protocols requiring ideal Gaussian modulation and the constrained, discrete-modulated signals dictated by practical high-speed hardware. Current security proofs for discrete modulation rely on semidefinite programming, which suffers from prohibitive computational overhead for high-order constellations and lacks direct physical insight into non-Gaussian modulation.In this Letter, we overcome this limitation by developing a security framework that obviates semidefinite programming in favor of an approach grounded fundamentally in the Heisenberg uncertainty principle. By introducing a multi-mode entanglement-source model to characterize non-Gaussian state preparation, we establish an explicit mapping between constellation geometry and the secret key rate. This framework effectively quantifies the security implications of hardware-limited, finite state preparation, enabling both numerical and analytical security analysis under high-order constellations. We experimentally validate our method on both discrete-component and integrated photonic platforms, demonstrating that a quadrature amplitude modulation format with 256 constellation points can asymptotically approach the Gaussian capacity limit. Beyond quantum key distribution, the principle of tightening uncertainty-constrained bounds via source-mode expansion offers a paradigm for exploring the information-theoretic properties of complex non-Gaussian systems.
Jiale Mi, Yiming Bian, Song Yu et al.· 0 citations
Quantum secret sharing is a fundamental protocol for securely transmitting quantum as well as classical information. However, in practical quantum communication scenarios, the transmission of quantum information is inevitably influenced by environmental noise. Therefore, in this work, we analyze the robustness of multi‐dimensional quantum secret sharing schemes under four different noise models, namely amplitude damping (ad), depolarizing (d), dit flip (df), and phase flip (dpf). Each model captures a distinct type of quantum disturbance, providing insights into how different noise models affect the fidelity of secret reconstruction. In addition to state‐specific fidelity, we also evaluate the average fidelity over arbitrary pure qutrit secret states using the Haar, equivalently Fubini–Study, measure. This provides a state‐independent robustness indicator and allows a more meaningful comparison of the considered quantum secret sharing schemes when the dealer's secret state is arbitrary. Moreover, we observe that protocols involving a larger number of qudits generally exhibit higher implementation complexity and increased sensitivity to noise. Consequently, the fidelity degrades more rapidly. Moreover, it is observed that the amplitude damping noise shows the highest fidelity across most parameter ranges, suggesting a better preservation of quantum secret.
By applying the framework of entropic uncertainty relation (EUR) and the Quantum Leftover Hash Lemma (QLHL), we introduce a security-proof method for variable-length side-channel-secure (SCS) quantum key distribution (QKD) against coherent attacks. This method reframes composable security as a statistical fluctuation problem of phase errors, enabling direct proofs against coherent attacks through observables and virtual observables. It yields tight key rates for the SCS protocol and reduces pulse requirements by over two orders of magnitude compared to prior works that employ the post-selection technique. We prove that the secure key length for the SCS protocol can be determined after error correction by exploiting the fact that untagged bits are free from bit-flip errors, using the actual information leakage during error correction and the post-error-correction statistics of each state to calculate the final key rate. We further identify sufficient conditions under which the final key length may be determined after error correction in a broader class of QKD protocols. Under the framework of EUR and QLHL, we clarify the applicability of several commonly used concentration bounds to variable-length QKD and the appropriate manner of their implementation. This work enhances the practical value of the SCS protocol and clarifies the security justification of key-rate formulas used in practical variable-length QKD implementations.
