Perfect state distinguishability and computational speedups with postselected closed timelike curves

Bennett and Schumacher's postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch's model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement, and we discuss an important difference between "Deutschian" CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers.Comment: 15 pages, 4 figures; Foundations of Physics (2011

Current in Wave Driven Plasmas

A theory for the generation of current in a toroidal plasma by radio-frequency waves is presented. The effect of an opposing electric field is included, allowing the case of time varying currents to be studied. The key quantities that characterize this regime are identified and numerically calculated. Circuit equations suitable for use in ray-tracing and transport codes are given.Comment: LaTeX 2.09, 26 pages, 7 figure

Analysis and elimination of hysteresis and noisy precursors in power amplifiers

Power amplifiers (PAs) often exhibit instabilities leading to frequency division by two or oscillations at incommensurate frequencies. This undesired behavior can be detected through a large-signal stability analysis of the solution. However, other commonly observed phenomena are still difficult to predict and eliminate. In this paper, the anomalous behavior observed in a Class-E PA is analyzed in detail. It involves hysteresis in the power-transfer curve, oscillation, and noisy precursors. The precursors are pronounced bumps in the power spectrum due to noise amplification under a small stability margin. The correction of the amplifier performance has required the development of a new technique for the elimination of the hysteresis. Instead of a trial-and-error procedure, this technique, of general application to circuit design, makes use of bifurcation concepts to suppress the hysteresis phenomenon through a single simulation on harmonic-balance software. Another objective has been the investigation of the circuit characteristics that make the noisy precursors observable in practical circuits and a technique has been derived for their elimination from the amplifier output spectrum. All the different techniques have been experimentally validated

The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions

We show that the widely used homotopy method for solving fixpoint problems, as well as the Harsanyi-Selten equilibrium selection process for games, are PSPACE-complete to implement. Extending our result for the Harsanyi-Selten process, we show that several other homotopy-based algorithms for finding equilibria of games are also PSPACE-complete to implement. A further application of our techniques yields the result that it is PSPACE-complete to compute any of the equilibria that could be found via the classical Lemke-Howson algorithm, a complexity-theoretic strengthening of the result in [Savani and von Stengel]. These results show that our techniques can be widely applied and suggest that the PSPACE-completeness of implementing homotopy methods is a general principle.Comment: 23 pages, 1 figure; to appear in FOCS 2011 conferenc

Two-message quantum interactive proofs and the quantum separability problem

Suppose that a polynomial-time mixed-state quantum circuit, described as a sequence of local unitary interactions followed by a partial trace, generates a quantum state shared between two parties. One might then wonder, does this quantum circuit produce a state that is separable or entangled? Here, we give evidence that it is computationally hard to decide the answer to this question, even if one has access to the power of quantum computation. We begin by exhibiting a two-message quantum interactive proof system that can decide the answer to a promise version of the question. We then prove that the promise problem is hard for the class of promise problems with "quantum statistical zero knowledge" (QSZK) proof systems by demonstrating a polynomial-time Karp reduction from the QSZK-complete promise problem "quantum state distinguishability" to our quantum separability problem. By exploiting Knill's efficient encoding of a matrix description of a state into a description of a circuit to generate the state, we can show that our promise problem is NP-hard with respect to Cook reductions. Thus, the quantum separability problem (as phrased above) constitutes the first nontrivial promise problem decidable by a two-message quantum interactive proof system while being hard for both NP and QSZK. We also consider a variant of the problem, in which a given polynomial-time mixed-state quantum circuit accepts a quantum state as input, and the question is to decide if there is an input to this circuit which makes its output separable across some bipartite cut. We prove that this problem is a complete promise problem for the class QIP of problems decidable by quantum interactive proof systems. Finally, we show that a two-message quantum interactive proof system can also decide a multipartite generalization of the quantum separability problem.Comment: 34 pages, 6 figures; v2: technical improvements and new result for the multipartite quantum separability problem; v3: minor changes to address referee comments, accepted for presentation at the 2013 IEEE Conference on Computational Complexity; v4: changed problem names; v5: updated references and added a paragraph to the conclusion to connect with prior work on separability testin

Methods to Localize Shorts Between Power and Ground Circuits

In the competitive world of microprocessor design and manufacturing, rapid advancements can be facilitated by learning from the components made by one’s closest rivals. To make this possible, Orisar Inc. (formerly Semiconductor Insights) provides reverse engineering services to integrated circuit (IC) manufacturers. The process produces a circuit diagram from a chip and allows the manufacturer to learn about a competitor’s product. These services are also used to determine if any intellectual property infringements have been committed by their competitor. Reverse engineering of integrated circuit is made difficult by the shrinking form factor and increasing transistor density. To perform this complex task Orisar Inc. employs sophisticated techniques to capture the design of an IC. Electron microscope photography captures a detailed image of an IC layer. Because a typical IC contains more than one layer, each layer is photographed and physically removed from the IC to expose the next layer. A noise removal algorithm is then applied to the pictures, which are then passed to pattern recognition software in order to transfer the layer design into a polygonal representation of the circuit. At the last step a knowledgeable human expert looks at the polygonal representation and inputs the design into a standard electronic schematic with a CAD package. This process us currently very time consuming. We propose a method which can be easily automated thereby saving valuable worker time and accelerating the process of reverse engineering

Beyond 'Global Production Networks': Australian Fashion Week's Trans-Sectoral Synergies

When studies of industrial organisation are informed by commodity chain, actor network, or global production network theories and focus on tracing commodity flows, social networks, or a combination of the two, they can easily overlook the less routine trans-sectoral associations that are crucial to the creation and realisation of value. This paper shifts attention to identifying the sites at which diverse specialisations meet to concentrate and amplify mutually reinforcing circuits of value. These valorisation processes are demonstrated in the case of Australian Fashion Week, an event in which multiple interests converge to synchronize different expressions of fashion ideas, actively construct fashion markets and enhance the value of a diverse range of fashionable commodities. Conceptualising these interconnected industries as components of a trans-sectoral fashion complex has implications for understanding regional development, world cities, production location, and the manner in which production systems “touch down” in different places