Generalized form of optimal teleportation witnesses

TL;DR

This paper introduces a generalized optimal teleportation witness that enhances detection of entangled states for quantum teleportation, linking it to entanglement characterization and practical measurement techniques.

Contribution

It presents a new form of teleportation witness, establishes its relation to entanglement witnesses, and demonstrates its decomposability and experimental measurability.

Findings

Teleportation witness can characterize mixed state entanglement using Schmidt numbers.

Every teleportation witness is an entanglement witness, but not vice versa.

Teleportation witness is equivalent to a decomposable entanglement witness.

Abstract

We propose a generalized form of optimal teleportation witness to demonstrate their importance in experimental detection of the larger set of entangled states useful for teleportation in higher dimensional systems. The interesting properties of our witness reveal that teleportation witness can be used to characterize mixed state entanglement using Schmidt numbers. Our results show that while every teleportation witness is also a entanglement witness, the converse is not true. Also, we show that a hermitian operator is a teleportation witness iff it is a decomposable entanglement witness. In addition, we analyze the practical significance of our study by decomposing our teleportation witness in terms of Pauli and Gell-Mann matrices, which are experimentally measurable quantities.