A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach

Operator entanglement of two-qubit joint unitary operations is revisited. Schmidt number is an important attribute of a two-qubit unitary operation, and may have connection with the entanglement measure of the unitary operator. We found the entanglement measure of two-qubit unitary operators is classified by the Schmidt number of the unitary operators. The exact relation between the operator entanglement and the parameters of the unitary operator is clarified too.Comment: To appear in the Brazilian Journal of Physic

Quantum uniqueness

In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two different quantum systems cannot yield always identical results, provided the possible measurement results belong to a non orthogonal set. This is interpreted as quantum uniqueness - a quantum feature which has no classical analog. Its tight relation with objective randomness of quantum measurements is discussed.Comment: Presented at 4th Feynman festival, June 22-26, 2009, in Olomouc, Czech Republic

Structure and optical properties of Lu <inf>2</inf>SiO <inf>5</inf>:Ce phosphor thin films

Luminescent, cerium doped Lu 2SiO 5 thin films with C2/c symmetry have been prepared by pulsed laser deposition (PLD) at temperatures much lower than the crystallization temperature (2150°C) of the corresponding bulk crystals. The PLD grown films show the typical luminescence resulting from the Ce 3+ 5d-4f transition. Maximum luminescence efficiency was observed for films prepared at an oxygen partial pressure of 200 mTorr at 600°C. These conditions reflect a balance between Ce 4+/Ce 3+ interconversion and the crystalline quality of the films. The results indicate that PLD offers a low temperature deposition technique for complex oxide phosphor materials. © 2006 American Institute of Physics

Scaling of Entanglement close to a Quantum Phase Transitions

In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.Comment: 4 pages, 4 figures, revtex. Stylistic changes and format modifie

Von Bezold assimilation effect reverses in stereoscopic conditions

Lightness contrast and lightness assimilation are opposite phenomena: in contrast, grey targets appear darker when bordering bright surfaces (inducers) rather than dark ones; in assimilation, the opposite occurs. The question is: which visual process favours the occurrence of one phenomenon over the other? Researchers provided three answers to this question. The first asserts that both phenomena are caused by peripheral processes; the second attributes their occurrence to central processes; and the third claims that contrast involves central processes, whilst assimilation involves peripheral ones. To test these hypotheses, an experiment on an IT system equipped with goggles for stereo vision was run. Observers were asked to evaluate the lightness of a grey target, and two variables were systematically manipulated: (i) the apparent distance of the inducers; and (ii) brightness of the inducers. The retinal stimulation was kept constant throughout, so that the peripheral processes remained the same. The results show that the lightness of the target depends on both variables. As the retinal stimulation was kept constant, we conclude that central mechanisms are involved in both lightness contrast and lightness assimilation

Preparation of distilled and purified continuous variable entangled states

The distribution of entangled states of light over long distances is a major challenge in the field of quantum information. Optical losses, phase diffusion and mixing with thermal states lead to decoherence and destroy the non-classical states after some finite transmission-line length. Quantum repeater protocols, which combine quantum memory, entanglement distillation and entanglement swapping, were proposed to overcome this problem. Here we report on the experimental demonstration of entanglement distillation in the continuous-variable regime. Entangled states were first disturbed by random phase fluctuations and then distilled and purified using interference on beam splitters and homodyne detection. Measurements of covariance matrices clearly indicate a regained strength of entanglement and purity of the distilled states. In contrast to previous demonstrations of entanglement distillation in the complementary discrete-variable regime, our scheme achieved the actual preparation of the distilled states, which might therefore be used to improve the quality of downstream applications such as quantum teleportation

Quantum Communication

Quantum communication, and indeed quantum information in general, has changed the way we think about quantum physics. In 1984 and 1991, the first protocol for quantum cryptography and the first application of quantum non-locality, respectively, attracted a diverse field of researchers in theoretical and experimental physics, mathematics and computer science. Since then we have seen a fundamental shift in how we understand information when it is encoded in quantum systems. We review the current state of research and future directions in this new field of science with special emphasis on quantum key distribution and quantum networks.Comment: Submitted version, 8 pg (2 cols) 5 fig

Bell Correlations and the Common Future

Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of explaining Bell correlations through a mechanism in that spirit can be read as questioning either the principle or even its basis: causality. In the former case, the principle can be replaced by its quantum version, accepting as a common cause an entangled state, leaving the phenomenon as mysterious as ever on the classical level (on which, after all, it occurs). If, more radically, the causal structure is questioned in principle, closed space-time curves may become possible that, as is argued in the present note, can give rise to non-local correlations if to-be-correlated pieces of classical information meet in the common future --- which they need to if the correlation is to be detected in the first place. The result is a view resembling Brassard and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure

Specific staining of human chromosomes in Chinese hamster x man hybrid cell lines demonstrates interphase chromosome territories

In spite of Carl Rabl's (1885) and Theodor Boveri's (1909) early hypothesis that chromosomes occupy discrete territories or domains within the interphase nucleus, evidence in favor pf this hypothesis has been limited and indirect so far in higher plants and animals. The alternative possibility that the chromatin fiber of single chromosomes might be extended throughout the major part of even the whole interphase nucleus has been considered for many years. In the latter case, chromosomes would only exist as discrete chromatin bodies during mitosis but not during interphase. Both possibilities are compatible with Boveri's well established paradigm of chromosome individuality. Here we show that an active human X chromosome contained as the only human chromosome in a Chinese hamster x man hybrid cell line can be visualized both in metaphse plates and in interphase nuclei after in situ hybridization with either 3H- or biotin-labeled human genomic DNA. We demonstrate that this chromosome is organized as a distinct chromatin body throughout interphase. In addition, evidence for the territorial organization of human chromosomes is also presented for another hybrid cell line containing several autosomes and the human X chromosome. These findings are discussed in the context of our present knowledge of the organization and topography of interphase chromosomes. General applications of a strategy aimed at specific staining of individual chromosomes in experimental and clinical cytogenetics are briefly considered