Economical quantum cloning in any dimension

Highly asymmetric quantum cloning in arbitrary dimension

We investigate the universal asymmetric cloning of states in a Hilbert space of arbitrary dimension. We derive the class of optimal and fully asymmetric 1→ 3 cloners, which produce three copies, each having a different fidelity. A simple parametric expression for the maximum achievable cloning fidelity triplets is then provided. As a side-product, we also prove the optimality of the 1 → 2 asymm...

Optimal asymmetric 1 → 4 quantum cloning in arbitrary dimension

We present an optimal asymmetric 1 → 4 quantum cloner. Our derivation generalizes the constructions of optimal asymmetric 1 → 2 and 1 → 3 quantum cloners in [Quantum Inf. Comput 5, 583 (2005)]. We explicitly prove the optimality of this cloner and give the maximum achievable fidelities. We also present the relation between the optimal quantum cloner with the multipartite entangled state which s...

Monotone Subsequences in Any Dimension

We exhibit sequences of n points in d dimensions with no long monotone subsequences, by which we mean when projected in a general direction, our sequence has no monotone subsequences of length n+d or more. Previous work proved that this function of n would lie between n and 2 n; this paper establishes that the coefficient of n is one. This resolves the question of how the Erdo s Szekeres result...

Any-Dimension Algorithms

Quantum-information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit

We show that for any Hilbert-space dimension, the optimal 1→2 universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions ~which includes continuous variable quantum systems! the universal cloner reduces to an essentially classical device. More generally, we construct a universa...