Realization schemes for quantum instruments in finite dimensions

TL;DR

This paper introduces a general dilation scheme for finite-dimensional quantum instruments with continuous outcomes, enabling their realization through indirect measurements and feed-forward operations, generalizing quantum teleportation methods.

Contribution

It provides a novel dilation framework for quantum instruments using finite-dimensional ancillas, encompassing group-covariant instruments and extending teleportation schemes.

Findings

Dilation scheme for quantum instruments with continuous outcomes

Application to operator frame-generated instruments

Generalization of quantum teleportation and telecloning

Abstract

We present a general dilation scheme for quantum instruments with continuous outcome space in finite dimensions, in terms of an indirect POVM measurement performed on a finite dimensional ancilla. The general result is then applied to a large class of instruments generated by operator frames, which contains group-covariant instruments as a particular case, and allows to construct dilation schemes based on a measurement on the ancilla followed by a conditional feed-forward operation on the output. In the case of tight operator frames our construction generalizes quantum teleportation and telecloning, producing a whole family of generalized teleportation schemes in which the instrument is realized via a joint POVM at the sender combined with a conditional feed-forward operation at the receiver.