Transforming quantum operations: quantum supermaps

TL;DR

This paper introduces quantum supermaps, a comprehensive framework for transforming quantum operations, with a proof of their physical implementability and applications across various quantum information tasks.

Contribution

It provides the axiomatic foundation and realization theorem for quantum supermaps, enabling new ways to manipulate quantum operations.

Findings

Quantum supermaps can be physically realized as quantum circuits.

Supermaps unify transformations of states, effects, and measurements.

Applications include quantum programming, cloning, and channel estimation.

Abstract

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.