Local Unambiguous Discrimination with Remaining Entanglement

TL;DR

This paper introduces a local discrimination method for unknown entangled states that either identifies the state or distills pure entanglement, enabling deterministic extraction from multiple copies.

Contribution

It presents a novel local manipulation technique allowing the identification or entanglement distillation of unknown pure states, applicable to any finite set with multiple copies.

Findings

Any finite set of entangled pure states can be locally distinguished with multiple copies.

Pure entanglement can be deterministically extracted from unknown pure entanglement.

Locally distinguishable operations include those globally distinguishable, like certain unitaries and measurements.

Abstract

A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown state, we introduce a new way to locally manipulate the original quantum system: either identify the state successfully or distill some pure entanglement. Remarkably, if many copies are available, we show that any finite set of entangled pure states, whatever orthogonal or not, can be locally distinguished in this way, which further implies that pure entanglement can be deterministically extracted from unknown pure entanglement. These results make it clear why a large class of entangled bipartite quantum operations including unitary operations and measurements that are globally distinguishable can also be locally distinguishable: they can generate pure entanglement consistently.