A New Method for Quick and Precise Measurement of Quantum States

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Nuclear spin tomography is an application in (human) medicine known from medical institutions. The patient absorbs and re-emits electromagnetic radiation in all directions in space. They are detected and 3D images or 2D slice images are reconstructed from that data. Set in the framework of a fundamental science laboratory, the patient is replaced by a quantum object and the electromagnetic radiation by quantum measurement. The result is a procedure referred to as quantum state tomography.

Reconstructing quantum states without post-processing

Quantum state tomography is the process of reconstructing – or more precisely completely characterizing – the quantum state of an object as it is emitted by its source, before a possible measurement or interaction with the environment takes place. This technique has become an essential tool in the emerging field of quantum technologies.

The theoretical framework of quantum state tomography dates back to the 1970s. Its experimental implementations are nowadays routinely carried out in a wide variety of quantum systems. The basic principle of quantum state tomography – as of is medical counterpart – is to repeatedly perform measurements from different spatial directions on the quantum systems in order to uniquely identify the system’s quantum state.

Nevertheless, for quantum state tomography a lot of computational post-processing of the measured data is required to deduce the initial quantum state from the observed measurement results – all together a high expenditure.

Consequently, in 2011 a novel, more direct tomographical method was established that makes it possible to determine the quantum state without the need for post-processing. However, that novel method had a major drawback: it uses minimally disturbing measurements, so called weak measurements, to determine the system’s quantum state.

The basic idea behind weak measurements is to gain very little information about the observed system, by keeping the disturbance, caused by the measurement process, (negligible) small. Usually, a measurement has a huge impact on a quantum system, causing typical quantum phenomena, such as entanglement or interference, to vanish irretrievably. Since the amount of information gained in this procedure is very small, the measurements have to be repeated multiple times – a huge disadvantage of this measurement procedure in practical applications.

A research team at the Institute of Atomic and Subatomic Physics of TU Wien headed by Stephan Sponar now managed to combine these two methods, benefitting from both.


Schematic illustration of an interferometric setup

“We were able to further develop the established method so that the need of weak measurements becomes obsolete. Thus, we were able to integrate usual, so-called strong measurements, in the direct measurement procedure of the quantum state. Consequently, it is possible to determine the quantum state with higher precision and accuracy in a much shorter time compared to the approach with weak measurements – a tremendous progress.”, explains Tobias Denkmayr the first author of the paper.

These results have now been published in the journal Physical Review Letters ("Experimental Demonstration of Direct Path State Characterization by Strongly Measuring Weak Values in a Matter-Wave Interferometer").


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