We correct an error in the proof of Theorem 11 in our paper “Approximate Degradable Quantum Channels”, IEEE Trans. Inf. Theory, vol. 63, no. 12, pp. 7832-7844, 2017, concerning an upper bound on the private capacity of an approximate anti-degradable channel. Furthermore, we show how to obtain a tighter bound for the quantum capacity.

Abstract I will investigate the capacities of noisy quantum channels through a combined analytical
and numerical approach. First, I introduce novel flagged extension techniques that embed
a channel into a higher-dimensional space, enabling single-letter upper bounds on
quantum and private capacities. My results refine previous bounds and clarify noise
thresholds beyond which quantum transmission vanishes. Second, I present a simulation
framework that uses coherent information to estimate channel capacities in practice,
focusing on two canonical examples: the amplitude damping channel (which we confirm is
degradable and thus single-letter) and the depolarizing channel (whose capacity requires
multi-letter superadditivity). By parameterizing input qubit states on the Bloch sphere, I
numerically pinpoint the maximum coherent information for each channel and validate the
flagged extension bounds. Notably, I capture the abrupt transition to zero capacity at high
noise and observe superadditivity for moderate noise levels.

Abstract Quantum communication enables secure information transmission and entanglement distribution, but these tasks are fundamentally limited by the capacities of quantum channels. While quantum repeaters can mitigate losses and noise, entanglement swapping via a central node is ineffective against the Pauli dephasing channel due to degradation from Bell-state measurements. This suggests that purifying distributed Bell states before entanglement swapping is necessary. Although one-way hashing codes are known to saturate the dephasing channel capacity, no explicit two-way purification protocol has previously been shown to achieve this bound. In this work, we present a two-way entanglement purification protocol with an explicit, scalable circuit that asymptotically achieves the dephasing channel capacity. With each iteration, the fidelity of Bell states increases. At the final round, the residual dephasing error is suppressed doubly-exponentially, scaling as Θ(p 2 n ), enabling near-perfect Bell pairs for any fixed number of purification rounds n. The explicit circuit we propose is versatile and applicable to any number of Bell pairs, offering a practical solution for mitigating decoherence in quantum networks and distributed quantum computing.

With steady progress in the development of quantum networks, the question on how to best provide end-to-end characterization of such networks (Quantum Network Tomography) is quickly becoming more pressing. Initial results demonstrated how we can utilize multipartite entanglement distribution to determine error probabilities of single-Pauli channels and depolarizing channels. In this work, we show how the analysis of quantum capacity regions can be used as a powerful new tool in quantum network tomography. As a first application of the proposed method, we demonstrate how we can characterize the loss on quantum channels in the network directly from quantum capacity region diagrams, even in the presence of bit-flip errors. Our results indicate that quantum capacity regions are not only valuable for network design, resource allocation, and protocol benchmarking, but also show promise for applications in quantum network tomography, particularly in loss tomography.

We derive exact analytical expressions for the quantum capacity of a broad subclass of generalized dephasing channels of the form $\mathrm{\ensuremath{\Lambda}}(\ensuremath{\rho})=(1\ensuremath{-}x)\ensuremath{\rho}+xD(\ensuremath{\rho})$, where $D(\ensuremath{\rho})$ represents a structured decoherence process. These channels are degradable for all noise parameters and in arbitrary dimensions, yielding closed-form single-letter capacity formulas. Our analysis includes fully decohering, block-decohering, and weakly decohering channels, the latter involving coherence preservation within overlapping subspaces. Surprisingly, even under maximal decoherence, the channel may retain nonzero capacity due to residual coherence structure. These results reveal a quantitative role for decoherence-free and partially coherent subspaces in preserving quantum information, offering guidance for encoding strategies in quantum memories and fault-tolerant quantum communication systems.

Abstract Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a natural barrier function was proved for this set, and various implementations of interior-point methods have been made available to solve this class of optimization problems. In this paper, we show how common structures arising from applications in quantum information theory can be exploited to improve the efficiency of solving quantum relative entropy optimization problems using interior-point methods. First, we show that the natural barrier function for the epigraph of the quantum relative entropy composed with positive linear operators is self-concordant, even when these linear operators map to singular matrices. Compared to modeling problems using the full quantum relative entropy cone, this allows us to remove redundant log-determinant expressions from the barrier function and reduce the overall barrier parameter. Second, we show how certain slices of the quantum relative entropy cone exhibit useful properties which should be exploited whenever possible to perform certain key steps of interior-point methods more efficiently. We demonstrate how these methods can be applied to applications in quantum information theory, including quantifying quantum key rates, quantum rate-distortion functions, quantum channel capacities, and the ground state energy of Hamiltonians. Our numerical results show that these techniques improve computation times by up to several orders of magnitude, and allow previously intractable problems to be solved.

In this paper, we focus on discrete-variable quantum systems of odd prime dimension. We investigate the quantum capacity of stabilizer convolution channels under a variety of environmental states. Inspired by the recent result of Bu and Jaffe [Phys. Rev. Lett. 134, 050202 (2025)], our main contribution is to generalize the analysis beyond the discrete beam splitter---which is only applicable for odd prime dimensions $d\ensuremath{\ge}7$---to broader classes of stabilizer convolutions, allowing us to explore the behavior of magic resources in lower dimensions such as $d=3$ and $d=5$, where their role in enhancing quantum capacity has remained unclear. In fact, many of our mathematical results are derived under the broader setting of positive convolutions, not limited strictly to stabilizer convolutions.

Abstract: We develop a governance framework that aligns sovereign AI infrastructure and strategic quantum capacity to improve national technological autonomy. Using a synthetic multi-country benchmark, we quantify how policy levers—sovereign compute procurement, data trusts, frontier model access and safety, quantum roadmaps, export-control alliances, and supply-chain/talent programs—jointly reduce deployment latency, increase capability, and mitigate risk. Our analysis compares a baseline to the proposed framework, demonstrating material improvements in autonomy scores and risk reduction with realistic capital outlays. Keywords: Sovereign AI, quantum capacity, national autonomy, governance, export controls, data sovereignty

Abstract Scalable, reliable quantum light sources are essential for increasing quantum channel capacity and advancing quantum protocols based on photonic qubits. Although recent developments in solid‐state quantum emitters have enabled the generation of single photons with high performance, the scalable integration of multiple quantum light sources onto practical optical platforms remains a challenging task. Here, a breakthrough in achieving a multiple, tunable array of quantum photonic devices is presented. An individual device transfer process allows post‐characterization and selective integration of multiple single‐photon sources onto a V‐groove fiber platform. The nanophotonic cavity ensures efficient coupling of single photons into a standard SMF 28 fiber. Moreover, applying an electric field enables a frequency shift of the integrated single‐photon device. Therefore, the fiber‐integrated quantum platform realizes a scalable and reliable single‐photon array within a compact fiber chip at telecom wavelengths.

In this paper, using the notion of nonlinear coherent states, we define a deformed bosonic dephasing channel modelling the impact of a Kerr medium on a quantum state, as it occurs, for instance, in quantum communication based on optical fibers. We show that, in certain regimes, the Kerr nonlinearity is able to compensate the dephasing. In addition, our studies reveal that the quantum capacity of the deformed bosonic dephasing channel can be greater than that of the undeformed, standard bosonic dephasing channel for certain nonlinearity parameters.

Abstract Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits1. However, many impactful applications demand quantum computations with millions of logical qubits2, necessitating highly scalable quantum error correction. In classical information theory, low-density parity-check (LDPC) codes3 can approach channel capacity efficiently4. Yet, no quantum error-correcting codes with efficient decoding have been shown to approach the hashing bound—a fundamental limit on quantum capacity—despite decades of research5–7. Here, we present quantum LDPC codes that not only approach the hashing bound but also allow decoding with computational cost linear in the number of physical qubits. This breakthrough paves the way for large-scale, fault-tolerant quantum computation. Combined with emerging hardware that manages many qubits, our approach brings quantum solutions to important real-world problems significantly closer to reality.

Abstract: Quantum computing and quantum information science constitute a rapidly evolving discipline at the intersection of physics, computer science, and information theory. This paper presents a systematic analysis of the conceptual foundations, theoretical frameworks, and technological challenges shaping the field. The discussion begins with the quantum-mechanical principles underpinning computation and information, followed by a rigorous framework analysis of key models such as qubits, entanglement, and quantum channels. The central problem addressed is the fragility of quantum states under noise and the corresponding need for reliable methods of computation, communication, and security. Methodologically, the paper integrates formal analysis of entropy and channel capacities with the study of error-correcting codes, fault-tolerant architectures, and emerging hardware platforms. The results synthesize advances in quantum algorithms, quantum error correction, quantum cryptography, and hybrid quantum–classical systems, highlighting both their theoretical limits and engineering realizations. The impact is evaluated through implications for secure communication, computational complexity, and future architectures, alongside ethical and societal reflections. By bridging foundational theory with practical challenges, the book offers a comprehensive resource that informs both academic inquiry and technological development. Its neutral, integrative perspective emphasizes not only the purpose of advancing reliable quantum technologies but also their broader implications for science, security, and society. Keywords Quantum computing, quantum information theory, quantum algorithms, quantum error correction, fault-tolerant quantum computation, quantum cryptography, quantum key distribution, post-quantum cryptography, entanglement, quantum channels, von Neumann entropy, quantum capacity, hybrid quantum–classical systems, quantum machine learning, quantum networks, emerging quantum architectures

The description of how different quantum features, such as non-Markovianity and quantumness, interact in quantum channels is an important step in designing and managing quantum systems. Here, we look at three non-Markovian dephasing channels: pink, brown, and static noise. We investigate and evaluate various measures of non-Markovianity in these channels. Indeed, the proposed measurements include trace norm, entropy, and quantum capacity. We investigate the effect of non-Markovianity on the quantum nature of these channels. Our results show that increasing the degree of non-Markovianity in the suggested channels does not always improve the channel's quantumness. Furthermore, given the aforementioned quantum channels, the l2 norm of quantum coherence and mixedness satisfies the trade-off relation, which is critical for understanding how quantum resources and noise interact in open quantum systems.

Abstract In high-dimensional quantum systems, qudits offer a richer resource than traditional two-dimensional qubits, increasing the capacity of quantum channels and enhancing the efficiency of fault-tolerant quantum computation. These advantages can be utilized to solve complex problems across various fields. In the paper, we propose a 2-qudit controlled-NOT (CNOT) gate in a 4 × 4 -dimensional space and a 3-qudit controlled-controlled-NOT (Toffoli) gate in a 4 × 4 × 4 -dimensional space, both equipped with error-heralded units. Our designs do not require auxiliary photons or extra negatively charged nitrogen-vacancy (NV−) center, resulting in saving resources. Moreover, since the imperfect NV−-cavity interaction processes are predicted in real-time by sensitive single-photon detectors, both high-dimensional CNOT and Toffoli gates boast robust fidelities using existing technology. Furthermore, our protocols simplify circuits with error-heralded units, significantly contributing to the effectiveness of quantum information technology and paving the way for advanced high-dimensional quantum computing.

Reaching for the stars: How I helped Africa grow its quantum capacity

ABSTRACTThis study introduces a novel composite cathode for aqueous zinc‐ion batteries (ZIBs), leveraging porous basil‐derived activated carbon (BAC) and nanostructured manganese dioxide (MnO2) synthesized through a one‐step hydrothermal process. For the first time, basil‐derived carbon is integrated with MnO2, resulting in enhanced electrochemical performance. The MnO2/BAC composite delivers a remarkable specific capacity of 237 mAh/g at 0.5 A/g, along with an energy density of 314 Wh/kg and a power density of 0.66 kW/kg, outperforming cathodes made from pristine MnO2 or BAC. These improvements stem from reduced particle size and a synergistic balance of capacitive and diffusive charge storage mechanisms. Density functional theory calculations corroborate the experimental results, revealing the composite's superior quantum capacity (158.7 µC/cm2) and quantum capacitance (80.4 µF/cm2). Stability assessments highlight excellent cycle life, with > 90% capacity retention and 100% Coulombic efficiency over 300 cycles. The exceptional performance is attributed to the material's unique nanostructure, high surface area (1090 m2/g), and optimized porosity. Additionally, practical applications of ZIBs in pouch cell form using the MnO₂/BAC cathode are demonstrated, showcasing its capability to power a toy car over a satisfactory distance. This study establishes a new benchmark for sustainable and cost‐effective cathode materials, significantly advancing ZIB technology for high‐efficiency energy storage applications.

Bosonic pure-loss channel, which represents the process of photons decaying into a vacuum environment, has zero quantum capacity when the channel’s transmissivity is less than 50%. Modeled as a beam splitter interaction between the system and its environment, the performance of bosonic pure-loss channel can be enhanced by controlling the environment state. We show that by choosing the ideal Gottesman-Kitaev-Preskill (GKP) states for the system and its environment, perfect transmission of quantum information through a beam splitter is achievable at arbitrarily low transmissivities. Our explicit constructions allow for experimental demonstration of the improved performance of a quantum channel through passive environment assistance, which is potentially useful for quantum transduction where the environment state can be naturally controlled. In practice, it is crucial to consider finite-energy constraints, and high-fidelity quantum communication through a beam splitter remains achievable with GKP states at the few-photon level.

Quantum capacity of quantum channels with localization characteristics

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spatial region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We study specifically the Unruh channel that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound that pertains to the decoder Bob. In contrast, even at high temperatures, the Unruh channel can transmit a significant number of zero-bits, which are quantum communication resources that can be used for quantum identification and many other primitive protocols. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are generally not constrained by the Bekenstein bound. However, we further show that when both the encoder and the decoder are restricted, the Bekenstein bound does constrain the channel capacities, including the zero-bit capacity.

Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity measure. However, this cannot be achieved for a few quantities that have been established as capacity measures. Asymptotic regularization is generically necessary making the study of capacities notoriously hard. In this work, by a proper refinement of the physical settings of quantum communication using restricted encodings, we prove additive quantities for quantum channel capacities that can be employed for quantum Shannon theorems. This refinement is consistent with the principles of quantum theory, and it further demonstrates von Neumann entropy as the cornerstone of quantum information.