arXiv subjects

René Bødker Christensen

Publications and source records attributed to René Bødker Christensen.

17 recordsLinked to original sources

arXiv2026

Puncturing for Adaptive Entanglement-Assisted Stabilizer Codes

Quantum error-correcting codes are essential for reliable quantum communication. The achievable parameters can be improved by using entanglement-assisted stabilizers at the cost of consuming pre-shared Bell pairs. If the availability of such Bell pairs is intermittent, the ability to adapt the code to available resources is beneficial. That is, to pick a single mother code that can be adapted to different entanglement budgets. To achieve this, we extend an existing puncturing construction for standard/unassisted stabilizers to the entanglement-assisted setting through a three-step procedure: Interpreting the code as an unassisted stabilizer, puncturing a receiver-side qubit, and recovering an entanglement-assisted representation. This procedure reduces the number of required Bell pairs by one while preserving the number of transmitted and logical qubits. We derive a bound on the resulting distance loss and establish conditions for preserving the original code distance. Finally, we analyse distinct, randomly generated, entanglement-assisted stabilizers with five to eight transmitted qubits. Of these codes, 14.75% have a greater distance than their associated unassisted representations. Among this subset, 81.4% admit at least one puncturing choice that preserves the original entanglement-assisted distance. These results illustrate how puncturing can reduce entanglement requirements while maintaining code distance.

quant-ph↗

arXiv2026

Classical Communication Protocol based on Joint Classical-Quantum Coding

We introduce a robust quantum communication protocol that integrates classical error-control coding, entanglement distribution, and superdense coding. Classical error-correcting codes are used to mitigate dark counts and photon losses by determining the positions of qubit transmissions and protecting the data embedded through superdense coding. We derive conditions on the employed codes that guarantee successful error correction under a bounded error-frequency model. Moreover, upper bounds are derived on the performance of conventional superdense coding protected by classical error correction. It is shown that, under the same constraints on error frequency, suitable code configurations of the proposed protocol can exceed those upper bounds both in terms of data rate and energy efficiency. Finally, we develop a physical error model based on fiber attenuation, detector efficiency, dark counts, and time-slot duration, and use it to evaluate the effective performance of different configurations of error-correcting codes. The proposed approach is primarily suited for short-distance quantum links, as in Quantum Local Area Network (QLAN) where it can provide high communication throughput while integrating entanglement distribution directly into the communication process.

quant-ph↗

arXiv2026

Task Concurrency and Compatibility in Measurement-Based Quantum Networks

Measurement-Based Quantum Networks (MBQNs) rely on multipartite pre-shared entanglement resources to satisfy entanglement requests. Traditional designs optimize these resources for individual tasks, neglecting that multiple tasks may arrive concurrently and compete for the same entanglement. We introduce compatibility as a design-level metric, capturing whether concurrent tasks can be satisfied by the same entanglement resources. We define a worst-case notion of compatibility where nodes are prevented from coordinating after task arrival and illustrate why tasks may be incompatible. Furthermore, we explore compatibility extensions that account for stochastic arrivals and the capability to supplement the pre-shared entanglement with additional entanglement on-demand, and show that incompatibility differs structurally dependent on the set of concurrent tasks. We argue that compatibility should be used for resource state design, building the foundation for determining which task pairs the network should support with pre-shared entanglement and which require execution-time coordination. Numerical simulations demonstrate this potential, with $(G,1)$-compatibility achieving a 40%-55% gain in simultaneously supported tasks relative to the single-task baseline. By incorporating compatibility as a fundamental design objective, quantum networks can move beyond single-task optimization towards scalable, robust architectures that effectively balance proactive entanglement distribution and supplemental reactive coordination.

quant-ph↗

arXiv2026

Temporal Framework for Causality-Preserving Scheduling of Measurements in Quantum Networks

Distributed quantum protocols rely on classical feedforward information to process measurement outcomes, but heterogeneous hardware and uncertain local timing can make the causal order of measurements ambiguous when inferred solely from arrival times. Even in simple line networks with only Pauli measurements, end nodes cannot distinguish whether a missing outcome is caused by slow measurement or by delayed classical propagation. To resolve this ambiguity, we propose a time-division architecture for quantum networks in which nodes perform measurements in pre-assigned slots, ensuring a unique causal interpretation of outcomes. We formalize this temporal framework and derive the feedforward and adjacency constraints required to preserve measurement causality. For simple network topologies, we present an algorithm that yields optimal measurement schedules. Overall, the proposed time-division model provides a practical coordination layer that bridges the classical network timing with quantum measurement processing, enabling reliable and scalable measurement-based quantum networking.

quant-ph↗

arXiv2026

1Q: First-Generation Wireless Systems Integrating Classical and Quantum Communication

We introduce the concept of 1Q, the first wireless generation of integrated classical and quantum communication. 1Q features quantum base stations (QBSs) that support entanglement distribution via free-space optical links alongside traditional radio communications. Key new components include quantum cells, quantum user equipment (QUEs), and hybrid resource allocation spanning classical time-frequency and quantum entanglement domains. Several application scenarios are discussed and illustrated through system design requirements for quantum key distribution, blind quantum computing, and distributed quantum sensing. A range of unique quantum constraints are identified, including decoherence timing, fidelity requirements, and the interplay between quantum and classical error probabilities. Protocol adaptations extend cellular connection management to incorporate entanglement generation, distribution, and handover procedures, expanding the Quantum Internet to the cellular wireless.

cs.NI↗

arXiv2025

Puncturing Quantum Stabilizer Codes

Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its generators. In this work, we generalize the puncturing procedure to allow more freedom in the choice of which coded states are kept and which are removed. We describe this puncturing by focusing on the stabilizer matrix containing the generators of the code. In this way, we are able to explicitly describe the stabilizer matrix of the punctured code given the stabilizer matrix of the original stabilizer code. The additional freedom in the procedure also opens up new ways to construct new codes from old, and we present several ways to utilize this for the search of codes with good or even optimal parameters. In particular, we use the construction to obtain codes whose parameters exceed the best previously known. Lastly, we generalize the proof of the Griesmer bound from the classical setting to stabilizer codes since the proof relies heavily on the puncturing technique.

cs.IT↗

arXiv2025

Satellite-Aided Entanglement Distribution for Optimized Quantum Networks

Quantum internet needs to ensure timely provision of entangled qubits to be used in tasks that involve distributed quantum computing or sensing. This has been addressed by a top-down approach of optimized quantum networks [arXiv:2107.10275], in which entanglement is distributed prior to receiving tasks. Upon the task arrival, the desired entanglement state is attained with local operations and classical communication. The pre-distribution of entanglements should aim to minimize the amount of qubits used, as this decreases the risk of decoherence and thus degradation of the entangled state. The optimized quantum networks consider a multi-hop optical network and in this work we are supplementing it with Satellite-aided Entanglement Distribution (SED). The motivation is that satellites can shortcut the topology and place the entanglement at two nodes not directly connected through the optical network. We devise an algorithm for strategic placement of entanglements with SED, which results in a decrease in the number of qubits used in pre-distribution of entanglement. The numerical results show that SED can significantly enhance the performance of small quantum networks, while Entanglement-sharing Constraints (EC) are critical for large networks.

quant-ph↗

arXiv2025

Quantum Two-Way Protocol Beyond Superdense Coding: Joint Transfer of Data and Entanglement

In this article, we introduce a generalization of one-way superdense coding to two-way communication protocols for transmitting classical bits by using entangled quantum pairs. The proposed protocol jointly addresses the provision of entangled pairs and superdense coding, introducing an integrated approach for managing entanglement within the communication protocol. To assess the performance of the proposed protocol, we consider its data rate and resource usage, and we analyze this both in an ideal setting with no decoherence and in a more realistic setting where decoherence must be taken into account. In the ideal case, the proposal offers a 50% increase in both data rate and resource usage efficiency compared to conventional protocols. Even when decoherence is taken into consideration, the quantum protocol performs better as long as the decoherence time is not extremely short. Finally, we present the results of implementing the protocol in a computer simulation based on the NetSquid framework. We compare the simulation results with the theoretical values.

quant-ph↗

arXiv2024

Reliable Quantum Communications based on Asymmetry in Distillation and Coding

The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: (1) indirect transmission based on teleportation and distillation; (2) direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands distillation; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the distillation protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code (QECC), which sets the basis for unique hybrid distillation and coding design. Our results show that ad-hoc asymmetric codes give, compared to conventional QEC, a performance boost and codeword size reduction both in a single link and in a quantum network scenario.

quant-ph↗

arXiv2023

Private Product Computation using Quantum Entanglement

In this work, we show that a pair of entangled qubits can be used to compute a product privately. More precisely, two participants with a private input from a finite field can perform local operations on a shared, Bell-like quantum state, and when these qubits are later sent to a third participant, the third participant can determine the product of the inputs, but without learning more about the individual inputs. We give a concrete way to realize this product computation for arbitrary finite fields of prime order.

quant-ph↗

arXiv2023

Semi-Private Computation of Data Similarity with Applications to Data Valuation and Pricing

Consider two data providers that want to contribute data to a certain learning model. Recent works have shown that the value of the data of one of the providers is dependent on the similarity with the data owned by the other provider. It would thus be beneficial if the two providers can calculate the similarity of their data, while keeping the actual data private. In this work, we devise multiparty computation-protocols to compute similarity of two data sets based on correlation, while offering controllable privacy guarantees. We consider a simple model with two participating providers and develop methods to compute exact and approximate correlation, respectively, with controlled information leakage. Both protocols have computational and communication complexities that are linear in the number of data samples. We also provide general bounds on the maximal error in the approximation case, and analyse the resulting errors for practical parameter choices.

cs.IT↗

arXiv2023

Private Randomness Agreement and its Application in Quantum Key Distribution Networks

We define a variation on the well-known problem of private message transmission. This new problem called private randomness agreement (PRA) gives two participants access to a public, authenticated channel alongside the main channels, and the 'message' is not fixed a priori. Instead, the participants aim to agree on a random string completely unknown to a computationally unbounded adversary. We define privacy and reliability, and show that PRA cannot be solved in a single round. We then show that it can be solved in three rounds, albeit with exponential cost, and give an efficient four-round protocol based on polynomial evaluation.

cs.IT↗

arXiv2023

Transforming First-Year Calculus Teaching for Engineering Students -- Blocks with Field Specific Examples, Problems, and Exams

Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all students, ensuring economic viability. Background: Many first-year engineering students perceive mathematics courses as being too abstract and far from their chosen study programme. This may lead to a lack of motivation and effort, thus decreasing the learning outcomes. Intended outcomes: That engineering students recognize that the calculus and linear algebra courses are relevant for their future work within their specific field. This is intended to improve their learning outcomes. Application design: The courses have been restructured into smaller subunits, each of which has a corresponding workshop treating a real-world problem from the specific field of a given group of students. These workshops are developed in consultation with the relevant fields of study, and they are given a prominent role in the course for instance by forming the basis for the oral exams. Findings: Based on the feedback from students, we find that inclusion of field specific problems does help to highlight the applicability and importance of mathematics in engineering. When implementing such a solution, however, there are a number of challenges to keep in mind.

math.HO↗

arXiv2022

An Algorithmic Approach to Entanglement-Assisted Quantum Error-Correcting Codes from the Hermitian Curve

We study entanglement-assisted quantum error-correcting codes (EAQECCs) arising from classical one-point algebraic geometry codes from the Hermitian curve with respect to the Hermitian inner product. Their only unknown parameter is $c$, the number of required maximally entangled quantum states since the Hermitian dual of an AG code is unknown. In this article, we present an efficient algorithmic approach for computing $c$ for this family of EAQECCs. As a result, this algorithm allows us to provide EAQECCs with excellent parameters over any field size.

cs.IT↗

arXiv2020

On nested code pairs from the Hermitian curve

Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [Kurihara et al. 2012] and in the CSS construction of quantum codes [Ketkar et al. 2006]. The important parameters are (1) the codimension, (2) the relative minimum distance of the codes, and (3) the relative minimum distance of the dual set of codes. Given values for two of them, one aims at finding a set of nested codes having parameters with these values and with the remaining parameter being as large as possible. In this work we study nested codes from the Hermitian curve. For not too small codimension, we present improved constructions and provide closed formula estimates on their performance. For small codimension we show how to choose pairs of one-point algebraic geometric codes in such a way that one of the relative minimum distances is larger than the corresponding non-relative minimum distance.

cs.IT↗

arXiv2019

On Steane-Enlargement of Quantum Codes from Cartesian Product Point Sets

In this work, we study quantum error-correcting codes obtained by using Steane-enlargement. We apply this technique to certain codes defined from Cartesian products previously considered by Galindo et al. in [4]. We give bounds on the dimension increase obtained via enlargement, and additionally give an algorithm to compute the true increase. A number of examples of codes are provided, and their parameters are compared to relevant codes in the literature, which shows that the parameters of the enlarged codes are advantageous. Furthermore, comparison with the Gilbert-Varshamov bound for stabilizer quantum codes shows that several of the enlarged codes match or exceed the parameters promised by the bound.

cs.IT↗

arXiv2019

Steane-Enlargement of Quantum Codes from the Hermitian Curve

In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, the paper contains two constructions of quantum codes whose parameters are described by explicit formulae, and we show that these codes compare favourably to existing, comparable constructions in the literature.

cs.IT↗