Limits on classical communication from quantum entropy power inequalities

Abstract

Almost all modern communication systems rely on electromagnetic fields as a means of information transmission, and finding the capacities of these systems is a problem of significant practical importance. The Additive White Gaussian Noise (AWGN) channel is often a good approximate description of such systems, and its capacity is given by a simple formula. However, when quantum effects are important, estimating the capacity becomes difficult: a lower bound is known, but a similar upper bound is missing. We present strong new upper bounds for the classical capacity of quantum additive noise channels, including quantum analogues of the AWGN channel. Our main technical tool is a quantum entropy power inequality that controls the entropy production as two quantum signals combine at a beam splitter. Its proof involves a new connection between entropy production rates and a quantum Fisher information, and uses a quantum diffusion that smooths arbitrary states towards gaussians.

v2: slightly rewritten, fixed typos, updated references, fixed figures. High-level description of proof with emphasis on applications to classical capacity. 10 pages, 4 figures

References in corpus (11)

• Superadditivity of communication capacity using entangled inputs
• Classical capacity of the lossy bosonic channel: the exact solution
• Extremality of Gaussian quantum states
• Quantum properties of classical Fisher information
• Information Theoretic Proofs of Entropy Power Inequalities
• Covariance and Fisher information in quantum mechanics
• Minimum output entropy of bosonic channels: a conjecture
• Quantum broadcast channels
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results

Cited by in corpus (36)

• Quantum channels and memory effects
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• A solution of the Gaussian optimizer conjecture
• Quantum state majorization at the output of bosonic Gaussian channels
• The entropy power inequality for quantum systems
• A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
• Quantum Entropy and Central Limit Theorem
• Fundamental limits on the capacities of bipartite quantum interactions
• Passive states optimize the output of bosonic Gaussian quantum channels
• Gaussian states minimize the output entropy of one-mode quantum Gaussian channels
• Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator
• The conditional entropy power inequality for Gaussian quantum states
• Entropy power inequalities for qudits
• Equivalence Relations for the Classical Capacity of Single-Mode Gaussian Quantum channels
• Gaussian optimizers for entropic inequalities in quantum information
• Electromagnetic channel capacity for practical purposes
• Geometric inequalities from phase space translations
• Strong converse rates for classical communication over thermal and additive noise bosonic channels
• Geometric approach to quantum statistical inference
• Classical capacity per unit cost for quantum channels
• Quantum-optical channels that output only classical states
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Conditional quantum entropy power inequality for $d$-level quantum systems
• Thinning, photonic beamsplitting, and a general discrete entropy power inequality
• Quantum Ruzsa Divergence to Quantify Magic
• Coherent state coding approaches the capacity of non-Gaussian bosonic channels
• Classical capacity of phase-sensitive Gaussian quantum channels
• Upper bounds on the private capacity for bosonic Gaussian channels
• Universal upper bounds for Gaussian information capacity
• The multi-mode quantum Entropy Power Inequality
• Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems
• Extending the Shannon Upper Bound Using Spiral Modulation
• Two-particle indistinguishability and identification of boson-and-fermion species: a Fisher information approach
• Fluctuation and dissipation in memoryless open quantum evolutions
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory