Quantum teleportation is a foundational protocol for sending quantum information through entanglement distribution and classical communication. Assuming ideal classical communication, the reliability of quantum teleportation is limited by the fidelity of the shared EPR pairs. This reliability can be improved through two mechanisms: entanglement purification and quantum error correction (QEC). Using both techniques in concert requires flexible QEC rates, since purification alters the structure of errors induced by imperfect-EPR teleportation, and fixed-rate codes cannot be uniformly effective across purification regimes or reliability targets. In this work, we supplement purification with punctured QEC codes, providing a family of code variants that can be adapted to error-channel characteristics and reliability targets. Punctured codes improve teleportation reliability across a broader range of purification regimes, enabling target reliability to be met without hardware-level code switching. This is corroborated by numerical results, showing that different punctured codes achieve the lowest logical error probability in different operating regimes, and that selecting among them reduces logical error relative to fixed-rate encoded teleportation. This reduction relaxes the requirement on the initial EPR fidelity or purification needed to achieve a target reliability. Overall, puncturing enables adaptation to varying entanglement conditions and reliability requirements while reusing a single stabilizer structure.
Quantum teleportation is a foundational protocol for sending quantum information through entanglement distribution and classical communication. Assuming ideal classical communication, the reliability of quantum teleportation is limited by the fidelity of the shared EPR pairs. This reliability can be improved through two mechanisms: entanglement purification and quantum error correction (QEC). Using both techniques in concert requires flexible QEC rates, since purification alters the structure of errors induced by imperfect-EPR teleportation, and fixed-rate codes cannot be uniformly effective across purification regimes or reliability targets. In this work, we supplement purification with punctured QEC codes, providing a family of code variants that can be adapted to error-channel characteristics and reliability targets. Punctured codes improve teleportation reliability across a broader range of purification regimes, enabling target reliability to be met without hardware-level code switching. This is corroborated by numerical results, showing that different punctured codes achieve the lowest logical error probability in different operating regimes, and that selecting among them reduces logical error relative to fixed-rate encoded teleportation. This reduction relaxes the requirement on the initial EPR fidelity or purification needed to achieve a target reliability. Overall, puncturing enables adaptation to varying entanglement conditions and reliability requirements while reusing a single stabilizer structure.
Quantum teleportation is a foundational protocol for sending quantum information through entanglement distribution and classical communication. Assuming ideal classical communication, the reliability of quantum teleportation is limited by the fidelity of the shared EPR pairs. This reliability can be improved through two mechanisms: entanglement purification and quantum error correction (QEC). Using both techniques in concert requires flexible QEC rates, since purification alters the structure of errors induced by imperfect-EPR teleportation, and fixed-rate codes cannot be uniformly effective across purification regimes or reliability targets. In this work, we supplement purification with punctured QEC codes, providing a family of code variants that can be adapted to error-channel characteristics and reliability targets. Punctured codes improve teleportation reliability across a broader range of purification regimes, enabling target reliability to be met without hardware-level code switching. This is corroborated by numerical results, showing that different punctured codes achieve the lowest logical error probability in different operating regimes, and that selecting among them reduces logical error relative to fixed-rate encoded teleportation. This reduction relaxes the requirement on the initial EPR fidelity or purification needed to achieve a target reliability. Overall, puncturing enables adaptation to varying entanglement conditions and reliability requirements while reusing a single stabilizer structure.
Quantum teleportation is a key protocol for transmitting quantum information using entanglement and classical communication. Its reliability is constrained by both the availability and fidelity of shared entangled pairs, which are affected by stochastic generation and memory decoherence. In this work, we focus on encoded teleportation, in which quantum information is encoded using a quantum error-correcting code and transmitted as a codeword. We evaluate reliability in terms of logical error probability, considering latency-constrained settings where entanglement is accumulated over time and degrades while in memory. We develop a unified framework that captures the interaction between entanglement availability, decoherence, and coding decisions. Our results show that the benefits of longer codes depend on the availability and fidelity of entangled pairs, as acquiring additional resources introduces delays that can reduce their quality. To address this latency-reliability tradeoff, we leverage code puncturing to enable flexible encoded teleportation, allowing the effective code length to adapt across different latency regimes while preserving a common stabilizer structure. Numerical results show that encoded teleportation can provide substantial reliability gains over uncoded transmission under a common entanglement-acquisition latency constraint, and that selecting appropriate punctured codes improves performance across varying latency budgets. Overall, our results highlight the importance of resource-aware adaptation for reliable quantum networking.
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.
Quantum communications rely on quantum tele-portation, which requires high-fidelity entangled pairs between remote nodes. In realistic conditions, however, noise affects both the quantum states to be transmitted and entangled pairs used for teleportation, reducing overall communication reliability. This work proposes an adaptive framework for quantum error correction that selects the most suitable quantum code based on parameters estimated from the entanglement distillation process. By analyzing the fidelity and asymmetry of noisy channel induced by imperfect Einstein-Podolsky-Rosen (EPR) pairs, the scheme identifies how to adapt the quantum code for transmission. The proposed method can either reduce the number of required EPR pairs without compromising performance or enhance performance without increasing resource requirements.
Complex quantum networks can support a diverse set of long-range entanglement distribution schemes ranging from linear repeater protocols to multipath entanglement purification strategies. As a result, a network's resourcefulness, that is its ability to facilitate quantum communication, depends on the deployed distribution scheme. In this work, we analyse and compare the resourcefulness of quantum networks across a broad range of network topologies, including both regular and random networks, under two distinct entanglement distribution schemes. The first relies on entanglement swapping along a single path connecting a source-target pair, while the second exploits entanglement purification using multiple paths between the same source and target nodes. The resourcefulness of the network is quantified using a recently described metric [1] that averages over the maximum teleportation fidelity between arbitrary source-target pairs in the network. We present algorithms for estimating this metric under constraints of edge-usage and ordering of paths. Our results not only demonstrate the sensitivity of the average maximum teleportation fidelity metric to the choice of entanglement distribution protocol, but also highlight the significant improvements enabled by network purification schemes. In particular, purification-based approaches can substantially enhance average teleportation fidelity, thereby improving the overall teleportation capability of quantum networks.
This paper is a tutorial-style introduction to methods and protocols for reliable transmission of quantum information over noisy quantum links. The exposition is based on a design philosophy that parallels classical link-layer mechanisms such as forward error correction and Automatic Repeat reQuest (ARQ). It starts by drawing analogies and highlights differences between classical and quantum links. Such analogies are used as guiding principles, with explicit attention to where the classical correspondence no longer applies and where non-classical constraints and resources govern the protocol design. The emphasis is on the fact that classical reliability is achieved through fungible and cloneable bits, whereas unknown quantum states cannot be copied or freely retransmitted. In addition, quantum information is subject to stringent physical constraints due to decoherence as well as the need for transduction between stationary and flying qubits. Quantum error correction is presented as the analogue of classical forward error correction, where logical qubits are protected by encoding them into larger entangled code spaces and using syndrome measurements to infer and correct errors without collapsing the encoded state. It then introduces teleportation-based link abstractions, in which transmission of an unknown qubit is realized by consuming shared Bell pairs together with classical messages. Entanglement purification protocols play a role similar to ARQ-style reliability enhancement by converting many noisy entangled pairs into fewer, higher-fidelity pairs at the cost of additional resources. The paper is written from the perspective of classical communication engineering and is intended as a guide for translating the relevant ideas toward reliable quantum links and networks.