Reply to "Comment on: A Quantum Approach to Static Games of Complete Information"

This is a reply to the paper by S.C.Benjamin, quant-ph/0008127.Comment: 2 pages, Latex, submitted to Phys. Lett.

Reply to Marinatto's comment on "Bell's theorem without inequalities and without alignments"

Marinatto claims that in the proof of Bell's theorem without inequalities and without alignments [A. Cabello, Phys. Rev. Lett. 91, 230403 (2003)], local observables cannot be measured by means of tests on individual qubits. Marinatto's claim is incorrect. To support this, the proof is explicitly rewritten in terms of tests on individual qubits.Comment: REVTeX4, 1 pag

Quantum repeated games

In a two-stage repeated classical game of prisoners' dilemma the knowledge that both players will defect in the second stage makes the players to defect in the first stage as well. We find a quantum version of this repeated game where the players decide to cooperate in the first stage while knowing that both will defect in the second.Comment: Revised in the light of referee's comments. Latex, 10 pages, 1 eps figure, submitted to Physics Letters

Comment on: "A quantum approach to static games of complete information''

Recently Marinatto and Weber introduced an interesting new scheme for quantizing games, and applied their scheme to the famous game 'Battle of the Sexes'. In this Comment we make two observations: (a) the overall quantization scheme is fundamentally very similar to a previous scheme proposed by Eisert et al., and (b) in contrast to a main claim of the paper, the quantum Battle of the Sexes game does not have a unique solution - a similar dilemma exists in both the classical and the quantum versions.Comment: 2 pages, 1 figur

On deciding whether a Boolean function is constant or not

We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.Comment: 8 pages, Latex, 5 figures; accepted for publication on International Journal of Quantum Informatio

Which Kind of Two-Particle States Can Be Teleported through a Three-Particle Quantum Channel?

The use of a three-particle quantum channel to teleport entangled states through a slight modification of the standard teleportation procedure is studied. It is shown that it is not possible to perform successful teleportation of an arbitrary and unknown two-particle entangled state, following our version of the standard teleportation procedure. On the contrary, it is shown which, and in how many different ways, particular classes of two-particle states can be teleported.Comment: 11 pages, Latex, to appear in Found.Phys.Let

Nonlocality without inequalities

We prove that every conceivable hidden variable model reproducing the quantum mechanical predictions of almost any entangled state must necessarily violate Bell's locality condition. The proof does not involve the consideration of any Bell inequality but it rests on simple set theoretic arguments and it works for almost any noncompletely factorizable state vector associated to any number of particles whose Hilbert spaces have arbitrary dimensionality.Comment: 10 pages; Latex; Talk delivered at ICSSUR'05, Besancon, France, 2-6 May 2005; to be published on J. Opt. B (special issue

Entanglement and Properties

Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In particular we will focus our attention to composite quantum systems composed of identical constituents, with the purpose of dealing with subtle issues, which have never been adequately discussed in the literature, originating from the true indistinguishability of the subsystems involved.Comment: 10 pages, Latex, corrected typo

Hardy's criterion of nonlocality for mixed states

We generalize Hardy's proof of nonlocality to the case of bipartite mixed statistical operators, and we exhibit a necessary condition which has to be satisfied by any given mixed state $\sigma$ in order that a local and realistic hidden variable model exists which accounts for the quantum mechanical predictions implied by $\sigma$. Failure of this condition will imply both the impossibility of any local explanation of certain joint probability distributions in terms of hidden variables and the nonseparability of the considered mixed statistical operator. Our result can be also used to determine the maximum amount of noise, arising from imperfect experimental implementations of the original Hardy's proof of nonlocality, in presence of which it is still possible to put into evidence the nonlocal features of certain mixed states.Comment: 7 pages, RevTe