Semidefinite programs for completely bounded norms

Abstract

The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them.

17 pages, references added in version 2

References in corpus (8)

• Distance measures to compare real and ideal quantum processes
• Statistical distinguishability between unitary operations
• Using entanglement improves precision of quantum measurements
• Optimal discrimination of quantum operations
• Quantum information and precision measurement
• All entangled states are useful for channel discrimination
• Unbounded violation of tripartite Bell inequalities
• Entanglement can enhance the distinguishability of entanglement-breaking channels

Cited by in corpus (25)

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• Adaptive versus non-adaptive strategies for quantum channel discrimination
• Fast and efficient exact synthesis of single qubit unitaries generated by Clifford and T gates
• Generalized Entropies
• A Family of Norms With Applications In Quantum Information Theory
• Quantum and private capacities of low-noise channels
• Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
• Robustness Verification of Quantum Classifiers
• Relative Thermalization
• Pretty good measures in quantum information theory
• Efficient rate-adaptive reconciliation for continuous-variable quantum key distribution
• A quantum primality test with order finding
• Robustness of QMA against witness noise
• Usefulness of adaptive strategies in asymptotic quantum channel discrimination
• Quantum Strategies and Local Operations
• Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy
• Dimensionality reduction of SDPs through sketching
• Computational Distinguishability of Quantum Channels
• Universality and Optimality in the Information-Disturbance Tradeoff
• A lower bound on the space overhead of fault-tolerant quantum computation
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Decoherence and Quantum Error Correction for Quantum Computing and Communications
• Quantum error pre-compensation for quantum noisy channels
• Relations between different quantum Rényi divergences
• Conditions for the approximate correction of algebras