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arXiv:1605.04792 · Physical Review X

Compressively Characterizing High-Dimensional Entangled States with Complementary, Random Filtering

Gregory A. Howland, Samuel H. Knarr, James Schneeloch, Daniel J. Lum, John C. Howell

Published May 12, 2016• 23 citations
arXivHTMLPDF

Abstract

In quantum mechanics, Heisenberg's uncertainty principle prevents the determination of precise, simultaneous measurements of two quantities. A new approach extracts position and momentum information from the same group of entangled photons by dramatically undersampling the system.
DOI
10.1103/physrevx.6.021018

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Abstract Heisenberg’s uncertainty principle states that: The product of the uncertainties in the simultaneous specifications of two °complementary observables can never be less than a small quantity of the order of h. The precise form of the principle is given in Box U.1. It implies that as one observable is constrained to have a more precise value, so its partner becomes more ill-defined. An experiment designed to measure the two observables simultaneously will be able to determine one precisely only at the expense of losing information about the other (see °duality). The principle was established by Werner Heisenberg in 1927, as a consequence of his formulation of °matrix mechanics.
In quantum mechanics, measurements disturb the state of the system being measured. This disturbance is largest for complementary properties (e.g. position and momentum) and hence limits the precision with which such properties can be determined simultaneously. Often, this fact is conflated with Heisenberg's uncertainty principle, which refers to an uncertainty relation between complementary properties that is intrinsic to quantum states. In this thesis, the distinction between these two fundamental characteristics of quantum mechanics is made clear. At the intersection of the two are "joint measurements", which circumvent measurement disturbance to simultaneously determine complementary properties. They have applications in quantum metrology and enable a direct measurement of quantum states. The focus of this thesis is on the latter. The thesis is structured in the following way. The first chapter serves as an introduction to joint measurements. It surveys the seminal works in the field, doing so in a chronological manner to provide some historical context. The remainder of the thesis discusses two strategies to experimentally achieve joint measurements. The first strategy is to sequentially measure the complementary properties, making these measurements weak so that they do not disrupt each other. The second strategy is to first clone the system being measured, and then measure each complementary property on a separate clone. Both strategies are experimentally demonstrated on polarized photons, but can be readily extended to other systems.