Entanglement trimming in stabilizer formalism

TL;DR

This paper establishes a necessary and sufficient condition, called the "bigger man principle," for transferring entanglement in stabilizer states across quantum networks, extending the concept to qudits and continuous variables.

Contribution

It introduces the "bigger man principle" providing a constructive criterion for entanglement trimming in stabilizer states, including qudits and continuous variables.

Findings

Derived a necessary and sufficient condition for entanglement transfer.

Extended the principle to qudits with square-free dimension.

Generalized the concept to continuous variable stabilizer states.

Abstract

Suppose in a quantum network, there are $n$ qubits hold by Alice, Bob and Charlie, denoted by systems $A$, $B$ and $C$, respectively. We require the qubits to be described by a stabilizer state and assume the system $A$ is entangled with the combined system $BC$. An interesting question to ask is when it is possible to transfer all the entanglement to system $A$ and $B$ by local operation on $C$ and classical communication to $AB$, namely \textit{entanglement trimming}. We find a necessary and sufficient condition and prove constructively for this entanglement trimming, which we name it as "the bigger man principle". This principle is then extended to qudit with square-free dimension and continuous variable stabilizer states.