Achievable rates for the Gaussian quantum channel

Abstract

We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.

12 pages, 4 eps figures, REVTeX

Cited by in corpus (59)

• Gaussian Quantum Information
• Fundamentals of Quantum Information Theory
• Performance and structure of single-mode bosonic codes
• Quantum channels and their entropic characteristics
• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• Quantum information processing with bosonic qubits in circuit QED
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Operator-sum Representation for Bosonic Gaussian Channels
• Analog quantum error correction with encoding a qubit into an oscillator
• Cat codes with optimal decoherence suppression for a lossy bosonic channel
• Distillation of continuous-variable entanglement with optical means
• Encoding an oscillator into many oscillators
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Entanglement assisted capacity of the broadband lossy channel
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Broadband channel capacities
• Equivalence of approximate Gottesman-Kitaev-Preskill codes
• Building a large-scale quantum computer with continuous-variable optical technologies
• Enhanced noise resilience of the surface-GKP code via designed bias
• Encoding qubits in multimode grid states
• Information trade-offs for optical quantum communication
• Quantum Operations, State Transformations and Probabilities
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• Quantum transduction with adaptive control
• Enhanced energy-constrained quantum communication over bosonic Gaussian channels
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
• The capacity of black holes to transmit quantum information
• Lower bound for the quantum capacity of a discrete memoryless quantum channel
• Tracking Quantum Error Correction
• Phase-space methods for representing, manipulating, and correcting Gottesman-Kitaev-Preskill qubits
• The Near-optimal Performance of Quantum Error Correction Codes
• Estimation of Gaussian random displacement using non-Gaussian states
• Non-divisibility vs backflow of information in understanding revivals of quantum correlations for continuous-variable systems interacting with fluctuating environments
• The $2T$-qutrit, a two-mode bosonic qutrit
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• Coherent-state constellations and polar codes for thermal Gaussian channels
• Designing good bosonic quantum codes via creating destructive interference
• Quantum Decoherence of Phonons in Bose-Einstein Condensates
• Single-shot single-mode optical two-parameter displacement estimation beyond classical limit
• Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem
• Optimal encoding of oscillators into more oscillators
• Efficient Concatenated Bosonic Code for Additive Gaussian Noise
• Continuous-variable phase-estimation with unitary and random linear disturbance
• Information Rates Achievable with Algebraic Codes on Quantum Discrete Memoryless Channels
• Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
• Stabilizer Codes with Exotic Local-dimensions
• Interfacing Gottesman-Kitaev-Preskill Qubits to Quantum Memories
• Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes
• Perturbational approach to the quantum capacity of additive Gaussian quantum channel
• Topological stabilizer models on continuous variables
• Fiber Bundle Fault Tolerance of GKP Codes
• Achievable rates for concatenated square Gottesman-Kitaev-Preskill codes
• Quantum Computation and Communication in Bosonic Systems
• Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing
• Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding
• Gottesman-Kitaev-Preskill codes: A lattice perspective
• Enlarging the GKP stabilizer group for enhanced noise protection