Power of unentangled measurements on two antiparallel spins

We consider a pair of antiparallel spins polarized in a random direction to encode quantum information. We wish to extract as much information as possible on the polarization direction attainable by an unentangled measurement, i.e., by a measurement, whose outcomes are associated with product states. We develop analytically the upper bound 0.7935 bits to the Shannon mutual information obtainable by an unentangled measurement, which is definitely less than the value 0.8664 bits attained by an entangled measurement. This proves our main result, that not every ensemble of product states can be optimally distinguished by an unentangled measurement, if the measure of distinguishability is defined in the sense of Shannon. We also present results from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio

Paul Erdős (1913–1996) 1. Prologue

at Kerepesi Cemetery in Budapest to pay their last respects to Paul Erdős. If there was one theme suggested by the farewell orations, it was that the world of mathematics had lost a legend, one of its great representatives. On October 21, 1996, in accordance with his last wishes, Paul Erdős ’ ashes were buried in his parents ’ grave at the Jewish cemetery on Kozma street in Budapest. Paul Erdős was one of this century’s greatest and most prolific mathematicians. He is said to have written about 1500 papers, withalmost 500 co-authors. He made fundamental contributions in numerous areas of mathematics. There is a Hungarian saying to the effect that one can forget everything but one’s first love. When considering Erdős and his mathematics, we cannot speak of “first love”, but of “first loves”, and approximation theory was among them. Paul Erdős wrote more than 100 papers that are connected, in one way or another, with the approximation of functions. In these two short reviews, we try to present some of Paul’s fundamental contributions to approximation theory. A list of Paul’s papers in approximation theory is given at the end of this article

Closing the detection loophole in Bell experiments using qudits

We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an efficiency arbitrarily close to 1/N can be tolerated using N-dimensional systems, and a symmetric Bell test for which the efficiency can be lowered down to 61.8% using four-dimensional systems. Experimental perspectives for our schemes look promising considering recent progress in atom-photon entanglement and in photon hyperentanglement.Comment: 7 pages, 4 figures. v2: improved experimental schem

Control of quantum transverse correlations on a four-photon system

Control of spatial quantum correlations in bi-photons is one of the fundamental principles of Quantum Imaging. Up to now, experiments have been restricted to controlling the state of a single bi-photon, by using linear optical elements. In this work we demonstrate experimental control of quantum correlations in a four-photon state comprised of two pairs of photons. Our scheme is based on a high-efficiency parametric downconversion source coupled to a double slit by a variable linear optical setup, in order to obtain spatially encoded qubits. Both entangled and separable pairs have been obtained, by altering experimental parameters. We show how the correlations influence both the interference and diffraction on the double slit.Comment: 14 pages, 6 figure

Classical and quantum partition bound and detector inefficiency

We study randomized and quantum efficiency lower bounds in communication complexity. These arise from the study of zero-communication protocols in which players are allowed to abort. Our scenario is inspired by the physics setup of Bell experiments, where two players share a predefined entangled state but are not allowed to communicate. Each is given a measurement as input, which they perform on their share of the system. The outcomes of the measurements should follow a distribution predicted by quantum mechanics; however, in practice, the detectors may fail to produce an output in some of the runs. The efficiency of the experiment is the probability that the experiment succeeds (neither of the detectors fails). When the players share a quantum state, this gives rise to a new bound on quantum communication complexity (eff*) that subsumes the factorization norm. When players share randomness instead of a quantum state, the efficiency bound (eff), coincides with the partition bound of Jain and Klauck. This is one of the strongest lower bounds known for randomized communication complexity, which subsumes all the known combinatorial and algebraic methods including the rectangle (corruption) bound, the factorization norm, and discrepancy. The lower bound is formulated as a convex optimization problem. In practice, the dual form is more feasible to use, and we show that it amounts to constructing an explicit Bell inequality (for eff) or Tsirelson inequality (for eff*). We give an example of a quantum distribution where the violation can be exponentially bigger than the previously studied class of normalized Bell inequalities. For one-way communication, we show that the quantum one-way partition bound is tight for classical communication with shared entanglement up to arbitrarily small error.Comment: 21 pages, extended versio

Experimental estimation of the dimension of classical and quantum systems

An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system only from the results of measurements performed on it, without any extra assumption? The concept of a dimension witness answers this question, as it allows one to bound the dimension of an unknown classical or quantum system in a device-independent manner, that is, only from the statistics of measurements performed on it. Here, we report on the experimental demonstration of dimension witnesses in a prepare and measure scenario. We use pairs of photons entangled in both polarization and orbital angular momentum to generate ensembles of classical and quantum states of dimensions up to 4. We then use a dimension witness to certify their dimensionality as well as their quantum nature. Our results open new avenues for the device-independent estimation of unknown quantum systems and for applications in quantum information science.Comment: See also similar, independent and jointly submitted work of J. Ahrens et al., quant-ph/1111.127

Correlations of electrons from heavy flavor decay in p+p, d+Au and Au+Au collisions

In relativistic heavy ion collisions heavy flavor probes are crucial to understand the interactions between partons and the produced hot nuclear matter. Measurements in p+p collisions provide information about how the heavy quarks are produced and fragment and in d+Au collisions are sensitive to possible effects from cold nuclear matter. Azimuthal correlation measurements involving heavy flavor probes are complementary to single particle spectra measurements and provide additional information about production and interactions of heavy quarks. Measurements of electrons with heavy flavor decay with other hadrons from the event can provide information about how the heavy quark interacts with the produced matter and can be compared to similar measurements from light hadron correlations. Correlations between electrons from heavy flavor decay with muons, also from heavy flavor decay, can provide further information about heavy flavor production and cold nuclear matter effects in d+Au collisions with a very clean signal. We present PHENIX results for electron-hadron correlations in p+p and Au+Au collisions and electron-muon correlations in p+p and d+Au collisions and discuss the implications of these measurements