Multi-partite entanglement monotones

TL;DR

This paper introduces a family of entanglement monotones for multipartite quantum states, which help quantify the success probability of state transformations under local operations and classical communication.

Contribution

It constructs locally invariant, easily computable monotones from polynomial invariants, providing bounds on transformation success probabilities in multipartite quantum systems.

Findings

Defined new multipartite entanglement monotones

Bound the success probability of state transformations

Monotones are computationally accessible for pure states

Abstract

If we want to transform the quantum state of a system to another using local measurement processes, what is the probability of success? This probability is bounded by quantifying entanglement in both the states. In this paper, we construct a family of local unitary invariants of multipartite states that are monotonic under local operations and classical communication on average. These monotones are constructed from local unitary invariant polynomials of the state and its conjugate, and hence are easy to compute for pure states. Using these measures we bound the success probability of transforming a given state into another state using local quantum operations and classical communication.