In this work, we propose a soft covering problem for fully quantum channels using relative entropy as a criterion for operator closeness. We establish covering lemmas by deriving one-shot bounds on the achievable rates in terms of smooth min-entropies. In the asymptotic regime, we show that the infimum of the rate, defined as the logarithm of the minimum rank of the encoded input state, is given by the minimal coherent information between the reference and output systems that yields the target output state. Furthermore, we present a one-shot quantum decoupling theorem that also employs a relative-entropy criterion. Due to the Pinsker inequality, our one-shot results based on the relative-entropy criterion are tighter than the corresponding results based on the trace norm considered in the literature. In addition, we establish achievable error exponents and second-order rates for quantum soft covering under both trace-distance and relative-entropy criteria.
Block-encoding constructions are often stated as: if a normalized matrix is stored in a quantum-accessible data structure (QRAM), then efficient state preparation or block-encoding can be achieved. We show that “stored” admits two distinct interpretations. In the oracle reading, the required normalized object is assumed, and the implication holds. In the operational reading, storage is the outcome of a discrete preprocessing map applied to classical data, and the conclusion need not follow. By using an order-theoretic circuit-schedule formalism for QRAM-based access, we formalize this gap and show that these constructions hold only under oracle semantics.
In this paper, we investigate secure quantum teleportation (SQT) of squeezed coherent states in the presence of a noisy Gaussian environment. Unlike most previous studies that consider coherent states as the input to be teleported, we take squeezed coherent states as the information carriers and analyze how the squeezing of the input state influences the performance and security of the teleportation protocol. The quantum channel is modeled by a two-mode squeezed vacuum state shared between Alice and Bob, which interacts with a common squeezed thermal reservoir. The security of teleportation is ensured by simultaneously satisfying two conditions: a teleportation fidelity exceeding the classical limit F > 2/3 and the existence of two-way quantum steering of the resource state. Using the covariance matrix formalism and the Lindblad master equation for open quantum systems, we study the time evolution of teleportation fidelity and Gaussian steering under the combined effects of dissipation, temperature and environmental squeezing. The results show that the squeezing of the input coherent state plays a significant role in modifying the robustness of secure quantum teleportation against environmental noise. In particular, for suitable parameter regimes, input-state squeezing can enhance the tolerance of the protocol to thermal fluctuations and de-coherence, extending the temporal range in which SQT is achievable. These findings highlight the importance of the choice of input states in continuous-variable quantum communication protocols and provide new insights for optimizing secure quantum teleportation in realistic noisy environments.
We derive explicit process matrices (effective channels) for the Shor code (a nine-qubit code) and the Steane code (a seven-qubit code) under any unital error channel applied to each physical qubit. These matrices provide valuable insights into the performance of these codes. The derived process matrix enables a rigorous proof that a concatenated code with a symmetric decoder can map an open set of arbitrary error channels to the identity channel. This result generalizes a previously established theorem, which was limited to an open set of diagonal error channels. For commonly studied coherent error models, we leverage the process matrices to perform precise analyses of code performance in terms of average gate infidelity and diamond distance, comparing the physical error channels to the resulting effective channels after error correction. These results refine and extend related findings in prior works.
We discuss how to enhance the charging performance of quantum battery via two entangled auxiliary qubits. The results demonstrate that the quantum battery achieves optimal charging performance when the two auxiliary qubits are in the initial state of maximum entanglement. On this basis, we further discuss the impacts of dissipation and driving strength of the classical field on the charging performance of the quantum battery. It is shown that the quantum battery exhibits higher energy when the dissipation is low. Weak driving strength plays a regulatory role in the energy storage of the quantum battery. Additionally, we compare the performance differences of the quantum battery when the two entangled auxiliary qubits are in different initial states. Our research findings reveal the advantages of entangled auxiliary qubits in enhancing the charging performance of the quantum battery.
By using order rearrangements to generate sub-secrets, we propose a novel multi-party quantum secret sharing protocol based on single photons. Obviously, the method to form sub-secrets is special and interesting here. We analyze the security of the proposed protocol, and detect that it can resist the general attacks: the intercept-resend attack, the entangle-measure attack and Trojan horse attack. We calculate the efficiency of the proposed protocol, and show that it is higher than those of some quantum secret sharing protocols.
We investigate the non-Markovian features of the Adapted Caldeira-Leggett model, a computationally efficient framework recently proposed to capture the essential physics of the standard Caldeira-Leggett model. While this effective model has been previously validated for decoherence and einselection, its ability to reproduce memory effects remains to be explored. By exploiting the model's capability to explicitly track both system and environment degrees of freedom, we provide a detailed characterization of non-Markovianity through the lens of information backflow. We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics. Our results, obtained by comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence, show that while correlations are primarily sensitive to coupling strength, environmental state changes are more heavily influenced by temperature. Our analysis substantiates the physical interpretation of the distinguishability-based approach to non-Markovianity, and confirms this variant of the Caldeira-Leggett model as a reliable tool for exploring the microscopic origins of different fundamental phenomena in quantum mechanics.
Quantum Resource Theories (QRTs) provide a powerful framework for characterizing and quantifying quantum advantages in information processing. While most existing results focus on convex resource theories, many physically relevant resources such as non-Gaussianity and quantum discord naturally exhibit nonconvex structures. In this work, we conduct our study centered around projective robustness. We rigorously establish the dual representation of projective robustness through resource witness, which not only deepens the theoretical understanding of quantum resource quantification but also provides experimentally verifiable detection protocols for nonconvex resource theories. Moreover, we investigate the operational significance of projective robustness in general quantum resource theories without convexity constraints. Our analysis also reveals how projective robustness quantifies the advantage of resourceful states in fundamental quantum processing tasks, extending beyond conventional convex-resource settings. At last, we give an example which shows that projective robustness effectively quantifies quantum advantage in phase discrimination with nonconvex and non-orthogonal free states. It adapts to nonconvex structures, captures the correlation between phase shift and quantum advantage, and satisfies Theorem 1's tight lower bound conclusion. Generalized robustness, however, fails here due to its reliance on convex closure transformation. The results demonstrate the broad applicability of projective robustness across both convex and nonconvex quantum resource theories, offering new perspectives on the fundamental limitations and potential of quantum resources in information processing.
The rapid growth of data and the collective complexity of high-dimensional classification issues have pushed traditional computer technologies to their limits. However, quantum computing has emerged as a possible paradigm to address these difficulties. In this study, a novel quantum machine learning procedure for classification tasks is proposed. The research is separated into three phases: Pre-processing, clustering and classification. Initially, collect the data from the dataset and perform pre-processing using min-max normalization. Clustering and classification methods are essential constituents of this research because they enable the efficient organization and interpretation of complex datasets related to power generation and other features. Novel clustering methods are used to group similar data points based on their characteristics without requiring labelled data. This clustering approach has been performed by quantum assisted adaptive k-harmonic means (Quant-AdKharmonic) algorithm, which can group similar data effectively. After a clustering approach-based label creation, the classifier model, namely Entanglement-Variational Quantum Recurrent Classifier, is used for the classification task (En-VarQuantum). The integration of both models has handled noisy data for better power prediction and analysis. The performance of the suggested model is assessed employing two datasets: TWTDUS and SDWTT18. Thus, the findings of the TWTDUS dataset, utilizing clustering and classification methods, achieve the highest accuracy of 97.18%. Similarly, for the SDWTT18 dataset, the proposed method achieves an accuracy of 98.17%.
We introduce Present Quantum Gravity (PQG), a novel framework grounded in an informational ontology in which only the present instant exists. The Present is described as a quantum memory updating in discrete ticks, encoding entanglement as closed loop structures in a Wick-rotated, relational space. Building on time-symmetric quantum mechanics, holographic principles and entropic gravity, rest mass is reinterpreted as information hidden through temporal entanglement and gravity emerges from a local symmetry breaking of spatial entanglement to compensate for hidden information. From this informational asymmetry, we recover the Newtonian potential and weak-field gravitational time dilations, interpreted as reductions in accessible degrees of freedom. PQG is conceptually compatible with established interpretations, while providing predictions that are in principle falsifiable. Limitations, such as the absence of a field theoretic dynamics or the full Einstein equations, and research avenues, including connections to Einstein-Cartan theory, are discussed at the end of the paper. This work synthesizes the status of the framework as presented at Quantum2025 (Torino, IT), emphasizing its conceptual advances, experimental proposals and roadmap toward a fully dynamical theory, while leaving the details to the referenced literature.
We propose an adaptive quantum routing protocol designed for dynamic network topologies in which link fidelity and availability vary stochastically over time. By introducing a novel Link Stability Metric that integrates predictive fidelity estimation with historical reliability analysis, the protocol can make real-time routing decisions that balance communication quality, latency and quantum resource consumption. The routing problem is formulated as a Markov Decision Process and solved using a deep reinforcement learning (RL) framework, enabling intelligent entanglement path selection and adaptive switching in response to channel degradation. We derive a fundamental bound on achievable end-to-end fidelity in dynamic quantum networks and provide convergence guarantees for the learning-based policy. Extensive simulations on scale-free and random geometric networks demonstrate significant improvements in success probability, fidelity and latency compared with state-of-the-art benchmarks, validating the theoretical analysis and showing the potential of adaptive learning approaches for robust, scalable quantum internetworking.
This paper provides a theoretical analysis of a Mach-Zehnder interferometer (MZI) enhanced by optical parametric amplifiers (OPA) placed inside its arms and fed by a coherent input source. Contrary to most cases found in literature, we perform a wider analysis by considering the MZI unbalanced and two internal phase shifts. We discuss the theoretical best-case phase sensitivity of this setup via the quantum Cram & eacute;r-Rao bound (QCRB) and we consider scenarios having - or not - access to an external phase reference. We also assess the realistic performance of the OPA-enhanced MZI by employing a balanced homodyne detection (asymmetric and symmetric phase shifts) scheme and a difference-intensity detection scheme. We are thus able to find the optimum beam splitter (BS) transmissivity (transmission coefficient) of the first BS via the quantum Fisher information (QFI), while for the second one, we need to take the detection scheme into account. We are able to find these optimal values for all considered scenarios and thus assess the best-case phase sensitivity provided by this setup.
In this paper, we investigate the number of independent vector variables in an n-qubit Orthogonal Product Basis (OPB). Here, the term "independent vector variable" refers to a structural element in the construction of a Unextendible Orthogonal Matrix (UOM). Intuitively, since fixing one state |x > in a qubit basis {|x >,|x '>} uniquely determines its orthogonal partner |x '>, we treat the pair as a single degree of freedom - one variable - rather than two. Based on this counting measure, we propose the conjecture that the number is upper bounded by 2(n) - 1. We show that if the number of orthogonal pairs of variables is minimum, then the matrix corresponding to the OPB contains a column consisting of exactly one variable. In this case the conjecture holds. We also demonstrate more OPBs true for the conjecture, when they have a column containing a small number of independent variables.
This study systematically investigates unconventional photon blockade in two coupled Kerr nonlinear cavities at resonance. By solving the master equation in the steady-state limit and calculating the equal-time second-order correlation function, the photon antibunching effect within the nonlinear regime is revealed. Through analytical derivations, four sets of optimal antibunching conditions are obtained and validated through numerical simulations, unveiling new characteristics of photon blockade. Furthermore, the influence of system parameters on photon blockade is discussed, providing valuable theoretical support for optimizing the design and implementation of single-photon sources.
Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.
The ability of individuals or organizations to initiate user-driven sharing of sensitive data, such as confidential financial information, is critical in cloud storage services. Numerous authentication and key agreement schemes have been proposed as solutions for encrypted data access and sharing, tailored to various scenarios. However, most of these solutions only support third-party authentication or internal cloud sharing, which can restrict the data owner's control over access and limit the scope of data sharing. To address this issue, we propose a Cross Cloud-Domain Quantum Entanglement Swapping (CCQES) architecture that incorporates quantum circuits into the network connecting service providers and users. Within this CCQES framework, we introduce an authentication and key agreement scheme that enables two cross cloud-domain data owners to utilize quantum measurements for mutual authentication. Additionally, data owners can negotiate a session key for bidirectional data sharing through quantum gates. These features empower cloud users to maintain sovereign control over their stored data while facilitating collaboration with users from other cloud domains. Performance evaluation experiments conducted using the IBMQ QASM (Quantum Assembly Language) simulator on the cloud platform demonstrate that any user within the CCQES can authenticate with foreign users and negotiate a random key.
This paper presents a novel approach for solving fractional partial differential equations (FPDEs) by integrating annealing optimization techniques with the Sinc-Galerkin method. Fractional PDEs, characterized by their nonlocal and memory-dependent properties, pose significant challenges for traditional numerical methods. The Sinc-Galerkin method provides an efficient and accurate discretization framework for such equations due to its spectral-like convergence and flexibility. To improve the solution efficiency and robustness, we employ annealing-based optimization, particularly quantum annealing, to efficiently minimize the residuals arising from the discretized system. This optimization framework leverages the natural ability of annealing algorithms to escape local minima, enabling robust solution of the resulting high-dimensional linear and nonlinear systems. Numerical experiments demonstrate the effectiveness and scalability of the proposed method. The synergy between annealing optimization and the Sinc-Galerkin discretization offers a promising computational paradigm for tackling complex fractional PDEs encountered in physics, engineering and applied sciences.
This study advances economical Quantum Teleportation (QT) schemes for cat states across arbitrary dimensional Hilbert spaces. First, we develop a protocol for teleporting an unknown two-dimensional cat state using a three-dimensional maximally entangled three-qutrit quantum channel. The approach involves constructing a complete orthogonal nonsymmetric measurement basis, where the sender performs joint measurements on three particles. The receiver then applies dimension-specific unitary operations conditioned on measurement outcomes to reconstruct the target state. Subsequently, we extend this protocol by replacing the maximally entangled channel with a nonmaximally entangled three-qutrit state. Through auxiliary qubit introduction and optimized operations, the two-qubit cat state is probabilistically recovered. We derive the success probability for both protocols, demonstrating that the nonmaximally entangled case generalizes the former scheme. Further generalization is achieved through two nonsymmetric basis constructions: (i) Scaling quantum channel dimension from 3 to d dimensions; (ii) Extending transmitted cat states from 2 to f dimensions (f < d). These dual-dimensional generalizations establish distinct economical advantages over existing QT schemes.
In this paper, we study single-qubit coherence with the central question: when and why do different measures disagree enough to reverse channel orderings? First, we compile closed-form expressions and analyze behavior on pure and mixed states across widely used quantifiers. Next, we compare noisy evolutions using two resource-theoretic measures the & ell;(1) norm C-& ell;1 and the relative entropy of coherence C-r - on a common basis, enabling unbiased cross-model comparison via an iso-measure protocol (fix one measure, read off the other). Finally, we delineate conditions for ranking reversal: we establish a no-reversal regime for basis-consistent unital, phase-covariant evolutions on equatorial inputs and identify mechanisms that permit reversals nonunital population bias and axis mixing that couples transverse and longitudinal components. The framework yields actionable, side-by-side rankings and clarifies when conclusions depend on the chosen quantifier.
