Optimal cloning of pure states, testing single clones

Abstract

We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state σ into M > N systems of the same kind, in an approximation of the Mfold tensor product of the state σ. In a previous paper it was shown that this problem has a unique optimal solution, when the quality of the output is judged by arbitrary measurements, involving also the correlations between the clones. We show in this paper, that if the quality judgement is based solely on measurements of single output clones, there is again a unique optimal cloning device, which coincides with the one found previously.

Game-theoretic discussion of quantum state estimation and cloning

“…For example, the referee may perform a one-particle test or multiple-particle test on the qubits he/she receives. However it turns out that the strategies at the Nash equilibrium are equivalent [8,14]. Unfortunately, their equivalence cannot be deduced from game-theoretic arguments since the payoff vectors R differ for these two games, and consequently they are distinct in the game-theoretic formalism.…”

Separability in asymmetric phase-covariant cloning

“…In d = 2, this machine simply reduces to the original universal cloning machine [5], with η = 2 3 or F = 5 6 . This machine is proved to be optimal in that it produces maximal fidelity considering its requirements [9,10,11,12,13]. It can be justified that symmetry of the outputs is a consequence of equality of the coefficients of the terms |ij AB |j X and |ji AB |j X in Eq.…”

“…However, extension to triplicators is also straightforward. The question of how well one can design an approximate duplicator of a qubit (or qudit), provided that the qualities of the two outputs be independent of the input states, has been investigated by Bužek and Hillery [5,6] and the others [7,8,9,10,11,12,13].…”

“…For example in BB84 protocol [4] there is a link between optimal cloning of equatorial states and optimal eavesdropping attack. There have been extensive studies on this subject that illuminate some aspects of quantum cloning [5,6,7,8,9,10,11,12,13].…”

Probabilistic implementation of Hadamard and unitary gates

“…We also derive the best transformation efficiencies. [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] which operate either in a deterministic or probabilistic way. Corresponding to the quantum no-cloning theorem, Pati and Braunstein [23] demonstrated that the linearity of quantum mechanics also forbids one to delete one unknown state ideally against a copy [23], which is called the quantum no-deleting principle.…”