Strong Isomorphism in Eisert-Wilkens-Lewenstein Type Quantum Games

The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum scheme to generate the classical game in a particular case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We are concerned with the Eisert-Wilkens-Lewenstein quantum game scheme and the strong isomorphism between games in strategic form

Entanglement, Nonlocality, Superluminal Signaling and Cloning

The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referee's report to Herbert's paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.Comment: 29 pages, 4 figures, Book Chapter of: Advances in Quantum Mechanics, P. Bracken, ed. INTECH, 2013 Note: after having submitted this paper to the arXives, I realized that there is a mistake in eq.(1). In the last expression at the r.h.s. the p_{i} under the sum should appear square