Conditions for degradability of tripartite quantum states

TL;DR

This paper introduces the concept of state degradability in tripartite quantum systems, providing necessary and sufficient conditions for when one party's state can be simulated from another's, with applications to channel degradability testing.

Contribution

It defines and characterizes state degradability, offering an efficient method to determine it and linking it to quantum channel degradability analysis.

Findings

Derived necessary and sufficient conditions for state degradability.

Developed an efficient method to test degradability of states.

Connected state degradability to channel degradability testing.

Abstract

Alice, Bob, and Eve share a pure quantum state. We introduce the notion of state degradability by asking whether the joint density of Alice and Eve can be transformed to the joint density of Alice and Bob by processing Eve's part through a quantum channel, in order words, degrading Eve. We prove necessary and sufficient conditions for state degradability and provide an efficient method to quickly rule out degradability for a given state. The problem of determining degradability of states is different from that of quantum channels, although the notion is similar. One application of state degradability is that it can be used to test channel degradability. In particular, the degradability of the output state of a channel obtained from the maximally entangled input state gives information about the degradability of the channel.