Semidefinite Programming in Quantum Information Science
arXiv:2306.11637 · doi:10.1088/978-0-7503-3343-6
Abstract
Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum information science. Following a review of the theory of semidefinite programming, the book proceeds to describe how it can be used to address a wide range of important problems from across quantum information science. Specific applications include quantum state, measurement, and channel estimation and discrimination, entanglement detection and quantification, quantum distance measures, and measurement incompatibility. Though SDPs have become an increasingly important tool in quantum information science it's not yet the kind of mathematics students learn routinely. Assuming only a basic knowledge of linear algebra and quantum physics and quantum information, this graduate-level book provides a unified and accessible presentation of one of the key numerical methods used in quantum information science.
Chapter 3 'Quantum states' from the textbook "Semidefinite Programming in Quantum Information Science'', published by IOP ebooks as part of the IOP series in Quantum Technology
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- Parallel ergotropy: Maximum work extraction via parallel local unitary operations
- Thermodynamic Approach to Quantifying Incompatible Instruments
- Operational Interpretation of the Choi Rank Through k-State Exclusion
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- Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario
- Certification of quantum state functions under partial information
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- Deriving three-outcome permutationally invariant Bell inequalities
- QSlack: A slack-variable approach for variational quantum semi-definite programming
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- Semi-device-independent certification of quantum non-Markovianity using sequential Random Access Codes
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- Improving semi-device-independent randomness certification by entropy accumulation
- Computable entanglement cost under positive partial transpose operations
- Revealing hidden physical nonclassicality with nonnegative polynomials
- Communication with Quantum Catalysts
- Dual-VQE: A quantum algorithm to lower bound the ground-state energy
- Quantifying information flow in quantum processes
- Spin-bounded correlations: rotation boxes within and beyond quantum theory
- Choi-Defined Resource Theories
- Optimal discrimination of quantum sequences
- Simulating the quantum switch with quantum circuits is computationally hard
- Maximal intrinsic randomness of a quantum state
- Resource theory of interactive quantum instruments
- Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations
- Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs
- Thermodynamic criteria for signaling in quantum channels
- Bounding conditional entropy of bipartite states with Bell operators
- Efficient and operational quantifier of non-divisibility in terms of channel discrimination
- Practical Countermeasure Against Attacks Exploiting Detection Efficiency Mismatch in Quantum Key Distribution
- Quantum inputs in the prepare-and-measure scenario and stochastic teleportation
- Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds
- Finite Gaussian assistance protocols and a conic metric for extremizing spacelike vacuum entanglement
- Blind-spots of Randomized Benchmarking Under Temporal Correlations
- Improving shadow estimation with locally-optimal dual frames
- Semi-device-independent certification of high-dimensional quantum channels