On Entanglement Measures: Discrete Phase Space and Inverter-Chain Link Viewpoint

In contrast to abstract statistical analyses in the literature, we present a concrete physical diagrammatic model of entanglement characterization and measure with its underlying discrete phase-space physics. This paper serves as a pedagogical treatment of this complex subject of entanglement measures. We review the important inherent concurrence property of entangled qubits, as well as underscore its emergent qubit behavior. From the discrete phase space point of view, concurrence translates to translation symmetry of entangled binary systems in some quantitative measure of entanglement. Although the focus is on bipartite system, the notion is readily extendable to multi-partite system of qubits, as can easily be deduced from the physical inverter-chain link model. A diagrammatic analysis of the entanglement of formation for any multi-partite qubit system is givenComment: 21 pages, 6 figure

Dynamics of Functional Phase Space Distribution in QFT: A Third Quantization and Dynamical Unification of QFT and CMP

We proposed a third quantization scheme to derive the quantum dynamics of the functional phase space distribution in quantum field theory (QFT). The derivation is straightforward and algorithmic. This readily yields the ballistic quantum transport equation of QFT distribution in (p,q)- functional phase space, not in ordinary position-momentum (p,q)-space. Our starting point is the general mixed space representation in QFT. The end result serves as a unification of the quantum superfield transport theory of condensed matter physics (CMP) and QFT. This is summarized in a Table of correspondence. This third quantization scheme may have significance in quantum fluctuation theory of systems with many degrees of freedom. It may have relevance to cosmology: gravity, multi-universes, and Yang-Mills theory.Comment: 24 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2204.0769

Data-Discriminants of Likelihood Equations

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to solve a very structured parameterized polynomial system called likelihood equations. For general choices of data, the number of complex solutions to the likelihood equations is finite and called the ML-degree of the model. The only solutions to the likelihood equations that are statistically meaningful are the real/positive solutions. However, the number of real/positive solutions is not characterized by the ML-degree. We use discriminants to classify data according to the number of real/positive solutions of the likelihood equations. We call these discriminants data-discriminants (DD). We develop a probabilistic algorithm for computing DDs. Experimental results show that, for the benchmarks we have tried, the probabilistic algorithm is more efficient than the standard elimination algorithm. Based on the computational results, we discuss the real root classification problem for the 3 by 3 symmetric matrix~model.Comment: 2 table

Charging effects in the ac conductance of a double barrier resonant tunneling structure

There have been many studies of the linear response ac conductance of a double barrier resonant tunneling structure (DBRTS). While these studies are important, they fail to self-consistently include the effect of time dependent charge density in the well. In this paper, we calculate the ac conductance by including the effect of time dependent charge density in the well in a self-consistent manner. The charge density in the well contributes to both the flow of displacement currents and the time dependent potential in the well. We find that including these effects can make a significant difference to the ac conductance and the total ac current is not equal to the average of non-selfconsitently calculated conduction currents in the two contacts, an often made assumption. This is illustrated by comparing the results obtained with and without the effect of the time dependent charge density included properly

An inverter-chain link implementation of quantum teleportation and superdense coding

A new perspective in terms of inverter-chain link (ICL) diagrams of quantum entanglement faithfully captures the fundamental concept of quantum teleportation and superdense coding. The ICL may be considered a series of {\sigma}_{x} Pauli-matrix operations, where a physical/geometric representation provides the mysterious link raised by EPR. Here, we employ discrete phase space and ICL analyses of quantum entanglement as a resource for quantum teleportation and superdense coding. We underscore the quantum superposition principle and Hadamard transformation under a local single-qubit operation. On the fundamental question posed by EPR, our result seems to lend support to the geometric nature of quantum entanglement. In concluding remarks, we discuss very briefly a bold conjecture in physics aiming to unify general relativity with quantum mechanics, namely, ER=EPR.Comment: 12 pages 3 figures. arXiv admin note: text overlap with arXiv:2112.1029