Graduate texts
Develop definitions, notation, proofs, and the mathematical structure of quantum information.
Research interest · Mathematics-first preparation
Quantum Communication & Quantum-Safe Networks
Quantum communication and its intersection with information technology are among my research interests across future communication systems. I am learning the mathematical foundations of quantum information and am interested in state representation, physical channel modeling, quantum key distribution, repeaters, network protocols, and post-quantum security. This area offers a way to build on my communication-theory and simulation background while developing the required knowledge of quantum mechanics.
Transferable foundation
Detection and estimation, probability, BER analysis, channel modeling, and Monte Carlo validation
Building now
Quantum-state representation, noisy channels, QKD, quantum networking, error correction, and hybrid PQC–QKD security
Study practice
How I am building competence
I combine formal mathematical study with several source types so that concepts are understood from more than one perspective.
Open research literature
Study foundational protocols, open reviews, implementation limitations, and network-system challenges.
Public lectures
Use openly accessible university and research-institute courses, including official YouTube material, to reinforce difficult concepts visually.
Mathematical reconstruction
Work through states, measurements, channel models, error probabilities, and key-rate relationships step by step.
Technical foundation
Mathematics and systems under study
Quantum information representation
- Complex Hilbert spaces, bra–ket notation, tensor products, and Hermitian or unitary operators
- Pure states, mixed states, density matrices, reduced states, the Bloch sphere, and partial trace
- Qubits, qudits, continuous-variable states, and composite or entangled systems
- Photonic encodings in polarization, phase, time bins, and frequency bins, together with interfaces to matter-based quantum memories
- The Born rule, projective measurement, POVMs, state discrimination, and quantum tomography
- Shannon and von Neumann entropy, mutual information, relative entropy, and Holevo information
Communication, channels, and security
- CPTP maps and Kraus, Choi, and Stinespring representations of quantum channels
- Pure-loss and thermal-loss bosonic channels, plus dephasing, depolarizing, erasure, and amplitude-damping models
- QKD protocol families and techniques, including BB84 and E91, decoy-state methods, measurement-device-independent and twin-field QKD, and continuous-variable QKD
- QBER, secret-key rate, reconciliation, privacy amplification, composable security, and finite-key analysis
- Fiber, terrestrial free-space, and satellite optical links; sources, detectors, loss, dark counts, and side channels
- Quantum repeaters, memories, error correction, entanglement distribution, routing, and classical control
Research landscape
Areas within quantum communication and information technology
I am using this map to build breadth before selecting a tightly defined doctoral problem with a supervisor.
Information representation
State vectors and density matrices, discrete- and continuous-variable encodings, measurement, entanglement, and interfaces between flying and stationary qubits.
Quantum channel modeling
Mathematical noise maps and physical photon links, including loss, decoherence, atmospheric effects, detector behavior, channel capacity, and link-level simulation.
QKD and quantum cryptography
QKD uses a quantum channel and an authenticated classical channel to establish shared secret keys; it does not itself encrypt application data. I am studying protocol families, practical imperfections, finite-key security, authentication, and key-management integration.
Quantum networks and repeaters
Entanglement generation, swapping and purification, quantum memories, routing and scheduling, distributed protocols, network stacks, and hybrid classical control.
Quantum information and coding
Classical and quantum capacities, entanglement-assisted communication, quantum error correction, resource theories, and reliable transfer of quantum states.
Post-quantum and hybrid security
Post-quantum cryptography uses classical algorithms designed to resist quantum attacks; I am interested in how PQC, QKD, and conventional security can coexist in deployable networks.
Structured roadmap
From representation to deployable secure networks
Quantum mechanics for information
Linear algebra, states and density operators, composite systems, unitary evolution, measurement, entropy, and entanglement.
Encodings, devices, and propagation
Photonic encodings, sources and detectors, fiber and free-space loss, decoherence, link budgets, and interfaces to quantum memories.
Quantum channels and QKD performance
Noise maps, protocol operation, QBER, reconciliation, privacy amplification, secret-key rate, finite-key effects, and implementation limits.
Entanglement distribution and protocols
Repeaters, memories, swapping, routing, resource scheduling, probabilistic link generation, distributed applications, and classical control.
Hybrid quantum-safe infrastructure
Coexistence of QKD, post-quantum cryptography, authentication, conventional network security, and terrestrial, optical, satellite, or prospective future-generation infrastructure.
Selected study resources
Open learning references
These materials guide my current study. Listing a source does not imply that every chapter, paper, or lecture has been completed.
Every link below is openly accessible through a university, public research organization, standards body, arXiv, or an official educational YouTube channel.
The Theory of Quantum Information
John Watrous. Author-hosted chapters on states, channels, measurements, entropy, entanglement, and information-theoretic tasks.
University of WaterlooPrinciples of Quantum Communication Theory: A Modern Approach
Sumeet Khatri and Mark M. Wilde. A rigorous information-theoretic treatment of quantum communication, entanglement, secret key, and assisted capacities.
Read on arXivQuantum Information Science I
MIT's three-part graduate series covering quantum mechanics and measurement, teleportation and superdense coding, selected quantum algorithms, noise, quantum channels, and QKD.
MIT OpenCourseWareQuantum Optical Communication
MIT lecture slides and readings connecting optical modes, quantum states, detection, communication limits, teleportation, and QKD.
MIT OpenCourseWareQuantum Information: Single Systems
An IBM Quantum lesson introducing state vectors, qubits, measurements, and unitary operations.
IBM Quantum on YouTubeQuantum Channels
An IBM Quantum lesson covering dephasing and depolarizing examples together with Stinespring, Kraus, and Choi representations.
IBM Quantum on YouTubeThe BB84 Protocol
TU Delft OpenCourseWare presents the operation of BB84 as a foundation for studying QKD security and implementation.
TU Delft OpenCourseWareAdvances in Quantum Cryptography
Pirandola and coauthors review discrete- and continuous-variable QKD, device independence, satellite links, repeaters, networks, and related protocols.
Read on arXivBlueprint for a Quantum Internet
A U.S. Department of Energy workshop report on testbeds, memories, repeaters, networking milestones, and the path toward long-distance entanglement.
U.S. Department of EnergyBridge from completed work
What my NOMA research contributes to this learning track
My thesis does not establish quantum-communication experience, and classical NOMA models do not transfer directly to quantum systems. What transfers is the discipline of stating assumptions, deriving measurable performance relationships, and validating models computationally.
Analytical performance modeling The methodology used to formulate BER, throughput, and error-propagation models provides a disciplined foundation for learning QBER and key-rate analysis.
Monte Carlo validation The habit of checking analytical predictions against simulation is relevant when learning photon loss, dark counts, channel noise, and finite-sample effects.
Receiver and channel thinking Detection, estimation, and communication-channel concepts provide a classical foundation for learning quantum measurement and noisy-channel models.
Standards and architecture lens
Architecture, security, and interoperability references
IRTF RFC 9340
An informational research-community document describing architectural principles for a quantum internet; it is not an Internet Standards Track specification.
Read the RFCETSI Quantum Key Distribution
Industry specifications and work on QKD interfaces, components, security, and interoperability.
Visit ETSI QKDITU-T Y.3800
An open standards reference for QKD-network terminology, functional architecture, and networking requirements.
View Recommendation Y.3800NIST Post-Quantum Cryptography
Standards and migration guidance for classical public-key algorithms designed to resist attacks by quantum computers.
Explore the NIST project