dorsal/arxiv
View SchemaA Graphic Representation of States for Quantum Copying Machines
| Authors | Sara Felloni, Giuliano Strini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609230 |
| URL | https://arxiv.org/abs/quant-ph/0609230 |
| Journal | Electronic Journal of Theoretical Physics - EJTP 3, No. 11 (2006) 159-187 |
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.
{
"annotation_id": "c829b7f2-c145-42c4-a978-5babd6662b01",
"date_created": "2026-03-02T18:02:31.148000Z",
"date_modified": "2026-03-02T18:02:31.148000Z",
"file_hash": "de61d574f3102a1d6e10ff46e005f7b87779a6a49fef92eb85ca597b72f01eda",
"private": false,
"record": {
"abstract": "The aim of this paper is to introduce a new graphic representation of quantum\nstates by means of a specific application: the analysis of two models of\nquantum copying machines. The graphic representation by diagrams of states\noffers a clear and detailed visualization of quantum information\u0027s flow during\nthe unitary evolution of not too complex systems. The diagrams of states are\nexponentially more complex in respect to the standard representation and this\nclearly illustrates the discrepancy of computational power between quantum and\nclassical systems. After a brief introductive exposure of the general theory,\nwe present a constructive procedure to illustrate the new representation by\nmeans of concrete examples. Elementary diagrams of states for single-qubit and\ntwo-qubit systems and a simple scheme to represent entangled states are\npresented. Quantum copying machines as imperfect cloners of quantum states are\nintroduced and the quantum copying machines of Griffiths and Niu and of Buzek\nand Hillery are analyzed, determining quantum circuits of easier\ninterpretation. The method has indeed shown itself to be extremely successful\nfor the representation of the involved quantum operations and it has allowed to\npoint out the characteristic aspects of the quantum computations examined.",
"arxiv_id": "quant-ph/0609230",
"authors": [
"Sara Felloni",
"Giuliano Strini"
],
"categories": [
"quant-ph"
],
"journal_ref": "Electronic Journal of Theoretical Physics - EJTP 3, No. 11 (2006)\n 159-187",
"title": "A Graphic Representation of States for Quantum Copying Machines",
"url": "https://arxiv.org/abs/quant-ph/0609230"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b99d8b7a-6186-4a2c-891f-af127d704e0b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}