On the entanglement structure in quantum cloning

We study the entanglement properties of the output state of a universal cloning machine. We analyse in particular bipartite and tripartite entanglement of the clones, and discuss the ``classical limit'' of infinitely many output copies.Comment: 7 pages, 1 figure, contribution to "David Mermin Festschrift", Foundations of Physic

Structural approach to unambiguous discrimination of two mixed quantum states

We analyze the optimal unambiguous discrimination of two arbitrary mixed quantum states. We show that the optimal measurement is unique and we present this optimal measurement for the case where the rank of the density operator of one of the states is at most 2 ("solution in 4 dimensions"). The solution is illustrated by some examples. The optimality conditions proved by Eldar et al. [Phys. Rev. A 69, 062318 (2004)] are simplified to an operational form. As an application we present optimality conditions for the measurement, when only one of the two states is detected. The current status of optimal unambiguous state discrimination is summarized via a general strategy.Comment: 33 pages, 3 figures, minor correction

Relations between Entanglement Witnesses and Bell Inequalities

Bell inequalities, considered within quantum mechanics, can be regarded as non-optimal witness operators. We discuss the relationship between such Bell witnesses and general entanglement witnesses in detail for the Bell inequality derived by Clauser, Horne, Shimony, and Holt (CHSH). We derive bounds on how much an optimal witness has to be shifted by adding the identity operator to make it positive on all states admitting a local hidden variable model. In the opposite direction, we obtain tight bounds for the maximal proportion of the identity operator that can be subtracted from such a CHSH witness, while preserving the witness properties. Finally, we investigate the structure of CHSH witnesses directly by relating their diagonalized form to optimal witnesses of two different classes.Comment: 8 pages, 2 figure

Cloning a real d-dimensional quantum state on the edge of the no-signaling condition

We investigate a new class of quantum cloning machines that equally duplicate all real states in a Hilbert space of arbitrary dimension. By using the no-signaling condition, namely that cloning cannot make superluminal communication possible, we derive an upper bound on the fidelity of this class of quantum cloning machines. Then, for each dimension d, we construct an optimal symmetric cloner whose fidelity saturates this bound. Similar calculations can also be performed in order to recover the fidelity of the optimal universal cloner in d dimensions.Comment: 6 pages RevTex, 1 encapuslated Postscript figur

No Signalling and Probabilistic Quantum Cloning

We show that the condition of no faster-than-light signalling restricts the number of quantum states that can be cloned in a given Hilbert space. This condition leads to the constraints on a probabilistic quantum cloning machine (PQCM) recently found by Duan and Guo.Comment: 5 page

Optimal quantum repeaters for qubits and qudits

A class of optimal quantum repeaters for qubits is suggested. The schemes are minimal, i.e. involve a single additional probe qubit, and optimal, i.e. provide the maximum information adding the minimum amount of noise. Information gain and state disturbance are quantified by fidelities which, for our schemes, saturate the ultimate bound imposed by quantum mechanics for randomly distributed signals. Special classes of signals are also investigated, in order to improve the information-disturbance trade-off. Extension to higher dimensional signals (qudits) is straightforward.Comment: Revised version. To appear in PR

Bounds for state-dependent quantum cloning

Due to the no-cloning theorem, the unknown quantum state can only be cloned approximately or exactly with some probability. There are two types of cloners: universal and state-dependent cloner. The optimal universal cloner has been found and could be viewed as a special state-dependent quantum cloner which has no information about the states. In this paper, we investigate the state-dependent cloning when the state-set contains more than two states. We get some bounds of the global fidelity for these processes. This method is not dependent on the number of the states contained in the state-set. It is also independent of the numbers of copying.Comment: 13 pages, 1 figure, to appear in Phys. Rev.

Optimal N-to-M Cloning of Quantum Coherent States

The cloning of continuous quantum variables is analyzed based on the concept of Gaussian cloning machines, i.e., transformations that yield copies that are Gaussian mixtures centered on the state to be copied. The optimality of Gaussian cloning machines that transform N identical input states into M output states is investigated, and bounds on the fidelity of the process are derived via a connection with quantum estimation theory. In particular, the optimal N-to-M cloning fidelity for coherent states is found to be equal to MN/(MN+M-N).Comment: 3 pages, RevTe