Buzek-Hillery cloning revisited using the bures metric and trace norm
L. C. Kwek, C. H. Oh, Xiang‐Bin Wang, Yee‐Chia Yeo · Physical Review A · 2000
Buz\ifmmode \breve{}\else \u{}\fi{}ek and Hillery have recently analyzed the possibility of cloning imperfectly arbitrary states using a universal quantum cloning machine. They have analyzed their result using the Hilbert-Schmidt norm, although a better measure of fidelity is the Bures metric. In this paper, we repeat the Buz\ifmmode \breve{}\else \u{}\fi{}ek and Hillery result using the Bures metric and show that we can still obtain the same result with an improved measure. However, unlike the Hilbert-Schmidt norm, this computation may be extended to the case of continuous variable, infinite-dimensional spaces, or even Hilbert spaces of larger dimensions. For completeness, a similar analysis using the trace norm is also performed.