Quantum data gathering

Measurement of a quantum system – the process by which an observer gathers information about it – provides a link between the quantum and classical worlds. The nature of this process is the central issue for attempts to reconcile quantum and classical descriptions of physical processes. Here, we show that the conventional paradigm of quantum measurement is directly responsible for a well-known disparity between the resources required to extract information from quantum and classical systems. We introduce a simple form of quantum data gathering, “coherent measurement”, that eliminates this disparity and restores a pleasing symmetry between classical and quantum statistical inference. To illustrate the power of quantum data gathering, we demonstrate that coherent measurements are optimal and strictly more powerful than conventional one-at-a-time measurements for the task of discriminating quantum states, including certain entangled many-body states (e.g., matrix product states)

Automated operation of a home made torque magnetometer using LabVIEW

In order to simplify and optimize the operation of our home made torque magnetometer we created a new software system. The architecture is based on parallel, independently running instrument handlers communicating with a main control program. All programs are designed as command driven state machines which greatly simplifies their maintenance and expansion. Moreover, as the main program may receive commands not only from the user interface, but also from other parallel running programs, an easy way of automation is achieved. A program working through a text file containing a sequence of commands and sending them to the main program suffices to automatically have the system conduct a complex set of measurements. In this paper we describe the system's architecture and its implementation in LabVIEW.Comment: 6 pages, 7 figures, submitted to Rev. Sci. Inst

Compatibility of quantum states

We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some properties of this measure, and discuss its relation to the problem of combining two observers' states of knowledge.Comment: 4 pages, no figure

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

© 2016 American Physical Society. A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/N) - in contrast to that of classical probability estimation, which is O(1/N) - where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states

New insights from domain-averaged Fermi holes and bond order analysis into the bonding conundrum in C₂

The bonding in the ground state of C2 is examined using a combined approach based on the analysis of domain-averaged Fermi holes and of the contributions to covalent bond orders that can be associated with individual localised natural orbitals. The σ system in this molecule turns out to be particularly sensitive, evolving from a description that includes a fairly traditional shared electron pair σ bond, for a range of intermediate nuclear separations, to a somewhat different situation near equilibrium geometry, where non-classical repulsive interactions are particularly important. The various results provide further support for the view that the electronic structure of this molecule sufficiently exceeds the scope of traditional bonding paradigms that attempts to classify the bonding in terms of a classical bond multiplicity are highly questionable

Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data

We analyze the behavior of estimation errors evaluated by two loss functions, the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with finite data. We show numerically that there can be a large gap between the estimation errors and those predicted by an asymptotic analysis. The origin of this discrepancy is the existence of the boundary in the state space imposed by the requirement that density matrices be nonnegative (positive semidefinite). We derive an explicit form of a function reproducing the behavior of the estimation errors with high accuracy by introducing two approximations: a Gaussian approximation of the multinomial distributions of outcomes, and linearizing the boundary. This function gives us an intuition for the behavior of the expected losses for finite data sets. We show that this function can be used to determine the amount of data necessary for the estimation to be treated reliably with the asymptotic theory. We give an explicit expression for this amount, which exhibits strong sensitivity to the true quantum state as well as the choice of measurement.Comment: 9 pages, 4 figures, One figure (FIG. 1) is added to the previous version, and some typos are correcte

Practical learning method for multi-scale entangled states

We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of measurements is polynomial in the number of particles. Data post-processing for state reconstruction uses standard tools, namely matrix diagonalisation and conjugate gradient method, and scales polynomially with the number of particles. Our method prevents the build-up of errors from both numerical and experimental imperfections

Optimal, reliable estimation of quantum states

Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE), generally reports an estimate with zero eigenvalues. These cannot be justified. Furthermore, the MLE estimate is incompatible with error bars, so conclusions drawn from it are suspect. I propose an alternative procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues, its eigenvalues provide a bound on their own uncertainties, and it is the most accurate procedure possible. I show how to implement BME numerically, and how to obtain natural error bars that are compatible with the estimate. Finally, I briefly discuss the differences between Bayesian and frequentist estimation techniques.Comment: RevTeX; 14 pages, 2 embedded figures. Comments enthusiastically welcomed

Acid-Mediated N-Iodosuccinimide-Based Thioglycoside Activation for the Automated Solution-Phase Synthesis of α-1,2-Linked-Rhamnopyranosides

Carbohydrate structures are often complex. Unfortunately, synthesis of the range of sugar combinations precludes the use of a single coupling protocol or set of reagents. Adapting known, reliable bench-chemistry reactions to work via automation will help forward the goal of synthesizing a broad range of glycans. Herein, the preparation of di- and tri-saccharides of alpha 1→2 rhamnan fragments is demonstrated using thioglycoside donors with the development for a solution-phase-based automation platform of commonly used activation conditions using N-iodosuccinimide (NIS) with trimethylsilyl triflate. Byproducts of the glycosylation reaction are shown to be compatible with hydrazine-based deprotection conditions, lending broader functionality to this method as only one fluorous-solid-phase extraction step per coupling/deprotection cycle is required