5,189 research outputs found
Quantum system characterization with limited resources
The construction and operation of large scale quantum information devices
presents a grand challenge. A major issue is the effective control of coherent
evolution, which requires accurate knowledge of the system dynamics that may
vary from device to device. We review strategies for obtaining such knowledge
from minimal initial resources and in an efficient manner, and apply these to
the problem of characterization of a qubit embedded into a larger state
manifold, made tractable by exploiting prior structural knowledge. We also
investigate adaptive sampling for estimation of multiple parameters
Tomography of Quantum Operations
Quantum operations describe any state change allowed in quantum mechanics,
including the evolution of an open system or the state change due to a
measurement. In this letter we present a general method based on quantum
tomography for measuring experimentally the matrix elements of an arbitrary
quantum operation. As input the method needs only a single entangled state. The
feasibility of the technique for the electromagnetic field is shown, and the
experimental setup is illustrated based on homodyne tomography of a twin-beam.Comment: Submitted to Phys. Rev. Lett. 2 eps + 1 latex figure
An invitation to quantum tomography (II)
The quantum state of a light beam can be represented as an infinite
dimensional density matrix or equivalently as a density on the plane called the
Wigner function. We describe quantum tomography as an inverse statistical
problem in which the state is the unknown parameter and the data is given by
results of measurements performed on identical quantum systems. We present
consistency results for Pattern Function Projection Estimators as well as for
Sieve Maximum Likelihood Estimators for both the density matrix of the quantum
state and its Wigner function. Finally we illustrate via simulated data the
performance of the estimators. An EM algorithm is proposed for practical
implementation. There remain many open problems, e.g. rates of convergence,
adaptation, studying other estimators, etc., and a main purpose of the paper is
to bring these to the attention of the statistical community.Comment: An earlier version of this paper with more mathematical background
but less applied statistical content can be found on arXiv as
quant-ph/0303020. An electronic version of the paper with high resolution
figures (postscript instead of bitmaps) is available from the authors. v2:
added cross-validation results, reference
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
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