Information-theoretic aspects of the generalized amplitude damping channel
arXiv:1903.07747 · doi:10.1103/PhysRevA.102.012401
Abstract
The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.
arXiv comment33 pages, 9 figures; close to the published version
References in corpus (79)
- Mixed State Entanglement and Quantum Error Correction
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Review article: Linear optical quantum computing
- Quantifying Entanglement
- Quantum Communication Through an Unmodulated Spin Chain
- Entanglement Measures and Purification Procedures
- General Benchmarks for Quantum Repeaters
- Fundamental Limits of Repeaterless Quantum Communications
- Distillation of secret key and entanglement from quantum states
- The capacity of the noisy quantum channel
- Quantum data processing and error correction
- Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
- General Entanglement Breaking Channels
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- From Classical to Quantum Shannon Theory
- Fundamental rate-loss tradeoff for optical quantum key distribution
- "Squashed Entanglement" - An Additive Entanglement Measure
- Information transmission through a noisy quantum channel
- Additivity for a class of unital qubit channels
- On Quantum Fidelities and Channel Capacities
- Decoherence in Solid State Qubits
- Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
- Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
- Converse bounds for private communication over quantum channels
- One-mode Bosonic Gaussian channels: a full weak-degradability classification
- Information-capacity description of spin-chain correlations
- Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
- Controlling excess noise in fiber optics continuous variables quantum key distribution
- The structure of degradable quantum channels
- Approaches for approximate additivity of the Holevo information of quantum channels
- The squashed entanglement of a quantum channel
- On entanglement-assisted classical capacity
- Reverse Coherent Information
- Unbounded number of channel uses are required to see quantum capacity
- Degradability of Bosonic Gaussian channels
- Quantum Capacities of Channels with small Environment
- The private classical capacity with a symmetric side channel and its application to quantum cryptography
- Universal observable detecting all two-qubit entanglement and determinant based separability tests
- Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
- Multiplicativity of completely bounded p-norms implies a new additivity result
- Relative Entropy Bounds on Quantum, Private and Repeater Capacities
- Approximate Degradable Quantum Channels
- Simplifying additivity problems using direct sum constructions
- Majorization theory approach to the Gaussian channel minimum entropy conjecture
- A practical limitation for continuous-variable quantum cryptography using coherent states
- Semidefinite programming strong converse bounds for classical capacity
- Strong converse rates for quantum communication
- Parameter regimes for a single sequential quantum repeater
- Dephrasure channel and superadditivity of coherent information
- Unified approach to quantum capacities: towards quantum noisy coding theorem
- Narrow Bounds for the Quantum Capacity of Thermal Attenuators
- Efficient optimization of the quantum relative entropy
- Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
- Non-asymptotic entanglement distillation
- Useful states and entanglement distillation
- Improved Semidefinite Programming Upper Bound on Distillable Entanglement
- Entanglement cost and quantum channel simulation
- Closed formula for the relative entropy of entanglement
- The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit Unital Channels
- Quantum and private capacities of low-noise channels
- Semidefinite programming converse bounds for quantum communication
- Local two-qubit entanglement-annihilating channels
- Symmetric Extension of Two-Qubit States
- Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
- Superadditivity of private information for any number of uses of the channel
- Assessing the performance of quantum repeaters for all phase-insensitive Gaussian bosonic channels
- Quantum Codes from Neural Networks
- Versatile relative entropy bounds for quantum networks
- Squashed entanglement and approximate private states
- Amortization does not enhance the max-Rains information of a quantum channel
- Spectrum conditions for symmetric extendible states
- Energy-constrained two-way assisted private and quantum capacities of quantum channels
- Capacity Estimates via comparison with TRO channels
- Entanglement-Breaking Indices
- Ultimate entanglement robustness of two-qubit states against general local noises
- Qubit channels that achieve capacity with two states
- Lower and upper bounds on nonunital qubit channel capacities