Distinguishability and copiability of programs in general process theories

TL;DR

This paper introduces a probability-free notion of state distinguishability in general process theories, linking it to fundamental tasks like cloning and information extraction, revealing intrinsic operational constraints.

Contribution

It develops a theory-independent framework for state distinguishability based on programability, unifying key operational features without relying on probabilities.

Findings

State distinguishability relates to a set of states serving as programs for gates.

Cloning and disturbance are intrinsically linked to distinguishability.

Operational features are valid across different process theories.

Abstract

We propose a notion of state distinguishability that does not refer to probabilities, but rather to the ability of a set of states to serve as programs for a desired set of gates. Using this notion, we reconstruct the structural features of the task of state discrimination, such as the equivalence with cloning and the impossibility to extract information from two non-distinguishable pure states without causing a disturbance. All these features express intrinsic links among operational tasks, which are valid independently of the particular theory under consideration.