Perfect tight quantum teleportation without a shared reference frame

TL;DR

This paper introduces a quantum teleportation protocol that functions without shared reference frames, maintaining efficiency and security, and is robust against reference frame misalignments, with a comprehensive mathematical foundation.

Contribution

It presents a novel teleportation scheme that does not require shared reference frames and introduces a classification of related unitary error bases for qubits and higher dimensions.

Findings

Protocol requires same resources as standard teleportation

Scheme is robust against reference frame changes during operation

Provides classification and construction methods for unitary error bases

Abstract

We present a new scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other proposals, our scheme requires the same amount of classical communication and entangled resources as conventional teleportation, does not reveal any reference frame information, and is robust against changes in reference frame alignment while the protocol is underway. The mathematical foundation of our scheme is a unitary error basis which is permuted up to a phase by the conjugation action of the group. We completely classify such unitary error bases for qubits, exhibit constructions in higher dimension, and provide a method for proving nonexistence in some cases.