Holevo Capacity of Discrete Weyl Channels

Abstract

Holevo capacity is the maximum rate at which a quantum channel can reliably transmit classical information without entanglement. However, calculating the Holevo capacity of arbitrary quantum channels is a nontrivial and computationally expensive task since it requires the numerical optimization over all possible input quantum states. In this paper, we consider discrete Weyl channels (DWCs) and exploit their symmetry properties to model DWC as a classical symmetric channel. We characterize lower and upper bounds on the Holevo capacity of DWCs using simple computational formulae. Then, we provide a sufficient and necessary condition where the upper and lower bounds coincide. The framework in this paper enables us to characterize the exact Holevo capacity for most of the known special cases of DWCs.

arXiv commentClose to the published version except for some fixed typos and a new proof of Theorem 2 (upper bound on the Holevo capacity). Comments are welcome

References in corpus (14)

• Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
• Superadditivity of communication capacity using entangled inputs
• From Classical to Quantum Shannon Theory
• Bloch vectors for qudits
• Quantum Communication With Zero-Capacity Channels
• Additivity for a class of unital qubit channels
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Unbounded number of channel uses are required to see quantum capacity
• The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit Unital Channels
• Potential capacities of quantum channels
• Efficient Approximation of Quantum Channel Capacities
• Maximal output purity and capacity for asymmetric unital qudit channels
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula

Cited by in corpus (6)

• Classical capacity of the generalized Pauli channels
• Entanglement-Free Parameter Estimation of Generalized Pauli Channels
• On capacity of quantum channels generated by irreducible projective unitary representations of finite groups
• Efficient accessible bounds to the classical capacity of quantum channels
• Quantum Random Access Code in Noisy Channels
• Engineering classical capacity of generalized Pauli channels with admissible memory kernels