Energy-constrained diamond norms and their use in quantum information theory

Abstract

We consider the family of energy-constrained diamond norms on the set of Hermitian-preserving linear maps (superoperators) between Banach spaces of trace class operators. We prove that any norm from this family generates the strong (pointwise) convergence on the set of all quantum channels (which is more adequate for describing variations of infinite-dimensional channels than the diamond norm topology). We obtain continuity bounds for information characteristics (in particular, classical capacities) of energy-constrained quantum channels (as functions of a channel) with respect to the energy-constrained diamond norms which imply uniform continuity of these characteristics with respect to the strong convergence topology.

21 pages, any comments are welcome, in v.2 minor corrections and improvements are made

References in corpus (1)

• Continuity of quantum channel capacities

Cited by in corpus (45)

• Advances in Quantum Cryptography
• End-to-end capacities of a quantum communication network
• Theory of channel simulation and bounds for private communication
• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Quantum-limited loss sensing: Multiparameter estimation and Bures distance between loss channels
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Entanglement cost and quantum channel simulation
• Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
• Generic emergence of objectivity of observables in infinite dimensions
• Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
• Convergence rates for the quantum central limit theorem
• Bounds on amplitude damping channel discrimination
• Quantum data hiding with continuous variable systems
• Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
• All phase-space linear bosonic channels are approximately Gaussian dilatable
• Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
• Converse bounds for quantum and private communication over Holevo-Werner channels
• Optimal tests for continuous-variable quantum teleportation and photodetectors
• Characterizing the performance of continuous-variable Gaussian quantum gates
• Continuous-variable quantum state designs: theory and applications
• Bounding quantum capacities via partial orders and complementarity
• Quantum Optical Communication in the presence of strong attenuation noise
• Energy requirement for implementing unitary gates on energy-unbounded systems
• Operator E-norms and their use
• Refined diamond norm bounds on the emergence of objectivity of observables
• Maximal gap between local and global distinguishability of bipartite quantum states
• Optimal gain sensing of quantum-limited phase-insensitive amplifiers
• Trade-offs on number and phase shift resilience in bosonic quantum codes
• Uniform finite-dimensional approximation of basic capacities of energy-constrained channels
• Infinite-Dimensional Programmable Quantum Processors
• Error bounds for Lie Group representations in quantum mechanics
• In situ characterization of linear-optical networks in randomized boson sampling
• Continuous variable port-based teleportation
• Correlation measures of a quantum state and information characteristics of a quantum channel
• Computable lower bounds on the entanglement cost of quantum channels
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Entanglement cost for infinite-dimensional physical systems
• Optimal form of the Kretschmann-Schlingemann-Werner theorem for energy-constrained quantum channels and operations
• Energy preserving evolutions over Bosonic systems
• Energy-limited quantum dynamics
• Convergence Rates for the Trotter Splitting for Unbounded Operators
• Out-of-distribution generalisation for learning quantum channels with low-energy coherent states
• The complexity of Gottesman-Kitaev-Preskill states
• On quantum operations of photon subtraction and photon addition
• Quantum-optimal information encoding using noisy passive linear optics