On Bell's theorem, quantum communication, and entanglement detection

(A) Bell's theorem rests on a conjunction of three assumptions: realism, locality and ``free will''. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bell's theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states is be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EI's) emerging via this method contains entanglement witnesses (EW's), but they form only a subset of all EI's. Thus the method is more powerful than the one based on EW's.Comment: 10 pages, for proceedings of Foundations of Probability and Physics-5 at Vaxjo University, Swedish Southeast Academy August 24-27, 200

Unbounded-Error Classical and Quantum Communication Complexity

Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently, \cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum} communication complexity in the {\em one-way communication} model can also be investigated using the arrangement, and showed that it is exactly (without a difference of even one qubit) half of the classical one-way communication complexity. In this paper, we extend the arrangement argument to the {\em two-way} and {\em simultaneous message passing} (SMP) models. As a result, we show similarly tight bounds of the unbounded-error two-way/one-way/SMP quantum/classical communication complexities for {\em any} partial/total Boolean function, implying that all of them are equivalent up to a multiplicative constant of four. Moreover, the arrangement argument is also used to show that the gap between {\em weakly} unbounded-error quantum and classical communication complexities is at most a factor of three.Comment: 11 pages. To appear at Proc. ISAAC 200

Strengths and Weaknesses of Quantum Fingerprinting

We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomness SMP protocols by means of quantum SMP protocols without shared randomness ($Q^\parallel$-protocols). Our first result is to extend Yao's simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by $Q^\parallel$-protocols. We apply our technique to obtain an efficient $Q^\parallel$-protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols.Comment: 13 pages, no figures, to appear in CCC'0

Massive MIMO-based Localization and Mapping Exploiting Phase Information of Multipath Components

In this paper, we present a robust multipath-based localization and mapping framework that exploits the phases of specular multipath components (MPCs) using a massive multiple-input multiple-output (MIMO) array at the base station. Utilizing the phase information related to the propagation distances of the MPCs enables the possibility of localization with extraordinary accuracy even with limited bandwidth. The specular MPC parameters along with the parameters of the noise and the dense multipath component (DMC) are tracked using an extended Kalman filter (EKF), which enables to preserve the distance-related phase changes of the MPC complex amplitudes. The DMC comprises all non-resolvable MPCs, which occur due to finite measurement aperture. The estimation of the DMC parameters enhances the estimation quality of the specular MPCs and therefore also the quality of localization and mapping. The estimated MPC propagation distances are subsequently used as input to a distance-based localization and mapping algorithm. This algorithm does not need prior knowledge about the surrounding environment and base station position. The performance is demonstrated with real radio-channel measurements using an antenna array with 128 ports at the base station side and a standard cellular signal bandwidth of 40 MHz. The results show that high accuracy localization is possible even with such a low bandwidth.Comment: 14 pages (two columns), 13 figures. This work has been submitted to the IEEE Transaction on Wireless Communications for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl