Quantum Nondemolition Measurement

Quantum Nondemolition ( QND ) Measurement (German: nondestructive quantum measurement ) is a measurement of a quantum mechanical system that maintains the integrity of the system and the values ​​of the observed observables . This allows the same system to be measured repeatedly.

Non-destructive does not mean that the wave function will not collapse . A QND measurement can, however, be thought of as an ideal quantum projection measurement.

Most devices that are able to detect individual particles and measure their position destroy the particle in the process. In the more favorable case, the measurement disturbs the particle, so that it is no longer in its own measured state immediately after the measurement. In contrast, a perfect QND measurement of the location of a particle would leave the particle at the measured location.

QND measurements are extremely difficult to perform experimentally.

Technical definition

Consider a complete quantum mechanical measurement that is given by the quantum description of the system to be examined and the measuring apparatus . One can describe the dynamics with a Hamilton operator of the following form: ${\displaystyle |\psi \rangle }$ ${\displaystyle |A\rangle }$

${\displaystyle H=H_{\rm {selbst}}+H_{\rm {ww}}\,,}$

Here, H _{itself is} the self-interaction of the system and H _{ww is} the interaction of the coupling between the system and the measuring apparatus. In general, H _{ww is} modeled as switching on for a certain time and the following ideal (weak) Von Neumann measurement results:

${\displaystyle |\psi \rangle |A\rangle \rightarrow \sum _{n}c_{n}|\psi _{n}\rangle |A_{n}\rangle }$

The measurement is a QND measurement, though

${\displaystyle [H_{\rm {selbst}}\,,\,H_{\rm {ww}}]=0.}$

Description from literature

A. Lupascu and others described it as follows:

“In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system-detector interaction that preserves the Eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement. "

“In quantum mechanics, the process of measurement is a subtle interplay of extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes the disturbance by using a certain system-detector interaction, which preserves the eigenstate of a suitable operator of the quantum system. This leads to an ideal projective measurement. "

On the other hand, it is argued that the term QND does not add anything to the usual notion of strong quantum mechanical measurement and can be confusing because of the two different interpretations of destruction (loss of the quantum state versus loss of the particle).

credentials

1. ↑ A. Lupascu, et al .: Quantum non-demolition measurement of a superconducting two-level system . In: Nature Physics . 3, No. 2, 2007, pp. 119-125. arxiv : cond-mat / 0611505 . bibcode : 2007NatPh ... 3..119L . doi : 10.1038 / nphys509 .
2. ↑ C. Monroe: Demolishing Quantum Nondemolition Archived from the original on April 15, 2013. Information: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. In: Physics Today . 64, No. 1, 2011, p. 8. doi : 10.1063 / 1.3541926 . Retrieved October 13, 2012. 

Web links

• Physicsworld article
• Measuring quantum information without destroying it
• Counting photons without destroying them