The Theory of Quantum Information

2018/04/26 by John Watrous · 1 voice · 64 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications

paper · doi:10.1017/9781316848142

openalex publication_date 2018/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.

Citations

• On Information and Sufficiency
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• Separability Criterion for Density Matrices
• Discussion of Probability Relations between Separated Systems
• Statistical decision theory for quantum systems
• Die gegenw�rtige Situation in der Quantenmechanik
• Completely positive linear maps on complex matrices
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
• Subalgebras of C*-algebras
• Quantifying Entanglement
• Quantum entanglement

Cited by

• Non-signaling Approximations of Stochastic Team Problems
• Approximating quantum states by states of low rank
• Optimal lower bounds for quantum state tomography
• Conjugate queries can help
• Correlation Lengths for Stochastic Matrix Product States
• Polyhedral Classical Simulators for Quantum Computation
• The Knowledge Complexity of Quantum Problems
• Optimal ancilla-free Clifford+T synthesis for general single-qubit unitaries
• Computational Monogamy of Entanglement and Non-Interactive Quantum Key Distribution
• On Estimating the Quantum Tsallis Relative Entropy
• Linear-Size QAC0 Channels: Learning, Testing and Hardness
• Optimal Quantum Information Transmission Under a Continuous-Variable Erasure Channel
• AiDE-Q: Synthetic Labeled Datasets Can Enhance Learning Models for Quantum Property Estimation
• Quantum heuristics for linear optimization over large separable operators
• On the Limitations of Pseudorandom Unitaries
• Operational meanings of a generalized conditional expectation in quantum metrology
• Properties of computational entanglement measures
• Lower Bounds for Learning Hamiltonians from Time Evolution
• SoK: A Systematic Review of Malware Ontologies and Taxonomies and Implications for the Quantum Era
• Quantum Noncommutativity Uniquely Determines Relative Entropy
• Thermal Entanglement and Out-of-Equilibrium Thermodynamics in 1D Bose gases
• Hybrid Quantum Error Correction and Mitigation by Purification
• Poisson Quantum Information
• Entanglement Detection with Quantum-inspired Kernels and SVMs
• Quantum Insertion-Deletion Channels
• Explicit construction of a 2-design of \rm U(2) from the theory of angular momentum
• Structure-Fair Quantum Circuit Complexity: An Auditable Information-Theoretic Lower Bound
• Limitations on Uncloneable Encryption and Simultaneous One-Way-to-Hiding
• Quantum advantage without exponential concentration: Trainable kernels for symmetry-structured data
• Towards Universal Quantum Tamper Detection
• Practical Routing and Criticality in Large-Scale Quantum Communication Networks
• Optimal symmetry operators
• Strong-to-Weak Symmetry Breaking Phases in Steady States of Quantum Operations
• Asymptotic Behavior of Random Time-Inhomogeneous Markovian Quantum Dynamics
• Generalized Quantum Stein's Lemma for Classical-Quantum Dynamical Resources
• Tensor Network based Gene Regulatory Network Inference for Single-Cell Transcriptomic Data
• Unified formalism and adaptive algorithms for optimal quantum state, detector and process tomography
• Local transformations of bipartite entanglement are rigid
• A Deficiency-Based Approach for the Operational Interpretation of Quantum Resources with Applications
• Quantum no-signalling correlations and non-local games
• Measuring Less to Learn More: Quadratic Speedup in learning Nonlinear Properties of Quantum Density Matrices
• Counterfactual Local Friendliness: An epsilon-Bounded Interaction-Free Paradox and a Disturbance-Robust Three-Box Inequality
• Duality of extremal quantum states in verification and data hiding
• k-Positive Maps: New Characterizations and a Generation Method
• From Rotations to Unitaries: Reversible Quantum Processes and the Emergence of the SU(2)-SO(3) Homomorphism
• The Haemers bound of noncommutative graphs
• Quantification of Quantum Dynamical Properties with Two Experimental Settings
• Compilation-informed probabilistic logical-error cancellation
• Pretty Good Bounds on the worst-case Pretty Good Measurement
• Energy-independent tomography of Gaussian states
• Modified security analysis of device-independent quantum key distribution with random key basis
• BELT: Block Encoding of Linear Transformation on Density Matrices
• Entropy Measures for Transition Matrices in Random Systems
• Instrument-based quantum resources: quantification, hierarchies and towards constructing resource theories
• Approximate private quantum channels on fermionic Gaussian systems
• State-adaptive quantum error correction and fault-tolerant quantum computing
• Efficient certification of high-dimensional entanglement
• Density Operator Expectation Maximization
• Hierarchy of entanglement detection criteria for random high-dimensional states
• Heisenberg-Limited Quantum Hamiltonian Learning via Randomly Spread Product-States
• Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies
• Permutation Enhances Classical Communication Assisted by Entangled States
• Quantum State Discrimination for Supervised Classification
• <i>SU</i>(<i>p</i>,<i>q</i>) coherent states and a Gaussian de Finetti theorem
• Geometry of Information Structures, Strategic Measures and associated Control Topologies

Discussions

• The fact that the spectral radius of channels (actually: of all positive trace-preserving maps) cannot exceed $1$ encodes the operational fact that applying any channel $\Phi$ cannot increase the trac [stackexchange, 3 points]

Related

• Quantum Information Theory
• An Introduction to the Formalism of Quantum Information
• Quantum information and computation
• Introduction to quantum information theory
• Quantum Computation and Quantum Information