A Graphic Representation of States for Quantum Copying Machines

TL;DR

This paper introduces a new graphical method for visualizing quantum states, enhancing understanding of quantum copying machines and illustrating the complexity of quantum information flow compared to classical systems.

Contribution

The paper presents a novel diagrammatic representation of quantum states, applied to analyze quantum copying machines, simplifying the interpretation of quantum operations and highlighting their computational complexity.

Findings

Diagrams of states effectively visualize quantum information flow.

Analysis of quantum copying machines using the new representation.

Illustration of entangled states and quantum circuits.

Abstract

The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear and detailed visualization of quantum information's flow during the unitary evolution of not too complex systems. The diagrams of states are exponentially more complex in respect to the standard representation and this clearly illustrates the discrepancy of computational power between quantum and classical systems. After a brief introductive exposure of the general theory, we present a constructive procedure to illustrate the new representation by means of concrete examples. Elementary diagrams of states for single-qubit and two-qubit systems and a simple scheme to represent entangled states are presented. Quantum copying machines as imperfect cloners of quantum states are introduced and the quantum copying machines of Griffiths and Niu and of Buzek and Hillery are analyzed, determining quantum circuits of easier interpretation. The method has indeed shown itself to be extremely successful for the representation of the involved quantum operations and it has allowed to point out the characteristic aspects of the quantum computations examined.