Bounding the quantum capacity with flagged extensions

Abstract

In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum $Q$ and private $P$ capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than $1/2$. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish new state-of-the-art upper bounds on the quantum and private capacities of the depolarizing channel, BB84 channel and generalized amplitude damping channel. Moreover, the flagged construction can be naturally applied to tensor powers of channels with less restricting degradability conditions, suggesting that better upper bounds could be found by considering a larger number of channel uses.

arXiv comment22 pages, 6 figures, published version. Presentation improved, typos corrected, references added

References in corpus (46)

• Quantum cryptography: Public key distribution and coin tossing
• The capacity of the noisy quantum channel
• Superadditivity of communication capacity using entangled inputs
• Optimal Universal and State-Dependent Quantum Cloning
• From Classical to Quantum Shannon Theory
• Quantum Communication With Zero-Capacity Channels
• Hudson's Theorem for finite-dimensional quantum systems
• An improved bound on distillable entanglement
• Quantum Channel Capacity of Very Noisy Channels
• SIC-POVMs and the Extended Clifford Group
• Quantum cloning and the capacity of the Pauli channel
• On the von Neumann capacity of noisy quantum channels
• On Quantum Fidelities and Channel Capacities
• Decoherence in Solid State Qubits
• Information-capacity description of spin-chain correlations
• Degenerate Quantum Codes for Pauli Channels
• Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions
• The structure of degradable quantum channels
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Reverse Coherent Information
• Unbounded number of channel uses are required to see quantum capacity
• Quantum Capacities of Channels with small Environment
• The private capacity of quantum channels is not additive
• The quantum capacity with symmetric side channels
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
• Approximate Degradable Quantum Channels
• New lower bounds on the non-zero capacity of Pauli Channels
• Dephrasure channel and superadditivity of coherent information
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Useful states and entanglement distillation
• Quantum and private capacities of low-noise channels
• Quantum flags, and new bounds on the quantum capacity of the depolarizing channel
• Potential capacities of quantum channels
• Quantum Codes from Neural Networks
• A linearized stabilizer formalism for systems of finite dimension
• Positivity and nonadditivity of quantum capacities using generalized erasure channels
• Efficient simulation of sparse Markovian quantum dynamics
• Superdiffusive quantum stochastic walk definable of arbitrary directed graph
• Superadditivity of the Classical Capacity with Limited Entanglement Assistance
• Error Thresholds for Arbitrary Pauli Noise
• Enhanced energy-constrained quantum communication over bosonic Gaussian channels
• Estimating Quantum and Private capacities of Gaussian channels via degradable extensions
• Entropic singularities give rise to quantum transmission
• Pursuing the fundamental limits for quantum communication
• Experimental observation of coherent-information superadditivity in a dephrasure channel

Cited by in corpus (1)

• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation