Time-Reversed EPR and the Choice of Histories in Quantum Mechanics

When a single photon is split by a beam splitter, its two `halves' can entangle two distant atoms into an EPR pair. We discuss a time-reversed analogue of this experiment where two distant sources cooperate so as to emit a single photon. The two `half photons,' having interacted with two atoms, can entangle these atoms into an EPR pair once they are detected as a single photon. Entanglement occurs by creating indistinguishabilility between the two mutually exclusive histories of the photon. This indistinguishabilility can be created either at the end of the two histories (by `erasing' the single photon's path) or at their beginning (by `erasing' the two atoms' positions).Comment: 6 pages, 5 figures. Presented at the Solvay Conference in Physics, November 2001, Delphi, Greece. To be published in Quantum Computers and Computing, 2002 and in the Proceedings of XXII Solvay Conference in Physics. New York: World Scientific, 200

Representation of SO(3) Group by a Maximally Entangled State

A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the SO(3) sphere breaks an odd or even number of times, corresponding to the double connectedness of the SO(3) group. An odd number of breaks leads to an additional $\pi$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\pi$ phase.Comment: 4 pages, 3 figure

High-Fidelity Teleportation of Independent Qubits

Quantum teleportation is one of the essential primitives of quantum communication. We suggest that any quantum teleportation scheme can be characterized by its efficiency, i.e. how often it succeeds to teleport, its fidelity, i.e. how well the input state is reproduced at the output, and by its insensitivity to cross talk, i.e. how well it rejects an input state that is not intended to teleport. We discuss these criteria for the two teleportation experiments of independent qubits which have been performed thus far. In the first experiment (Nature {\bf 390},575 (1997)) where the qubit states were various different polarization states of photons, the fidelity of teleportation was as high as 0.80 $\pm$ 0.05 thus clearly surpassing the limit of 2/3 which can, in principle, be obtained by a direct measurement on the qubit and classical communication. This high fidelity is confirmed in our second experiment (Phys. Rev. Lett. {\bf 80}, 3891 (1998)), demonstrating entanglement swapping, that is, realizing the teleportation of a qubit which itself is still entangled to another one. This experiment is the only one up to date that demonstrates the teleportation of a genuine unknown quantum state.Comment: 13 pages, Latex, 5 figures(eps), to appear in Journal of Modern Optic

Experimental verification of the Heisenberg uncertainty principle for hot fullerene molecules

The Heisenberg uncertainty principle for material objects is an essential corner stone of quantum mechanics and clearly visualizes the wave nature of matter. Here we report a demonstration of the Heisenberg uncertainty principle for the most massive, complex and hottest single object so far, the fullerene molecule C70 at a temperature of 900 K. We find a good quantitative agreement with the theoretical expectation: dx * dp = h, where dx is the width of the restricting slit, dp is the momentum transfer required to deflect the fullerene to the first interference minimum and h is Planck's quantum of action.Comment: 4 pages, 4 figure

Information and The Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.Comment: 20 pages, two figures, last version. Section 4 is replaced by a new argument. Other sections are improved. An appendix and new references are adde

On a linear optical implementation of non local product states and on their indistinguishability

In a recent paper Bennett et al.[Phys. Rev.A 59, 1070 (1999)] have shown the existence of a basis of product states of a bipartite system with manifest non-local properties. In particular these states cannot be completely discriminated by means of bilocal measurements. In this paper we propose an optical realization of these states and we will show that they cannot be completely discriminate by means of a global measurement using only optical linear elements, conditional transformation and auxiliary photons

Security of Quantum Key Distribution with entangled quNits

We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by qu$N$its (i.e., N-dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quNit generalisations of the Ekert's protocol for qubits.Comment: 15 pages, equation 15 and conclusions corrected the 14th of April 2003, new results adde