Publication
Realizing a meaningful quantum advantage requires overcoming the pervasive effects of noise in quantum information processing systems. This thesis addresses key challenges in quantum information theory and quantum coding by developing protocols and codes that are optimized for a variety of noisy quantum channels and realistic operating regimes. A central focus is entanglement sharing over noisy quantum channels, a task fundamental to quantum communication and modular quantum computing. Current lower bounds on achievable rates have advanced slowly, particularly for the setting of two-way classical communication assistance. We propose improved protocols for both Pauli and non-Pauli channels, based on a novel channel reshaping paradigm. In this framework, parts of the protocol transform the original channel into a more tractable form, enabling the application of well-matched coding techniques. For instance, we design constant-weight codes that reshape the amplitude damping channel into an erasure channel, outperforming the best known bounds based on the reverse coherent information. We extend this approach to the damping-dephasing channel, demonstrating similar gains. In the case of Pauli channels, we improve upon the best known bounds for the depolarizing channel through a detailed analysis of existing protocols. Notably, we observe that a successful round of a finite-size entanglement sharing protocol reshapes the Pauli channel into an improved Pauli channel. These examples collectively highlight the effectiveness of the channel reshaping framework. In the setting of unassisted quantum communication, we investigate quantum error-correcting codes tailored for small to moderate blocklengths--crucial for near-term quantum devices. We introduce an interpolation scheme between quantum polar codes and quantum Reed-Muller codes, resulting in valid quantum codes with improved finite-blocklength performance under successive cancellation decoding. Additionally, we examine the robustness of quantum codes under uncertainty in channel parameters. We show that joint decoding of Pauli-X and Pauli-Z errors for quantum Reed-Muller codes significantly outperforms successive decoding, leveraging an analogy with classical multiple access channels. Collectively, the contributions of this thesis advance the theory and practice of quantum communication and coding, offering new tools and perspectives for building resilient quantum information systems.