Quantum optimal transport with quantum channels

DOI10.1007/s00023-021-01042-3OpenAlexW2988376948MaRDI QIDQ2231908

Dario Trevisan, Giacomo De Palma

Publication date: 30 September 2021

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.00803

Mathematics Subject Classification ID

Transport processes in time-dependent statistical mechanics (82C70) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Waves and radiation in optics and electromagnetic theory (78A40) Channel models (including quantum) in information and communication theory (94A40) Quantum state spaces, operational and probabilistic concepts (81P16) Quantum channels, fidelity (81P47)

Related Items

A dual formula for the noncommutative transport distance ⋮ Quantum concentration inequalities ⋮ A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature ⋮ The Wasserstein distance of order 1 for quantum spin systems on infinite lattices ⋮ Quantum Wasserstein distance of order 1 between channels ⋮ Wasserstein distance between noncommutative dynamical systems ⋮ On quantum optimal transport ⋮ A duality-based proof of the triangle inequality for the Wasserstein distances ⋮ Quantum Wasserstein isometries on the qubit state space ⋮ Optimal transport pseudometrics for quantum and classical densities ⋮ Monotonicity of a quantum 2-Wasserstein distance

Uses Software

• qWGAN
• Wasserstein GAN

Cites Work

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• Computational Optimal Transport: With Applications to Data Science
• On the mean field and classical limits of quantum mechanics
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• An analog of the 2-Wasserstein metric in non-commutative probability under which the fermionic Fokker-Planck equation is gradient flow for the entropy
• One-mode quantum Gaussian channels: structure and quantum capacity
• The Schrödinger equation in the mean-field and semiclassical regime
• Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality
• Existence and stability for Fokker-Planck equations with log-concave reference measure
• A mass transportation approach to quantitative isoperimetric inequalities
• Bell measurements and observables
• The conditional entropy power inequality for bosonic quantum systems
• Wave packets and the quadratic Monge-Kantorovich distance in quantum mechanics
• Convex functionals of probability measures and nonlinear diffusions on manifolds
• Supervised learning with quantum computers
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Quantum optimal transport is cheaper
• Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
• Ricci curvature for metric-measure spaces via optimal transport
• Quantum systems, channels, information. A mathematical introduction
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Quantum Rate Distortion, Reverse Shannon Theorems, and Source-Channel Separation
• Quantum Computation and Quantum Information
• Quantum information with continuous variables
• Gaussian optimizers and the additivity problem in quantum information theory
• Entanglement Information Rate Distortion of a Quantum Gaussian Source
• Gaussian optimizers for entropic inequalities in quantum information
• Concentration of quantum states from quantum functional and transportation cost inequalities
• Wasserstein Geometry of Quantum States and Optimal Transport of Matrix-Valued Measures
• The conditional entropy power inequality for quantum additive noise channels
• Quantum rate-distortion theory for memoryless sources
• Matrix Optimal Mass Transport: A Quantum Mechanical Approach
• Methods in Theoretical Quantum Optics
• Wigner–Yanase information on quantum state space: The geometric approach
• The quantumN-body problem in the mean-field and semiclassical regime
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Quantum Rate-Distortion Coding of Relevant Information
• Quantum Continuous Variables
• Geometry of Quantum States
• Quantum Rate-Distortion Coding With Auxiliary Resources
• Quantum-to-classical rate distortion coding
• Elements of Information Theory
• Quantum Information Theory
• Optimal Transport

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