1,444 research outputs found
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
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
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
Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect
We present an efficient quantum algorithm to measure the average fidelity
decay of a quantum map under perturbation using a single bit of quantum
information. Our algorithm scales only as the complexity of the map under
investigation, so for those maps admitting an efficient gate decomposition, it
provides an exponential speed up over known classical procedures. Fidelity
decay is important in the study of complex dynamical systems, where it is
conjectured to be a signature of quantum chaos. Our result also illustrates the
role of chaos in the process of decoherence.Comment: 4 pages, 2 eps figure
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