Majorization theory approach to the Gaussian channel minimum entropy conjecture

Abstract

A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space. We show that proving a Gaussian minimum entropy conjecture for a quantum-limited amplifier is actually sufficient to confirm this capacity conjecture, and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory.

References in corpus (1)

• One-mode Bosonic Gaussian channels: a full weak-degradability classification

Cited by in corpus (55)

• Gaussian Quantum Information
• Quantum channels and memory effects
• Performance and structure of single-mode bosonic codes
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Quantum channels and their entropic characteristics
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• The squashed entanglement of a quantum channel
• A fault-tolerant continuous-variable measurement-based quantum computation architecture
• Quantum state majorization at the output of bosonic Gaussian channels
• Fundamental limits of quantum illumination
• Quantum Limits in Optical Communications
• Distributed quantum sensing enhanced by continuous-variable error correction
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Approximate reversibility in the context of entropy gain, information gain, and complete positivity
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Fast simulation of bosonic qubits via Gaussian functions in phase space
• Gaussian optimizers and the additivity problem in quantum information theory
• Passive states optimize the output of bosonic Gaussian quantum channels
• Assessing the performance of quantum repeaters for all phase-insensitive Gaussian bosonic channels
• Gaussian states minimize the output entropy of one-mode quantum Gaussian channels
• Coherent-state discrimination via non-heralded probabilistic amplification
• Equivalence Relations for the Classical Capacity of Single-Mode Gaussian Quantum channels
• Gaussian optimizers for entropic inequalities in quantum information
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• Investigating Einstein-Podolsky-Rosen steering of continuous variable bipartite states by non-Gaussian pseudospin measurements
• Majorization uncertainty relations for mixed quantum states
• Electromagnetic channel capacity for practical purposes
• Majorization relations and entanglement generation in a beam splitter
• Security-proof framework for two-way Gaussian quantum-key-distribution protocols
• Optimal tests for continuous-variable quantum teleportation and photodetectors
• Gaussian benchmark for optical communication aiming towards ultimate capacity
• Continuous majorization in quantum phase space
• Strong converse rates for classical communication over thermal and additive noise bosonic channels
• The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have Gaussian Maximizers
• Entropy production in Gaussian bosonic transformations using the replica method: application to quantum optics
• Interconversion of pure Gaussian states using non-Gaussian operations
• Extreme points of the set of quantum states with bounded energy
• Gaussian optimizers and other topics in quantum information
• Majorization preservation of Gaussian bosonic channels
• Strong converse for the classical capacity of optical quantum communication channels
• Classical capacity of phase-sensitive Gaussian quantum channels
• Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation
• Fock majorization in bosonic quantum channels with a passive environment
• Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
• Multiparticle quantum interference in Bogoliubov bosonic transformations
• Information-theoretic aspects of the generalized amplitude damping channel
• Majorization of quantum polarization distributions
• A criterion for coincidence of the entanglement-assisted classical capacity and the Holevo capacity of a quantum channel
• Divergence-free approach for obtaining decompositions of quantum-optical processes
• Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positive
• Majorization ladder in bosonic Gaussian channels
• Majorization theoretical approach to entanglement enhancement via local filtration
• Information and majorization theory for fermionic phase-space distributions