Free encoding capacity: A universal unit for quantum resources

TL;DR

This paper introduces the free encoding capacity (FEC) as a universal unit for quantifying quantum resources under constrained encoding operations, linking it to resource theories and state transformations.

Contribution

It defines FEC within quantum resource theories, demonstrating its role as a universal resource unit and its faithfulness in pointed resource theories.

Findings

FEC acts as a universal quantum resource unit.

In pointed resource theories, FEC is a faithful resource measure.

FEC influences resource-theoretic state transformations.

Abstract

A perfect d-dimensional quantum channel can convey log d-bits of classical information by encoding messages in d-orthogonal quantum states. Alternatively, for every quantum state at the senders end, there exist d-encoding operations which produce d-orthogonal quantum states. Transmitting which via a d-level perfect quantum channel it is possible to communicate log d-bits of classical information. But what if the set of encoding operations is restricted only within a physically constrained class? Here, we consider such a class of encoding operations to be the set of free operations for any quantum resource theory and show that the constrained capacity - namely, the free encoding capacity (FEC) emerged as a unit of the corresponding quantum resource. Moreover, we show that for the pointed resource theories - a resource theory admitting only a single free state - FEC becomes a faithful resource measure also. We also discuss the implications of FEC in the question of resource-theoretic state transformations and the possibility of extending its faithfulness for general quantum resource theories.