Violating the Modified Helstrom Bound with Nonprojective Measurements

We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a non-guess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and non-guess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case. We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement. Notably, while the cost advantage of the latter protocol is destroyed with the introduction of any amount of experimental noise, other choices of cost function have optima for which nonprojective measurements robustly show an appreciable, and thus experimentally measurable, cost advantage. Such an experiment would be an unambiguous demonstration of a benefit from nonprojective measurements.Comment: 5 pages, 2 figure

Implementing generalized measurements with superconducting qubits

We describe a method to perform any generalized purity-preserving measurement of a qubit with techniques tailored to superconducting systems. First, we consider two methods for realizing a two-outcome partial projection: using a thresholded continuous measurement in the circuit QED setup, or using an indirect ancilla qubit measurement. Second, we decompose an arbitrary purity-preserving two-outcome measurement into single qubit unitary rotations and a partial projection. Third, we systematically reduce any multiple-outcome measurement to a sequence of such two-outcome measurements and unitary operations. Finally, we consider how to define suitable fidelity measures for multiple-outcome generalized measurements.Comment: 13 pages, 3 figure

Evolutionary consequences of behavioral diversity

Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This body of work has primarily focused on games in which players face a simple binary choice, to "cooperate" or "defect". Real individuals, however, often exhibit behavioral diversity, varying their input to a social interaction both qualitatively and quantitatively. Here we explore how access to a greater diversity of behavioral choices impacts the evolution of social dynamics in finite populations. We show that, in public goods games, some two-choice strategies can nonetheless resist invasion by all possible multi-choice invaders, even while engaging in relatively little punishment. We also show that access to greater behavioral choice results in more "rugged " fitness landscapes, with populations able to stabilize cooperation at multiple levels of investment, such that choice facilitates cooperation when returns on investments are low, but hinders cooperation when returns on investments are high. Finally, we analyze iterated rock-paper-scissors games, whose non-transitive payoff structure means unilateral control is difficult and zero-determinant strategies do not exist in general. Despite this, we find that a large portion of multi-choice strategies can invade and resist invasion by strategies that lack behavioral diversity -- so that even well-mixed populations will tend to evolve behavioral diversity.Comment: 26 pages, 4 figure

Size-Dependent Earth Impactor Warning Times And Corresponding Campaign Mission Recommendations

NASA seeks to reliably detect potential Earth Impactors (EI) in time to defend the planet by deflecting them. Congress has given an unfunded mandate to NASA to lead Spaceguard, a coalition of worldwide observatories and scientists who find, track, and determine impact probabilities for potential EIs (Udall, 2007). This effort fits within the first stages of a typical military targeting cycle, which begins by detecting and characterizing targets. In the first half of this analysis, military targeting is applied to the EI challenge through the development of a methodology to characterize early warning times for different size objects. In the second half, recommendations for acting on different warning time scenarios are presented, to include augmentation of observation technology and use of a precursor transponder implantation mission. An interdisciplinary approach is taken to measure the success of the Spaceguard efforts in increasing the warning times for approaches of variously sized bodies. A multi-step method is developed, beginning with determining past and present warning times for asteroids entering the 0.05 AU Astronomical Unit (AU) Minimum Orbit Intersection Distance (MOID) of Earth. Using source data from NASA\u27s NEO Program database of close approaches, JPL\u27s Small Body Database, and the IAU Minor Planet Center, the differences between the dates of first discovery of these Potentially Hazardous Asteroids (PHA) and the dates of 7300 penetrations of the MOID to graph warning times for known PHAs\u27 penetration of the MOID were aggregated. The method also includes the estimate of PHA discovery, rates of objects with high orbital uncertainties, and missed approach rates. A discussion of potential sources for error and directions to take for further development of the model is included. Finally, recommendations for campaigns against EIs are provided, given different warning time and size scenarios. The most significant of the conclusions is that, given current technology, and given the limitations of the model used, the 100-300 m size range appears to contain the most likely EI Spaceguard will discover with enough warning time (over 30 years) to take some form of action. A counterintuitive additional conclusion is that this size range also may yield an object that will strike with no warning time. Another conclusion is that EIs smaller than 100 m will provide negligible warning time for centuries. Targeting campaigns against the most-likely EI warning-time and size scenarios are discussed. These campaigns include first, additional observation technology; second, an inexpensive short-termed precursor transponder mission; third, a long-term observation mission; fourth, a suite of simultaneous observation and mitigation missions, and finally, evacuation and recovery operations. The overall conclusion is that additional resources should be allocated toward more robust survey technology, the first layer of defense, with continued development of precursor characterization transponder mission technology, the second layer of defense

A Comparative Study of Selected Marches of Kenneth Alford and John Phillip Sousa

[No abstract provided.

Instability in SU(2) gauge field theory

Classical solutions to SU(2) gauge theory with a static charge source or with wave-like behavior are examined. In both cases gauge rotations cause instability. A quantum mechanical model with a local gauge symmetry is constructed. The quantum numbers of the model are constrained by the local symmetry. The S-matrix elements of SU(2) gauge theory are analysed in terms of angular orientation in gauge space. Most S-matrix elements are found to vanish in a way that indicates that most states are unstable. This result is due to the ambiguity in the time evolution of the states inherent in the local symmetry and it indicates that the gauge must be fixed in the path integral for a well defined dynamical evolution. When the gauge is fixed the result reduces to the conservation of quantised isospin

A Recofigurable Tri-Band Interconnect for Future Network-On-Chip

The scaling of CMOS feature sizes has yielded the capability of integrating heterogeneous intellectual properties (IPs) like graphics processing units (GPUs), digital signal processors (DSPs) and central processing units (CPUs) on a single die. The collection of multiple IPs on a single die presents a problem of reliable communication due to congestion. The infrastructure that facilitates and manages communication among IPs is referred to as a network-on-chip (NoC). Its ultimate goal should be low latency with negligible power and area consumption. Unfortunately, as CMOS feature sizes have been scaling smaller, this has exacerbated latency and signal degradation due to increasing on-chip channel resistance. Furthermore, contemporary interfaces use baseband-only signaling and have critical limitations like exponential energy consumption, limited bandwidth and non-reconfigurable data access.;In this work, we propose an energy efficient tri-band (baseband + 2 RF bands) signaling interface that is capable of simultaneous bi-directional communication and reconfigurable data access. Additionally, communication is accomplished through a shared transmission line which reduces the overall number of global interconnections. As a result, this reduces area consumption and mitigates interconnection complexity. The primary signicance of this interconnect configuration compared to contemporary designs is an increase of bandwidth and energy efficiency.;The interconnect design is composed of a baseband transceiver and two RF (10Ghz and 20GHz) transceivers. The RF transceivers utilize amplitude-shift keying (ASK) modulation scheme. ASK modulation allows ease of circuit design, but most importantly it can be used for noncoherent communication, which we implemented in this system. Noncoherent ASK modulation is area conservative and power efficient since there is no longer a need for power-hungry frequency synthesizers. Moreover, noncoherent ASK demodulation accomplishes direct-down conversation through a passive self-mixer for additional power savings.;The results from our work show that a multi-band interconnect is a suitable remedy for future NoC communication that has been reaching its bandwidth limitation with baseband-only signaling. In conclusion, this work demonstrates a sustainable balance of energy efficiency and increased bandwidth for future on-chip interconnect designs