Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel

TL;DR

This paper investigates how state-dependent losses in quantum channels, modeled as generalized erasure channels, affect their capacities and reveals superadditivity of coherent information with significant implications for quantum communication.

Contribution

It introduces the concept of biased trace decreasing quantum operations and provides bounds and characterizations for capacities of generalized erasure channels, highlighting superadditivity effects.

Findings

Derived bounds for classical and quantum capacities.

Characterized degradability and antidegradability of the channel.

Discovered the largest superadditivity of coherent information among qubit channels.

Abstract

Losses in quantum communication lines severely affect the rates of reliable information transmission and are usually considered to be state-independent. However, the loss probability does depend on the system state in general, with the polarization dependent losses being a prominent example. Here we analyze biased trace decreasing quantum operations that assign different loss probabilities to states and introduce the concept of a generalized erasure channel. We find lower and upper bounds for the classical and quantum capacities of the generalized erasure channel as well as characterize its degradability and antidegradability. We reveal superadditivity of coherent information in the case of the polarization dependent losses, with the difference between the two-letter quantum capacity and the single-letter quantum capacity exceeding $7.197 \cdot 10^{-3}$ bit per qubit sent, the greatest value among qubit-input channels reported so far.